The Simple Analytics of Helicopter Money: Why It Works Always

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1 Vol. 8, Augus 21, 2014 hp://dx.doi.org/ /economics-ejournal.ja The Simple Analyics of Helicoper Money: Why I Works Always Willem H. Buier Absrac The auhor proides a rigorous analysis of Milon Friedman s parable of he helicoper drop of money a permanen/irreersible increase in he nominal sock of fia base money rae which respecs he ineremporal budge consrain of he consolidaed Cenral Bank and Treasury he Sae. Examples are a emporary fiscal simulus funded permanenly hrough an increase in he sock of base money and permanen QE an irreersible, moneized open marke purchase by he Cenral Bank of non-moneary soereign deb. Three condiions mus be saisfied for helicoper money always o boos aggregae demand. Firs, here mus be benefis from holding fia base money oher han is pecuniary rae of reurn. Second, fia base money is irredeemable iewed as an asse by he holder bu no as a liabiliy by he issuer. Third, he price of money is posiie. Gien hese hree condiions, here always exiss een in a permanen liquidiy rap a combined moneary and fiscal policy acion ha booss priae demand in principle wihou limi. Deflaion, lowflaion and secular sagnaion are herefore unnecessary. They are policy choices. JEL E2 E4 E5 E6 H6 Keywords Helicoper money; liquidiy rap; seigniorage; secular sagnaion; cenral bank; quaniaie easing Auhors Willem H. Buier, Ciigroup Global Markes Inc., 388 Greenwich Sree, New York, NY 10013, USA, [email protected] Ciaion Willem H. Buier (2014). The Simple Analyics of Helicoper Money: Why I Works Always. Economics: The Open-Access, Open-Assessmen E-Journal, Vol. 8, hp://dx.doi.org/ /economicsejournal.ja Receied May 21, 2014 Published as Economics Discussion Paper June 13, 2014 Reised Augus 6, 2014 Acceped Augus 17, 2014 Published Augus 21, 2014 Auhor(s) Licensed under he Creaie Commons License - Aribuion 3.0

2 1 Inrocion Le us suppose now ha one day a helicoper flies oer his communiy and drops an addiional $1000 in bills from he sky,... Le us suppose furher ha eeryone is coninced ha his is a unique een which will neer be repeaed, (Friedman 1969, pp 4 5). This paper aims o proide a rigorous analysis of Milon Friedman s famous parable of he helicoper drop of money (Friedman 1948, 1969). A helicoper drop of money is a permanen/irreersible increase in he nominal sock of fia base money wih a zero nominal ineres rae, which respecs he ineremporal budge consrain of he consolidaed Cenral Bank and fiscal auhoriy/treasury henceforh he Sae. An example would be a emporary fiscal simulus (say a oneoff ransfer paymen o households, as in Friedman s example), funded permanenly hrough an increase in he sock of base money. I could also be a permanen increase in he sock of base money hrough an irreersible open marke purchase by he Cenral Bank of non-moneary soereign deb held by he public ha is, QE. The reason is ha QE, iewed as an irreersible or permanen purchase of non-moneary financial asses by he Cenral Bank funded hrough an irreersible or permanen increase in he sock of base money, relaxes he ineremporal budge consrain of he Sae. Consequenly, here will hae o be some combinaion of curren and fuure ax cus or curren and fuure increases in public spending o ensure ha he ineremporal budge consrain of he Sae remains saisfied. QE relaxes he ineremporal budge consrain of he consolidaed Cenral Bank and Treasury eiher if nominal ineres raes are posiie or because fia base money is irredeemable. In our simple model, QE is he irreersible purchase by he Cenral Bank of soereign deb funded hrough irreersible base money issuance. The same resuls would hold, howeer, if he Cenral Bank purchased priae securiies ourigh insead of soereign deb, or expanded is balance shee hrough collaeralized lending. There are hree condiions ha mus be saisfied for helicoper money as defined here o always boos aggregae demand. Firs, here mus be benefis from holding fia base money oher han is pecuniary rae of reurn. Only hen will base money be willingly held despie being dominaed as a sore of alue by nonmoneary asses wih a posiie risk-free nominal ineres rae. This means ha in a cashless economy, like he Woodford-Gali (Woodford 2003, Gali 2008) worlds in 1

3 which somehing called money seres as a numéraire bu eiher has no exisence as a sore of alue (currency, an accoun wih he Cenral Bank or e-money) or yields no non-pecuniary benefis, earns he same pecuniary rae of reurn as bonds and is no irredeemable, helicoper money is ineffecie. Second, fia base money is irredeemable: i is iew as an asse by he holder bu no as a liabiliy by he issuer. This is necessary for helicoper money o work een in a permanen liquidiy rap, wih risk-free nominal ineres raes a zero for all mauriies. Third, he price of money is posiie. The paper shows ha, when he Sae can issue unbacked, irredeemable fia money or base money wih a zero nominal ineres rae, which can be proced a zero marginal cos and is held in posiie amouns by households and oher priae agens despie he aailabiliy of risk-free securiies carrying a posiie nominal ineres rae, here always exiss a combined moneary and fiscal policy acion ha booss priae demand in principle wihou limi. Deflaion, inflaion below arge, lowflaion, subflaion and he deficien demand-drien ersion of secular sagnaion are herefore unnecessary. 1 They are policy choices. This effecieness resul holds when he economy is away from he zero lower bound (ZLB), a he ZLB for a limied ime period or a he ZLB foreer. The feaure of irredeemable base money ha is key for his paper is ha he accepance of paymen in base money by he goernmen o a priae agen consiues a final selemen beween ha priae agen (and any oher priae agen wih whom he exchanges ha base money) and he goernmen. I leaes he priae agen wihou any furher claim on he goernmen, now or in he fuure. The helicoper money drop effecieness issue is closely relaed o he quesion as o wheher Sae-issued fia money is ne wealh for he priae secor, despie being echnically an inside asse, where for eery credior ha holds he asse here is a debor who owes a claim of equal alue (see Painkin 1965, Gurley and 1 The erm lowflaion is, I beliee, e o Moghadam e al. (2014). The erm subflaion has been around he blogosphere for a while. I use i o refer o an inflaion rae below he arge leel or lower han is opimal. Secular sagnaion heories go back o Alin Hansen (1939). I refer here o he Keynesian arian, which holds ha here will be long-erm sagnaion of employmen and economic aciiy wihou goernmen demand-side inerenion. There also is a long-erm supply side arian, associaed e.g. wih Rober Gordon (2014), which focuses on falering innoaion and prociiy growh. Larry Summers (2013) marries he demand-side and supply-side secular sagnaion approaches by inoking a number of hyseresis mechanisms. For a formal model see Eggersson and Mehrora (2014). 2

4 Shaw 1960 and Pesek and Saing 1967), Weil (1991). The discussions in Hall (1983), Sockman (1983), King (1983), Fama (1983), Helpman (1983), Sargen and Wallace (1984), Sargen (1987) and Weil (1991) of ouside money, priae money and he paymen of ineres on money ask some of he same quesions as his paper, bu do no offer he same answer, because hey don address he irredeemabiliy of fia base money. Krugman (1998), Sims (2001, 2004), Buier (2003a, 2004) and Eggersson and Woodford (2003, 2006) all sress ha o boos demand in a liquidiy rap, base money increases should no be, or expeced o be, reersed. None of hese papers recognized ha een a permanen increase in he sock of base money will no hae an expansionary wealh effec in a permanen liquidiy rap unless money is irredeemable in he sense deeloped here; wihou his, here is no wealh effec or real balance effec from irreersible base money issuance in a permanen liquidiy rap. Ben Bernanke spen years liing down he moniker helicoper Ben which he acquired following a (non-echnical) discussion of helicoper money (Bernanke 2003). The issue has also been reisied by Buier (2003b, 2007) and, in an informal manner, by Turner (2013), by Reichlin e al. (2013). The paper shows ha, because of is irredeemabiliy, sae-issued fia money is indeed ne wealh o he priae secor, in a ery precise way: he iniial sock of base money plus he presen discouned alue of all fuure ne base money issuance is ne wealh, an ouside asse o he priae secor, een afer he ineremporal budge consrain of he Sae (which includes he Cenral Bank) has been consolidaed wih ha of he household secor. This irredeemabiliy of base money and he resuling asymmeric reamen of base money in he solency consrains of households and of he sae accouns for our base money expansion/qe effecieness a he zero lower bound (ZLB), when Eggersson and Woodford (2003) (henceforh EW) esablished he exisence of a self-fulfilling deflaionary rap a he ZLB and ineffecie base money issuance or QE. In mos of he EW paper, base money is reaed symmerically in he solency consrains of he Sae and he household secor. When, owards he end of he EW paper, a fiscal rule is inroced ha effeciely imposes asymmeric reamen of base money in he solency consrains of he Sae and he household secor idenical o wha we assume, QE effecieness a he ZLB is presen, een in he EW model. 3

5 The paper also demonsraes ha fia base money issuance is effecie in boosing household demand regardless of wheher here is Ricardian equialence (deb neuraliy). Finally, he effecieness of helicoper money requires ha here is a rae-ofreurn dominaed (excep a he ZLB) sore of alue ha is willingly held by he priae secor and ha is irredeemable. Base money mus be rae-of-reurndominaed (equialenly, base money mus yield non-pecuniary benefis o he holder) if helicoper money is o hae wealh effecs away from he ZLB or if he economy is a he ZLB emporarily. Irredeemabiliy of base money is required for helicoper money o hae wealh effecs een if he economy is a he ZLB foreer. In a cashless economy, where money exiss only as a numéraire, he wealh effec of helicoper money drops canno exis eiher a or away from he ZLB and i is no possible do discuss he opic of helicoper money. In he Woodford (2003) cashless world, where here is a securiy issued by he goernmen called money which seres as he numéraire, yields he same pecuniary rae of reurn as nonmoneary securiies and yields no oher (non-pecuniary) benefis, here can be no effecie helicoper money drops away from he ZLB or if he economy is a he ZLB emporarily. If Woodford s money were irredeemable (his specificaion of he solency consrain of he Sae suggess i is no) here could be effecieness of helicoper money drops if he economy were a he ZLB foreer. 2 The model All imporan aspecs of how helicoper money drops work and wha makes helicoper money unique can be esablished wihou he need for a complee dynamic general (dis)equilibrium model. All ha is needed is a complee specificaion of he choice process of he household secor in a moneary economy, he period budge ideniy and solency consrain of he consolidaed general goernmen/treasury and Cenral Bank he Sae and he no-arbirage condiions equaing (in principle risk-adjused) reurns on all non-moneary sores of alue and consraining he insananeous nominal ineres rae o be nonnegaie. 4

6 I shall show ha, as long as he price of money is posiie, he issuance of fia base money can boos household consumpion demand by any amoun, gien he inheried socks of financial and real asses, gien curren and fuure wages and prices, and gien curren and fuure alues of public spending on goods and serices. Wheher such helicoper money drops change asse prices and ineres raes, goods prices, wages and/or oupu and employmen depends on he specificaion of he res of he model of he economy including, in more general models, he behaior of he financial secor and of non-financial businesses in driing inesmen demand, procion and labor demand, he res of he supply side of he economy and he res of he world, if he economy is open. The poin of his paper is o show ha, whaeer he equilibrium configuraion we sar from, helicoper money drops will boos household demand and mus disurb ha equilibrium. Wha gies ulimaely, in a fully ariculaed dynamic general equilibrium model nominal prices and wages, employmen or oupu, is no our concern here. The model of household behaior I use is as sripped-down and simple as I can make i wihou raising concerns ha he key resuls will no carry oer o more general and inricae models. The coninuous-ime Yaari-Blanchard ersion of he OLG model is used o characerize household behaior (see Yaari 1965, Blanchard 1985, Buier 1988 and Weil 1989). This model wih is easy aggregaion and is closed-form aggregae consumpion funcion includes he conenional (infinielied) represenaie agen model as a special case (when he birh rae is zero). Wih a posiie birh rae, here is no Ricardian equialence or deb neuraliy in he Yaari-Blanchard model. Wih a zero birh rae here is Ricardian equialence. This permis me o show ha helicoper money drops boos household demand regardless of wheher here is Ricardian equialence or no. Apar from he uncerain lifeime ha characerized households in he Yaari-Blanchard model (which plays no role eiher in Ricardian equialence or he effecieness of helicoper money drops), he model has no uncerainy. To sae on noaion I consider a closed economy. 5

7 2.1 The household secor We consider he household and goernmen secors of a simple closed economy. The holding of inrinsically worhless fia base money is moiaed hrough a money-in-he-direc uiliy funcion approach, bu alernaie approaches o making money essenial (cash-in-adance, legal resricions, money-in-he ransacions-funcion or money-in-he procion funcion, say) would work also. For exposiory simpliciy, here is only priae capial. The helicoper money we discuss could, howeer, be used equally well o fund goernmen inesmen programs as ax cus or ransfer paymens ha benefi households, or boos o curren exhausie public spending Indiial household behaior A each ime 0, a household born a ime s maximizes he following uiliy funcional: α θ( ) 1 α ms (,) max E e ln c ( s, ) d P ( ) { c( s, ), ms (, ), b( s, ), k( s, ); s, } (1) c( s, ), ms (, ) 0, θ > 0,0 < α < 1 where E is he condiional expecaion operaor a ime, θ > 0 is he pure rae of ime preference, c(,) s is consumpion a ime by a household born a ime s, ms (,), b(,) s and k(,) s are, respeciely, he socks of nominal base money, nominal risk-free consan marke alue bonds and real capial held a ime by a household born a ime s, and P( ) 0 is he general price leel a ime. 2 The cashless economy where money only seres as a numéraire is he special case of his model when α = 0. Each household faces a consan (age-independen) insananeous probabiliy 1 of deah, λ 0. The remaining expeced life ime λ is herefore also age- 2 If a uni of real capial is inerpreed as an ownership claim o a uni of capial (equiy), hen k can be negaie, zero or posiie. If i is inerpreed as a uni of physical capial iself, k has o be nonnegaie. 6

8 independen and consan. The randomness of he iming of one s demise in he only source of uncerainy in he model. I follows ha he objecie funcional in (1) can be re-wrien as: α ( θ+ λ)( ) 1 α ms (,) max e ln c ( s, ) d P ( ) (2) { c( s, ), ms (, ), b( s, ), k( s, ); } Households ac compeiiely in all markes in which hey operae, and asse markes are complee and efficien, wih free enry. In paricular, here exis acuarially fair annuiies markes ha offer a household an insananeous rae of reurn of λ on each uni of non-financial wealh i owns for as long as i lies, in exchange for he annuiy-issuing eniy claiming he enire sock of financial wealh owned by he household a he ime of is deah. The household has hree sores of alue: fia base money, which carries a zero nominal rae of ineres and is an irredeemable financial insrumen issued by he Sae (he consolidaed general goernmen and Cenral Bank, in his noe), nominal insananeous bonds wih an insananeous nominal ineres rae i and real capial yielding an insananeous gross real rae of reurn ρ. 3 Capial goods and consumpion goods consis of he same physical suff and can be coslessly and insananeously ransformed ino each oher. Capial depreciaes a he consan insananeous rae δ 0. The real wage earned a ime by a household born a ime s is denoed ws (,) and he real alue of he lump-sum ax paid o he Treasury (lump-sum ransfer paymen receied if negaie) a ime by a household born a ime s is τ (,) s. The nominal alue of he helicoper money drop receied a ime by a household born a ime s is d(,) s. This can be iewed as a lump-sum ransfer paymen from he Cenral Bank (which is par of our consolidaed Sae) o he household secor. Labor supply is inelasic and scaled o 1. Compeiion ensures ha pecuniary raes of reurn on bonds and capial are equalized. Wih money yielding posiie uiliy, here can be no equilibrium wih a 3 In Secions 3.5, 3.6 and 3.7 we inerpre bonds as bonds ne of loans. Bonds and loans are assumed o be perfec subsiues as sores of alue. 7

9 negaie nominal ineres rae. Le r () be he insananeous risk-free real ineres P () rae and π () = he insananeous rae of inflaion. I follows ha P () i () 0 ρ() δ() = r () = i () π() (4) The insananeous budge ideniy of a household born a ime s ha has suried ill period is: 4 ms (,) + b (,) s b (,) ( () ) (, ) ( ( ) ) (,) s ms k s + ρ δ + λ k s + i + λ + λ (,) P ( ) P ( ) P ( ) (5) d(,) s + ws (,) τ (,) s + c(,) s P ( ) The real alue of oal non-human wealh (or financial wealh) a ime of a household born a ime s is ms (,) + b(,) s a(,) s k(,) s + (6) P ( ) The flow budge ideniy (5) can, using (4) and (6) be wrien as: ms (,) d(,) s a (,) s ( r () + λ) a(,) s i () + ws (,) τ (,) s + c(,) s (7) P ( ) P ( ) The no-ponzi finance solency consrain for he household is ha he presen discouned alue of is erminal financial wealh be non-negaie in he limi as he ime horizon goes o infiniy: ( r( u) ) lim a( se, ) +λ 0 (3) 4 k(,) s The noaional conenion is ha k (,) s. 8

10 Because he insananeous uiliy funcion is increasing in boh consumpion and he sock of real money balances, he solency consrain will bind: ( r( u) ) lim a( se, ) +λ = 0 (8) The erminal ne financial wealh whose presen discouned alue (NPV) mus be non-negaie includes he household s sock of base money. Noe ha in (8) base money is iewed as an asse by he holder (he household). The household may know ha base money is irredeemable ha when i owns/holds X amoun of base money, i has no claim on he issuer for anyhing oher han X amoun of base money. Base money in his model is fia base money: i is no backed by inrinsically aluable goods and serices a any fixed exchange rae). Like all fia money, i will only hae posiie alue if households beliee i o hae posiie alue. A leas in a flexible nominal price and wage economy, here will always be an equilibrium wih a zero price of money in eery period he barer equilibrium. This is no an issue will shall address in wha follows. I will resric he analysis o sricly posiie sequences of he general price leel. The opimaliy condiions of he household s choice problem imply he following decision rules for he household: ( ) c(,) s = (1 α) θ + λ j(,) s (9) j(,) s a(,) s + h(,) s (10) d(,) s ( r(u) + λ ) h(,) s = ws (,) τ (,) s e + d P ( ) (11) ms (,) α 1 = c(,) s P () 1 α i () i () 0 (12) The ne presen discouned alue of household afer-ax and afer helicoper money drops labor income, h(,) s, will be referred o as human wealh. A shorer life expecancy (a higher alue of λ ) raises he marginal propensiy o consume 9

11 ou of comprehensie wealh, or he sum of financial and human wealh j a + h. We assume in wha follows ha j > The case of saiaion in real base money balances The Cobb-Douglas insananeous uiliy funcion does no hae saiaion in real money balances for finie holdings of real money balances. There is a maerial issue wih he exisence of a liquidiy rap equilibrium or ZLB equilibrium when he demand for real money balances goes o infiniy as he nominal ineres rae goes o zero. 5 An infinie demand for real money balances can only be accommodaed by a zero price leel and/or an infinie sock of nominal money balances. In a Keynesian world (Old- or New-) he price leel is predeermined and canno drop o zero insananeously. Een in a model wih a perfecly flexible general price leel, a zero general price leel would hardly be an aracie or plausible equilibrium. Een he mos QE-enamored moneary auhoriy will hae rouble coming up wih an infinie sock of nominal base money. Wih a sicky general price leel, wha happens when i = 0 and he demand for money becomes unbounded, depends on he raioning mechanism imposed by he moneary auhoriies on would-be holders of base money when heir demand becomes unbounded (a he ZLB), and on he consequences of he raioning mechanism and he response of he priae agens o his mechanism for he equilibrium configuraion of prices and quaniies in a fully ariculaed model. I do no propose o go here in his paper. Insead I will consider a simple alernaie insananeous direc uiliy funcion ha has saiaion in real money balances a a finie leel of he sock of real money balances. The model has he exposiional adanage ha, when he economy is suck in an enring liquidiy rap (a he ZLB foreer), i exhibis effeciely he same behaior for aggregae consumpion as he Cobb-Douglas uiliy funcion model does away from he ZLB. The model wih saiaion a he ZLB shares wih he Cobb-Douglas model away from he ZLB he propery ha a permanen increase in he sock of base money always simulaes consumpion demand. 5 This issue is considered a lengh and in deph in Eggersson and Woodford (2003). I am indebed o an anonymous referee for poining ou he releance of he issue. 10

12 Consider he case of an insananeous uiliy funcion which, unlike he Cobb- Douglas funcion used hus far, has saiaion in real money balances a a finie posiie leel of real money balances. We replace equaion (2) wih (2 ): ( θ λ)( ) max ln (, ) + ms (,) e c s + u P ( ) { c( s, ), ms (, ), b( s, ), k( s, ); } ms (,) ms (,) 1 ms (,) ms (,) η u ;0 ;, 0 P ( ) = η γ ηγ P ( ) 2 P ( ) > P ( ) γ 2 1 η ms (,) η = ; > 2 γ P ( ) γ 2 (2 ) The uiliy of real money balances increases in real money balances for 2 (,) 0 ms η P ( ) γ, reaches is maximum alue of 1 η ms (,) η a =, and is 2 γ P ( ) γ 2 1 η ms (,) η consan a for >. 2 γ P ( ) γ The firs-order condiions for a household opimum now imply: ( ) η 1 i ms (, ) = if i ( ) > 0 γ γ c(,) s η if i ( ) = 0 γ (12 ) For i ( ) > 0, household consumpion demand a ime is deermined from: 2 ( 2 r( u) θ+ λ) η ( r( u) + λ) c(,) s 1 ( i() ) e d + e d = j (,) s θ + λ γc(,) s (13) γ Equaion (13) defines indiial household consumpion a ime as an increasing funcion of comprehensie household wealh: 11

13 ( ) c(,) s = f j(,) s f' = 2 ( θ+ λγ ) c(,) s > 0 for c( s, ) > 0 γ θ λ [ 2 r( u) θ λ] c (,) s + ( + ) i() e d (9 ) This is hardly surprising, because boh consumpion and (unil saiaion ses in) real money balances are normal goods. From Engel aggregaion we know ha if we hae wo goods in he insananeous uiliy funcion, hey canno boh be inferior. Since, for i ( ) > 0,, real money balances and consumpion are posiiely relaed (see (12 )) consumpion demand and money demand are boh increasing in comprehensie wealh. So i suffices o show ha helicoper money can increase he comprehensie wealh of eery household o demonsrae is effecieness. This we do below. When i ( ) = 0, 0 we are in a permanen liquidiy rap and here is saiaion in real money balances a each insan. We assume ha real money balances remain finie. The household consumpion funcion for his case is gien by ( θ λ) c(,) s = + j(,) s (9 ) This is he same as he consumpion funcion deried in (9) from a Cobb- Douglas uiliy funcion wih α = 0. Noe, howeer, ha his is where he analogy wih he Cobb-Douglas funcion case ends: when α = 0 in he Cobb-Douglas model, he demand for real balances is, from equaion (12)zero we are in a cashless economy in which money will no be held if he nominal ineres rae is posiie, because money is rae-of-reurn dominaed as a sore of alue and does no yield any non-pecuniary benefis. When i = 0 base money is no longer rae-ofreurn dominaed and households will be indifferen beween holding money and non-moneary sores of alue. When i () = 0 households may end up holding real money balances in excess of η γ. To do so does, of course, use up comprehensie wealh wihou increasing insananeous uiliy oday. Wih he uiliy of consumpion increasing wihou bound in consumpion, would a uiliy maximizing household ake resources ou of 12

14 real money balances in excess of η γ and allocae hem o curren consumpion insead? If curren consumpion were he only opion i would, bu his household 1 has an expeced lifeime of raion λ, so i would wan o allocae more o fuure consumpion as well, since opimal consumpion oer ime is characerized, boh in he Cobb-Douglas model and in he model wih saiaion in real money balances for finie socks of real money, by c(,) s = c(,) s e ( r( u) θ ) So if faced wih rendan real money balances (a leel in excess of he saiaion leel), an opimizing household would wan o raise curren consumpion and consumpion in all fuure ime periods. To increase fuure consumpion oal comprehensie wealh has o be higher, bu he household will be indifferen beween holding ha wealh in he form of base money, bonds or real capial, as he nominal yield on all hese sores of alue is zero. In wha follows, I will, excep when I deal wih he permanen liquidiy rap case, work wih he Cobb-Douglas insananeous uiliy funcion. I permis a simple closed-form soluion - unlike he non-homoheic preferences ha generae insananeous uiliy funcions capable of procing saiaion for a finie sock of real money balances. When I consider he permanen liquidiy rap special case, in Secion 2.7, I will swich o he insananeous uiliy funcion wih saiaion, which, when i comes o aggregae consumpion behaior, in he special case under consideraion only requires one o se α = 0 in he aggregae consumpion funcion deried from he Cobb-Douglas insananeous uiliy funcion, bu wihou he implicaion ha he amoun of money held is zero Aggregaion We assume ha here is a consan and age-independen insananeous birh rae ( ) β 0. The size of he cohor born a ime is normalized o βe β λ. The size of he suriing cohor a ime which was born a ime s is herefore ( β λ) s λ( s) βe e. Toal populaion a ime is herefore gien, for β > 0 by 13

15 λ βs ( β λ) βe e ds = e. For he case β = 0 we se he size of he populaion a = 0 o equal 1, so populaion size a ime is again ( β λ e ) λ = e. For any indiial household ariable x(,) s, we define he corresponding populaion aggregae X() as follows: λ βs X () = βe x( s, ) e ds if β > 0 λ = x(0, e ) if β = 0 We assume ha each household earns he same wage, pays he same axes and receied he same helicoper money drop, regardless of age: ws (,) = w () τ (,) s = τ () d(,) s = d() I follows ha each household, regardless of age, has he same human wealh: h(,) s = h () Finally, here are neiher olunary nor inolunary bequess in his model, so as (,s) = 0 (14) By brue-force aggregaion, if follows ha aggregae consumpion and money demand for he Cobb-Douglas model is deermined as follows: C () = (1 α)( θ + λ) J () (15) M() α 1 = P () 1 α i ( ) C () (16) M() D () A () r () A () i( ) + W() T() + C () (17) P () P () 14

16 D ( ) ( r( u) + β ) H ( ) = W ( ) T ( ) e + d P ( ) (18) M() + B () A () = K() + P () J() = A () + H() (19) is For fuure reference, he solency consrain of he aggregae household secor r( u) lim Ae ( ) = 0 or (20) M( ) + B ( ) r( u) lim K ( ) e + = 0 P ( ) Comparing he aggregae household financial wealh dynamics equaion (17), wih he indiial suriing household financial wealh dynamics equaion (7) shows ha he reurn on he annuiies, λ A is missing from he aggregae dynamics. This is as i should be, because λ A () is boh he exra reurns oer and aboe he risk-free rae earned by all suriing households a ime and he amoun of wealh paid o he annuiies sellers by he (esaes of he) fracion λ of he populaion ha dies a ime. Comparing he aggregae human wealh equaion (18) describing he human wealh of all generaions currenly alie bu no of hose ye o be born and he indiial suriing household s human wealh equaion (11), we noe ha if he households alie a ime were o discoun all fuure afer-ax labor income a he indiially appropriae, annuiy premium-augmened rae of reurn r + λ, hey would fail o allow for he fac ha he labor force o whom ha afer-ax labor income accrues includes he suriing members of generaions born afer ime. In he absence of he insiuion of inheried slaery, hose currenly alie canno claim he labor income of he fuure suriing members of generaions as ye unborn. Populaion and labor force grow a he proporional rae β λ, so he appropriae discoun rae applied o he fuure aggregae sreams of labor income is r + β. 15

17 2.2 The Sae The Sae whose budge ideniy and solency consrain we model is he consolidaed general goernmen (he Treasury in wha follows) and Cenral Bank. Le G denoe real public spending on goods and serices (exhausie public spending by he sae, curren and or capial). The Sae s budge ideniy and solency consrain are gien in equaion (21) and (22) respeciely. The implici assumpion ha base money can be creaed a zero marginal real resource cos (and indeed ha goernmen bonds can be issued a zero marginal M M real resource cos) is refleced in he absence of erms like µ () M (), µ () > 0 B B and µ () B (), µ () > 0 on he RHS of equaion (21). We also ignore any fixed cos of fia base money issuance, alhough any fixed cos could be buried in G(). For simpliciy we assume ha he Sae ges ax reenue only from he household secor and makes ransfer paymens (including helicoper money drops) only o he household secor. ( ) M () + B () B () D i () + G () T () + P () P () P () Because of he irredeemabiliy of base money, money is in no meaningful sense a liabiliy of he Sae. The solency consrain of he Sae herefore requires ha he presen discouned alue of is erminal ne non-moneary liabiliies be non-posiie, no ha he presen discouned alue of is erminal ne financial liabiliies be non-posiie. (21) B ( ) r( u) lim e 0 P ( ) (22) Equaion (22) is he naural way o formalize he familiar noion ha fia base money is an asse (wealh) o he holder (he owner households in his simple model) bu does no consiue in any meaningful sense a liabiliy o he issuer (he borrower he Sae or he Cenral Bank as an agen of he Sae). The owner of a $20 dollar Federal Resere Noe may find comfor in he fac ha This noe is legal ender for all debs, public and priae, bu she has no claim on he Federal Resere, now or eer, oher han for an amoun of Federal Resere Noes adding up o $20 in alue. UK currency noes worh X carry he proud inscripion 16

18 promise o pay he bearer he sum of X bu his merely means ha he Bank of England will pay ou he face alue of any genuine Bank of England noe no maer how old. The promise o pay sands good for all ime bu simply means ha he Bank will always be willing o exchange one (old, faded) 10 Bank of England noe for one (new, crisp) 10 Bank of England noe (or een for wo 5 Bank of England noes). Because i promises only money in exchange for money, his promise o pay is, in fac, a saemen of he irredeemable naure of Bank of England noes. The asymmeric reamen of base money in he solency consrains of he households and he Sae is he key assumpion underlying our effecieness proposiions for base money expansions/qe een a he ZLB. I represens a deparure from he earlier lieraure, which specified he solency consrain of he sae in erms of he non-posiiiy of he NPV of he erminal deb boh moneary and non-moneary, of he Sae (see e.g. Leeper 1991). I beliee ha he irredeemabiliy propery of fia currency ha i is an asse o he holder bu no a liabiliy of he issuer exends also o he oher componen of base money (commercial bank reseres held wih he Cenral Bank), bu he simple heoreical model does no depend on his and does no make his disincion. Unil furher noice, we assume, alhough unlike wih he household secor, here is no opimizing jusificaion for i, ha he Sae saisfies is solency consrain wih sric equaliy. The case of he sae as NPV credior o he priae secor, een in he long run, is considered briefly in Secion 2.5. Equaion (21) implies ha M() + B () D ( ) M( ) r( u) T ( ) G( ) i( ) e d P ( ) + P ( ) P ( ) M( ) + B ( ) + lim e P ( ) r( u) (23) Because of he irredeemabiliy of base money (equaion (22)), assumed o hold wih sric equaliy, he ineremporal budge consrain of he Sae is 17

19 M() + B () D ( ) M( ) r( u) T ( ) G( ) i( ) e d P ( ) + P ( ) P ( ) M( ) + lim e P ( ) r( u) (24) Subsiuing he ineremporal budge consrain of he Sae ino he aggregae consumpion funcion (15), using (18) and (19), and rearranging yields, when i ( ) > 0, : 6 β ( ) ( ( ) ) ( ) ( ( ) ( )e ) r u + β K + W G e d D ( ) ( r ( u ) ) ( ) C( ) (1 )( ) T ( ) e + β β = α θ + λ 1 e d P ( ) i ( u ) i( ) M ( ) e d 1 + P () i ( u ) + lim M( e ) (25) ( ) ( ) ( ) M ( ) ( ) r u M r u i e d + lim e ( ) ( ) 6 P P Noe ha. 1 i( u) i( u) im ( ) ( e ) = d+ lim Me ( ) P () 18

20 From inegraion by pars i follows ha 7 ( ) ( ) ( ) ( ) i u i u im e d+ lim Me ( ) i ( u ) = M ( ) e d + M () (26) I follows ha (25) can also be wrien as: β ( ) ( ( ) ) ( ) ( ( ) ( )e ) r u β + K + W G e d D ( ) ( r ( u ) ) ( ) C( ) (1 )( ) T ( ) e + β β = α θ + λ 1 e d P ( ) 1 i ( u ) + M () + M ( ) e d P () (27) 7 If insead of haing a zero nominal ineres rae, fia base money carried he possibly ime-arying M nominal ineres rae i (), equaion (26) would become M ( ) ( ) ( ( ) ( )) ( ) i u i u i i Me d+ lim Me ( ) M i ( u ) = ( M ( ) i ( ) ) e d + M ( ) wih obious modificaions required in he ineremporal budge consrains of households and he Sae., 19

21 2.3 Deb neuraliy When he birh rae is zero, he consumpion funcion is equialen o he consumpion funcion of he represenaie agen model. From he perspecie of pure fiscal sabilizaion policy - a cu in lump-sum axes oday accompanied by a credible commimen o an increase in fuure axes equal in ne presen alue o he up-fron ax cu, will no boos household demand. Wih β > 0, an up-fron ax cu and he credible announcemen of a fuure increase in axes of equal ne presen discouned alue when discouned a he riskless rae r booss he human wealh of hose currenly alie because some of he deferred axes will fall on as ye unborn generaions. Wih β = 0 he wedge beween he goernmen s discoun rae for fuure axes, r, and he effecie discoun rae of he priae secor for fuure axes, r + β disappears, and Ricardian equialence or deb neuraliy preails. Wih β = 0, he aggregae consumpion funcion (27) becomes r ( u ) K( ) + ( W ( ) G( ) ) e d i ( u ) C ( ) = (1 α)( θ + λ) i( ) M ( ) e d 1 + P () i ( u ) lim M( e ) + or, equialenly r ( u ) K( ) + ( W ( ) G( ) ) e d C ( ) = (1 α)( θ + λ) 1 i ( u ) M () M ( ) e + + d P () Lump-sum axes and helicoper drops (ransfers) disappear from he aggregae consumpion funcion once he ineremporal budge consrain of he Sae is used o subsiue ou he iniial alues of he priae secor s holdings of moneary and (28) (29) 20

22 non-moneary soereign deb. The firs line on he RHS of equaions (28) and (29) shows he resul, familiar from non-moneary represenaie agens models ha he bie aken ou of priae comprehensie wealh by he goernmen is measured by he ne presen discouned alue of fuure exhausie public spending. 2.4 Helicoper money wih deb neuraliy Een in a represenaie agen model wih deb neuraliy/ricardian equialence, moneary injecions will boos priae consumpion demand, holding consan he sequences of curren and fuure spending on real goods and serices { G ( ); }, prices, wages and ineres raes. The pah of lump-sum axes and of non-moneary deb is irrelean wih β = 0, as long as he Sae saisfies is ineremporal budge consrain (24). I is immediaely obious from equaions (28) and (29) ha, holding consan he sequence of curren and fuure real exhausie public spending consan, moneary injecions will always boos consumpion demand, as long as he price leel P () is posiie. We can hink of moneary injecions, holding consan he pah of curren and fuure exhausie public spending, as being inroced eiher hrough lump-sum ransfer paymens, T, or by purchasing non-moneary deb (soereign bonds) from he priae secor (QE). If he Sae, saring a ime, increases he sock of base money by buying back non-moneary public deb from he public, say wih M ( ) = B ( ) > 0 for ', ' >, i is clear from he ineremporal budge consrain of he Sae, equaion (24), ha, holding consan he curren and fuure pahs of he price leel and ineres raes, he Sae will hae o raise he NPV of fuure public spending on goods and serices plus helicoper drops minus axes o saisfy is ineremporal budge consrain. Permanen open marke purchases of non-moneary public deb by he Cenral Bank (irreersible QE) are deferred helicoper money: fuure axes will be cu and/or fuure public spending will hae be raised if he Sae is o saisfy is ineremporal budge consrain. 8 8 Indeed, he Sae could choose o become a ne non-moneary credior o he priae secor, wih B < 0. The Sae s solency consrain afer all only requires he NPV of is erminal sock of nonmoneary deb o be non-posiie (equaion (22)). I could be sricly negaie in equilibrium, as long 21

23 This definiion of QE as a permanen or irreersible expansion of he moneary base is no mean o capure eeryhing cenral banks hae done on boh he liabiliy and he asse sides of heir balance shees ring he afermah of he Grea Financial Crisis (GFC). Because of he deerminisic naure of he model (he same would apply o any complee markes model wihou financial rading fricions), changes in he size and composiion of he asses held by he Cenral Bank canno be meaningfully considered. All asses oher han base money are, effeciely, equialen. 9 In a more general model wih incomplee and inefficien financial markes, pure QE would be defined as a permanen increase in he size of he Cenral Bank s balance shee hrough a permanen expansion of he moneary base wihou changes in he liquidiy or crediworhiness of he asses held and purchased by he Cenral Bank. Pure credi easing or qualiaie easing would be changes in he composiion of he asses held by he Cenral Bank, in he direcion of less liquid and less crediworhy securiies wihou any change in he size of he Cenral Bank s balance shee or in he moneary base, or collaeralized loans. Realworld balance shee expansions by he Cenral Banks ring he GFC hae ofen combined elemens of pure QE and pure qualiaie easing, or hae inroced ye oher exensions, such as an expansion of non-moneary Cenral Bank liabiliies. The model of his paper can only address pure QE. 2.5 The credior sae Remember ha equaion (22) does no hae o hold wih sric equaliy. The same holds for equaions (22), (24), (25), (27), (28) and (29). Consider he case as he household secor saisfies is solency consrain, ha he NPV of he erminal alue of is M + B financial asses K + is non-negaie. P 9 Such maers as he influence of unconenional moneary cenral bank policies on money marke spreads, considered e.g. in Lenza, Pill and Reichlin (2010) can herefore no be considered in his framework. 22

24 B ( ) r( u) lim e = Z < 0 P ( ), where he Sae is a ne (non-moneary) credior o he priae secor, een in he ery long run. We assume ha Z is finie. 10 The aggregae household solency consrain (20) implies B ( ) r( u) M( ) r( u) lim e lim K ( ) e Z 0 P ( ) = + = > P ( ) or i( u) i( u) ( ) lim Be ( ) = lim PK ( ) ( ) + M( ) e = pz ( ) > 0. The sae is a permanen credior o he household secor, somehing i can do when he long-run growh rae of fia base money is a leas as high as he long-run nominal ineres i( u) rae, since lim Me ( ) M ( ) > 0 requires lim limi( ) 0. M( ) β ( ) ( ( ) ) ( ) ( ( ) ( )e ) r u β + K + W G e d D ( ) ( r ( u ) ) ( ) C( ) (1 )( ) T ( ) e + β β = α θ + λ 1 e d P ( ) (30) 1 i ( u ) + i( ) M ( ) e d Z P () Acing as a long-run NPV credior sae o he priae secor herefore does no aler he capaciy of he Sae o boos he comprehensie wealh of he household secor, afer consolidaion of he ineremporal budge consrains of he household secor. This is because, unlike he Sae, he household secor s NPV of all financial asses has o be non-negaie in he long run. From he goernmen s ineremporal budge consrain (24) i is clear ha he M( ) r( u) fiscal space creaed by lim e > 0 P ( ) can be used o cu fuure axes or 10 In a model wih posiie real growh in he long run, he raio of real goernmen bonds o oupu would be resriced o be finie. 23

25 increase fuure helicoper drops or public spending on goods and serices, bu no o any greaer degree han when he NPV of non-moneary soereign deb in he long run was required o be zero. 2.6 Helicoper money in he normal case Consider wha is perhaps he normal case, when, in he long run, he Sae grows he nominal sock of fia base money a a proporional rae sricly below he insananeous risk-free nominal ineres rae, ha is, i ( u ) lim M( e ) = 0. In he represenaie agen case ( β = 0 ) he consumpion funcion becomes r ( u ) K( ) + ( W ( ) G( ) ) e d C ( ) = (1 α)( θ + λ). 1 i ( u ) + i( ) M ( ) e d P () The Sae can boos demand by moneary injecions, for gien sequences of exhausie public spending, he general price leel and ineres raes. A larger fuure money supply will, ceeris paribus, increase he comprehensie wealh or permanen income of he household secor by boosing he NPV of he ineres bills saed by borrowing hrough he issuance of zero-ineres-bearing base money raher han hrough (posiie) ineres-bearing deb. The same conclusion sares one in he face een more clearly when we use he equialen expression for he seigniorage blessings of moneary issuance, shown in equaion (29). The wealh-creaing effec of seigniorage is he ousanding sock of base money plus he NPV of fuure base money issuance: 1 i ( u ) M () + M ( ) e d. Again his can be made arbirarily large P () for gien sequences of G, P and i. 24

26 2.7 Helicoper money in a permanen liquidiy rap Consider an economy suck in he ulimae liquidiy rap wih he nominal ineres rae a zero foreer. To aoid he echnical and concepual problems wih unbounded money demand a a zero nominal ineres rae, we consider he permanen liquidiy rap for he model wih saiaion a a finie leel of real balances. The aggregae consumpion funcion and money demand for his case are gien by: C () = ( θ + λ) J () M() η e P () γ ( β λ) Wih i ( ) = 0,, moneary injecions lose none of heir poency. Sure, he NPV of he curren and fuure ineres saed by issuing base money raher han non-moneary securiies (bonds) is zero: i ( u ) i( ) M ( ) e d = 0 when i ( ) = 0,. Bu he NPV of he erminal sock of base money can be made anyhing he Sae (he moneary auhoriy) wans i o be: i ( u ) lim M( ) e = lim M( ) when i ( ) = 0,. The alernaie expression for he wealh represened by he seigniorage monopoly of he Sae i( u) M( ) + lim M ( ) e d = M( ) + lim M ( ) d = lim M( ), which encouragingly is he same as he one deried earlier, again shows ha he auhoriies can use helicoper money o boos consumer demand een in he seeres of all conceiable liquidiy raps. Wha his means is ha a fia money economy where he Sae conrols he issuance of fia money, a liquidiy rap is a choice, no a necessiy. Mos general equilibrium compleions of a model wih he consumpion funcion used in his paper will hae he propery ha if, in a perpe- 25

27 ual zero nominal ineres rae equilibrium, real demand is boosed by a sufficienly large magniude, he permanen liquidiy rap anishes. Equaions (28) or (29) wih α = 0 (which represens he aggregae consumpion funcion for he case wih saiaion a a finie leel of real money balances, or heir more general ersions wihou Ricardian equialence, make i clear ha i is also possible for he Sae o boos public spending on real goods and serices, curren or capial, and aoid any negaie impac of he anicipaion of higher fuure axes on demand by moneizing he resuling public secor deficis. How likely is an economy o find iself in a permanen liquidiy rap? The secular sagnaion hypohesis is one roue o such an unforunae equilibrium (see Summers 2013 and Buier e al. 2014). I is beyond he scope of his paper o work ou a comprehensie formal model (for recen examples of such a model see Eggersson and Krugman (2012) and Eggersson and Mehrora (2014)), bu he broad oulines of such a model will be familiar. Consider a Keynesian economy wih sicky money wages or prices. Oupu is demand-deermined. The iniial real ineres rae a full employmen is low and so are inflaion and he nominal ineres rae. There is a negaie shock o aggregae demand (say a cu in real public spending on goods and serices). This creaes an ex-ane saing minus inesmen glu a he old equilibrium real ineres rae. Equilibrium can only be resored a full employmen a a negaie real rae of ineres. There are wo ways o ge he real ineres rae o negaie leels. Eiher cu he nominal ineres rae or raise he (expeced) rae of inflaion. The iniial conracionary shock, howeer, lowers he rae of inflaion. The nominal ineres rae canno go ino negaie erriory by more han he carry cos of currency. The resul may be ha he new real equilibrium ineres rae a full employmen canno be achieed hrough conenional moneary policy. There has o be a posiie shock o demand o resore full employmen a a feasible real ineres rae. Expansionary fiscal policy is he obious policy insrumen. Helicoper money drops are a combined moneary and fiscal simulus ha can do he job. Wheher absen helicoper money he economy is likely o remain suck foreer a he ZLB is a moo poin. The real message of his paper is ha een in such a deeply pererse equilibrium, helicoper money drops could raise aggregae demand and hus lif he economy from he ZLB floor. The alue of sudying he 26

28 permanen liquidiy rap is herefore mainly he demonsraion ha here is no reason eer o ge suck in one. Helicoper money plus minimally inelligen and cooperaing moneary and fiscal auhoriies are sufficien o rule ou a permanen sojourn a he ZLB. 2.8 Why is his resul differen from he ineffecieness resul of Eggersson and Woodford? Eggersson and Woodford (2003) (hereafer EW) argue ha expansions of he moneary base, holding consan he Cenral Bank s ineres rae rule, will hae no effec a he ZLB. The effecieness of helicoper money (or permanen QE) in boosing household demand in he pure liquidiy rap case where he safe nominal rae of ineres is a he effecie lower bound/zlb a all mauriies is e o he asymmeric reamen of he NPV of he erminal sock of base money in he household solency consrain (equaion (20)) and in he Sae solency consrain (equaion (22)). This asymmery is a resul of he irredeemabiliy of base money, which implies ha base money is an asse o he holder bu no a liabiliy o he issuer. If he Sae insead were o rea base money as a liabiliy, ha is, if equaion (22) were o be replaced by M( ) + B ( ) r( u) lim e = 0 P ( ) (31) Then he aggregae consumpion funcion (25) or (27) would be replaced, respeciely, by equaion (32) and equaion (33) As regards equaion (32) noe ha ( ) ( ) ( ) M ( ) ( ) r u M r u i e d + lim e P ( ) P ( ). 1 i( u) i( u) im ( ) ( e ) = d+ lim Me ( ) P () 27

29 β ( ) ( ( ) ) ( ) ( ( ) ( )e ) r u β + K + W G e d D ( ) ( r ( u ) ) ( ) C( ) (1 )( ) T ( ) e + β β = α θ + λ 1 e d P ( ) 1 i ( u ) + i( ) M ( ) e d P () (32) β ( ) ( ( ) ) ( ) ( ( ) ( )e ) r u β + K + W G e d ( ) D ( r ( u ) ) ( ) C( ) (1 )( ) T ( ) e + β β = α θ + λ 1 e d P ( ) 1 i( u) i( u) M ( ) M( e ) + + d lim M( e ) P () (33) So in he pure liquidiy rap case ( iu ( ) = 0, u ) hese wo equialen ersions of he aggregae consumpion funcion rece o: β ( ) ( ( ) ) ( ) ( ( ) ( )e ) r u + β K + W G e d C ( ) = (1 α)( θ + λ) ( ) D ( r ( u ) ) ( ) T ( ) e + β β 1 e d P ( ) (34) For hose who are concerned abou he unbounded demand for real money balances a he ZLB in he Cobb-Douglas case, equaion (34) can be reinerpreed, by seing α = 0, as he aggregae consumpion demand when he economy is 28

30 suck permanenly a he ZLB for he model wih saiaion in real money balances a a finie leel of real money balances. In equaion (34), curren and/or fuure money socks don appear. Helicoper money is compleely ineffecie and so, of course, is any increase in he base money sock, een if i is permanen, say a permanen increase in he moneary base brough abou hrough irreersible QE. I assume ha he difference in resuls is e o a symmeric reamen of money in he household and Sae solency consrains by EW. I canno be compleely cerain of his, as EW specify he ineremporal budge consrain of he household (he firs equaion (no numbered) on heir p. 149) direcly - wihou explicily giing a no-ponzi finance solency consrain for he household. From he form of he ineremporal budge consrain ha he household solency consrain is ha he NPV of he household s erminal financial wealh, including base money balances be non-negaie base money is perceied as an asse by he household secor. The only ime we see somehing ha looks like a solency consrain for he Sae is EW s equaion 38 on page 196, which requires ha he NPV of he Sae s non-moneary liabiliies be zero. The ineremporal budge consrain of he Sae is no spelled ou, so we canno back ou wheher he solency consrain of he Sae requires he NPV of he erminal socks of all financial liabiliies of he Sae (including he base money sock) o be non-negaie or jus he NPV of he erminal socks of non-moneary liabiliies. The ineffecieness of base money expansions a he ZLB in he firs par of heir paper suggess ha EW hae, implicily, unil hey arrie a equaion 38 on page 196, adoped a symmeric role of he base money sock in he solency consrains of he household secor and of he Sae in he firs par of heir paper. B ( ) r( u) Howeer, when on page 196 EW impose lim e = 0 P ( ) hey hae he same asymmery as regards he way base money is iewed beween households on he one hand and he Sae on he oher hand, as does our paper. EW noe ha, wih he asymmeric solency consrain, base money expansion a he ZLB can be effecie. Thus a commimen of his kind can exclude he possibiliy of a selffulfilling deflaion of he sor aboe as a raional expecaions equilibrium. I follows ha here is a possible role for quaniaie easing undersood o mean 29

31 he supply of base money beyond he minimum quaniy required for consisency wih he zero nominal ineres rae as an elemen of an opimal policy commimen (Eggersson and Woodford 2003, p. 197). B ( ) r( u) EW, howeer, iew lim e = 0 P ( ) no as he solency consrain of he Sae (he consolidaed general goernmen and Cenral Bank) bu as a fiscal commimen, which need no hold all he ime. This probably accouns for he ineffecieness of base money expansions a he ZLB when he economy is in a self-fulfilling deflaionary rap and he fiscal commimen rule is no imposed. This is he only reason why we ge a general effecieness of permanen base money expansions resul, away from as well as a he ZLB while EW in much of heir paper (unil equaion 38 on page 196) ge an ineffecieness resul a he ZLB. The fac ha EW look a a specific Taylor-ype ineres rae rule away from he ZLB and a moneary base rule a he ZLB, while we esablish he effecieness resul for all sequences of curren and fuure ineres raes, does no accoun for he differences in our resuls. Neiher is he difference in our resuls e o he fac ha EW work wih a general equilibrium model while I work wih an incomplee or parial equilibrium model conaining only he household and he Sae secors. In his parial equilibrium framework I show ha for any sequences of ineres raes, (posiie) price leels and oher ariables ha are aken as exogenous by he indiial households bu will be endogenous in a fully-fledged general equilibrium model, household demand can be boosed hrough helicoper money drops by any desired amoun. Wheher such an increase in consumer demand raises prices and money wages alone, or employmen and oupu as well, will depend on he general equilibrium closure rule ha is adoped. Esablishing he poin ha household demand can be boosed does no require a general equilibrium model. 2.9 Helicoper money wihou Ricardian equialence The way helicoper money affecs household demand is he same in he oerlapping generaions model (he Yaari-Blanchard model wih β > 0 ) as in he represenaie agen model ( β = 0 ). A comparison of equaions (25) and (27) wih equaions (28) and (29) shows ha he comprehensie wealh erm in he aggregae 30

32 consumpion funcion is augmened by base money issuance o he une of ( ) i u i( u) ( ) ( ) ime d+ lim M( e ) or, equialenly, i ( u ) M () + M ( ) e d. I is clear from he model wihou Ricardian equialence ha permanen moneary base expansions of a gien magniude in NPV erms will now hae differen effecs when hey are implemened hrough up-fron lump-sum ransfer paymens/helicoper money drops/ax cus han hrough up-fron QE (open marke purchases of soereign bonds) followed by deferred ransfer paymens, helicoper money drops or ax cus. Because he deferred ransfer paymens, helicoper money drops and ax cus will in par be enjoyed by generaions no ye born oday, he up-fron QE and deferred ransfer paymen boos ersion will be less expansionary, for a gien NPV of base money issuance, han he ersion wih he up-fron ransfer paymen boos The cashless economy The cashless economy is he special case of our Cobb-Douglas insananeous uiliy funcion when α = 0. Wihou a non-pecuniary reurn moie for holding base money, base money, een if here were such a securiy, will no be held as long as he nominal ineres rae on non-moneary securiies is posiie, proided here is a fixed money price for hese securiies. If here were a ariable exchange rae beween non-ineres-bearing base money and posiie ineres-bearing securiies, here could be an equilibrium in which he ineres bearing securiies depreciae in erms of base money, hus compensaing for he ineres differenial. In he exreme form of he cashless economy where here is no non-ineresbearing Sae-issued insrumen called base money, money is reced o a pure numéraire and any form of helicoper money is impossible, away from he ZLB or a he ZLB. This case is considered by Gali (2008). If here is no non-pecuniary reurn moie for holding base money, bu base money pays he same ineres rae i as he non-moneary securiy (he case sudied by Woodford 2003), here is no wealh effec on consumpion from helicoper base 31

33 money drops if nominal ineres raes are posiie, a leas in he long run. If he economy is in a permanen liquidiy rap, helicoper money drops would hae wealh effecs if and only if base money is irredeemable. Consider a sequence of economies indexed by α for which α 0. As long as he alue of α is posiie and he price of money (he inerse of he general price leel) is posiie, helicoper money will boos aggregae demand, as is clear from equaions (25) and (27). I is rue ha, for any gien leel of aggregae consumpion, real money balances held willingly are lower for lower alues of α. Bu, a gien sequences of curren and fuure prices, wages, ineres raes ec. real consumpion would be higher by enough o equae money demand and supply. Of course, higher aggregae consumpion demand will falsify he assumpion ha he sequences of curren and fuure prices, wages, ineres raes ec. can be aken as gien, once a plausible supply side and marke clearing condiions complee he model. Bu ha is jus anoher way of saying ha helicoper money is effecie, in he Cobb Douglas model, as long as α is posiie and i is posiie. The case where i is zero and α is posiie was discussed is Secion 2.1.2; i is unlikely o be well-defined because of he unbounded demand for real money balances. The case where boh i and α are zero is also beyond my ken. The limi as α 0 when i > 0 is unlikely o be he soluion when α = 0. This is because when α = 0 we are in he cashless economy where money is no alued inrinsically and is rae-of-reurn dominaed as a sore of alue. Consequenly, i does no hae posiie alue in any reasonable general equilibrium compleion of our aggregae demand model. Helicoper money does no work. Howeer, for any posiie alue of α, no maer how small, helicoper money is effecie and here herefore can be an equilibrium in which money has posiie alue. Such disconinuiies a zero are no uncommon. In Nickelsburg (1984) a fricion is inroced in he Kareken and Wallace (1981) model of exchange rae deerminaion in he form of a posiie probabiliy of currency conrols being imposed in he fuure. This fricion makes for a deerminae exchange rae in wha, wihou he fricion, would be an indeerminae exchange rae. As ha fricion goes o zero (he probabiliy of currency conrols being imposed goes o zero), he exchange rae remains deerminae een for iny bu posiie probabiliies. Howeer, when he probabiliy of currency conrols equals zero, here is exchange rae indeerminacy a qualiaiely differen oucome. 32

34 3 Some furher consideraions 3.1 Fia base money is special In his model unbacked fia base money is unique for wo reasons. Firs, i performs liquidiy or ransacions funcions ha cause i o be willingly held by priae agens despie carrying a zero nominal ineres rae, een when oher safe asses are presen ha yield a posiie nominal ineres raes. I shoe-horned his uniqueness ino he model by haing money as an argumen in he household s direc uiliy funcion. This is no ery saisfacory. The only jusificaion is simpliciy and he robusness of he resuls of he paper o using oher mechanisms for making fia base money a superior asse (money in he procion funcion, cash in-adance or legal resricions). Wha makes somehing (or some class of objecs) desirable because of is unique ransacions-faciliaing properies differs in he many differen approaches ha hae been adoped for generaing a willingness o hold somehing ha is pecuniary-rae-of-reurn-dominaed as a sore of alue. I is he oucome of a collecie, decenralized social choice. I may help if somehing is graned legal ender saus by he Sae, bu his no a necessary condiion. Should fia base money issued by he Sae lose his unique adanages i has in faciliaing ransacions, i will hae o pay ineres a he same rae as he oher safe, liquid financial asses bonds in his model, or i will no be held olunarily by priae agens. We are in he Wallace (1981, 1990) world of he Modigliani-Miller heorem for open marke operaions. The ne presen discouned alue of fuure ineres saed is, of course zero in his case. Howeer, if he moneary asse is irredeemable, he NPV of he erminal base money sock would sill be ne wealh. For his o be posiie, he growh rae of he nominal sock of base money would hae o be a leas equal o he nominal rae of ineres in he long run. In he liquidiy rap case, wih a zero nominal ineres rae foreer, a helicoper money drop would sill be effecie in boosing household consumpion demand, een hough a helicoper bond drop would no be. 3.2 Fia base money is ne wealh Fia base money is ne wealh for he consolidaed priae secor and Sae secor. Despie fia money echnically being inside money and an inside asse (issued by 33

35 one economic agen and held by anoher), fia base money behaiorally or effeciely is like naure s bouny: an asse and wealh o he owner bu no a claim on or liabiliy of he issuer. Indeed, looking a he ersion of he aggregae consumpion funcion in 1 i ( u ) equaion (27) or (29), noe ha he erm M () + M ( ) e d P () could equally well represen rue ouside asses, like inrinsically worhless pe rocks or Rai, he sone money used on he Isle of Yap. The sock of rare bis of rock deposied on earh by meeories, say, could be represened by M() and he ne presen alue of fuure meeorie deposis could be represened by i ( u ) M ( ) e d. Wih some sligh modificaions, almos inrinsically worhless commodiies like gold and inrinsically worhless irual media of exchange like Bicoin could also fi ino our consumpion funcion. Boh are, of course, cosly o proce or mine. Helicoper drops of Rai, gold or Bicoin would no share wih fia base money he propery ha hey are issued by he Sae and can be used o fund he Sae. They don roll off he prining presses bu are gifs from naure (Rai and gold) and from human ingenuiy (in he case of Bicoin). 3.3 When is a helicoper money drop preferred o a bond-financed fiscal simulus? When here is no Ricardian equialence, aggregae demand can be simulaed hrough soereign bond-financed ax cus (or hrough higher exhausie public spending) as well as hrough helicoper money. Which mehod one prefers depends on how he model of he economy is compleed and on policy preferences. The formal model of his noe is no well suied o deal wih problems like soereign defaul risk or inflaion risk, bu richer models ha permi a meaningful discussion of hese issues would likely hae he propery ha if (1) he soereign has a high sock of non-moneary ne deb ousanding and (2) here are poliical limis o is curren and fuure capaciy o raise axes or cu public spending, adding o he sock of non-moneary deb hrough furher soereign bond issuance could raise soereign defaul risk. Tha would call for moneary 34

36 financing as he preferred funding mehod for a fiscal simulus. The case for moneary financing would be sronger if inflaion is below arge and if one or more key financial markes are illiquid. If he public finances are healhy (low soereign deb and defici, considerable poliical scope for cuing public spending or raising axes) and inflaion is aboearge, using soereign bonds o fund a simulus would make sense. In he curren economic condiions faced by he euro area, Japan and, o a slighly lesser degree, by he US and he UK, wih quesion marks behind he susainabiliy of he public finances and wih inflaion well below arge, moneizing a fiscal simulus would seem o be he obious firs choice. 3.4 The insiuional implemenaion of helicoper money drops In mos conemporary adanced economies, he issuance of fia base money (ofen wih legal ender saus) is performed by an agency of he Sae, he Cenral Bank, ha has some degree of operaional independence (and in a few cases een a measure of arge independence) in he design and implemenaion of moneary policy. Some Cenral Banks can ac as fiscal agens for he Sae (cenral goernmen or federal Treasury/Minisry of Finance) bu none ha I know of acs openly as fiscal principals, sending checks o he ciizens on heir own behalf or engaging in public inesmen oer and aboe he consrucion of heir own offices. Cenral Banks ypically ransfer heir profis (oer and aboe wha hey wan o add o reseres or proisions) o heir beneficial owner, he cenral goernmen or federal Treasury. 12 Specifically, Cenral Banks do no ley axes, make ransfer paymens or pay oer subsidies o oher domesic economic eniies, nor do hey engage in exhausie public spending oher han wha is ineiably inoled in he running of he Cenral Bank (payroll, capial expendiure on buildings and equipmen, supplies, uiliies ec.). The fac ha many Cenral Banks hae engaged in large-scale quasi-fiscal inerenions, mos recenly ring and afer he Norh-Alanic financial crisis of , does no change he basic 12 The European Cenral Bank (ECB) is unique in ha is shareholders are he naional Cenral Banks (NCBs) of he 28 (as of May 2014) European Union member saes. The profis of he ECB are disribued o he 18 (as of May 2014) NCBs of he EU member saes ha are also members of he euro area. 35

37 legal and insiuional realiy ha a Cenral Bank canno implemen helicoper money on is own. Cooperaion and coordinaion beween he Cenral Bank and he Treasury is required for he real-world implemenaion of helicoper money drops. In pracice, o implemen he emporary fiscal simulus permanenly/irreersibly financed hrough he issuance of fia base money ha is closes o he original Friedman helicoper money parable a lump-sum ransfer paymen households permanenly funded hrough base money issuance, he following coordinaed fiscal-moneary acions would ake place. There would be a one-off cash ransfer o all eligible households by he Treasury. The Treasury funds hese paymens by selling Treasury deb o he Cenral Bank, which credis he accoun held by he Treasury wih he Cenral Bank (which is no normally couned as par of he moneary base). As he Treasury pays ou he cash o he eligible households, he Treasury s accoun wih he Cenral Bank is drawn down. The moneary base increases because he ransfer paymen o he households eiher ends up as increased cash/currency held by households, corporaes or banks or as increased bank reseres held wih he Cenral Bank. A irually idenical sory can be old if insead of a ransfer paymen o he household secor, he Treasury were o engage in a program of curren or capial expendiure. 3.5 The irreleance of he cancellaion of Treasury deb held by he Cenral Bank From a fundamenal economic perspecie, i makes no difference wheher he Cenral Bank cancels he soereign bonds i buys (as proposed e.g. by Turner 2013) or holds hem indefiniely (rolling hem oer as hey maure). This is because he Treasury is he beneficial owner of he Cenral Bank. The Treasury herefore receies he Cenral Bank s profis and is responsible for is losses. Their accouns (including balance shees and P&L accoun) herefore can be or indeed ough o be consolidaed o ge a proper perspecie on he flow of funds and balance shee accouns ha maer. The only reason o prefer cancellaion of soereign deb held by he Cenral Bank oer he Cenral Bank holding he soereign deb permanenly is ha cancellaion may be seen as a more credible commimen deice. 36

38 The disaggregaed period (insananeous) budge ideniy, he ineremporal budge ideniy and he solency consrain of he Treasury are gien in equaions (37), (38) and (39). Those of he Cenral Bank are gien in equaions (40), (41) and (42). As before, B sands for he ne non-moneary claims on he Sae held by he priae secor (he household secor, for simpliciy); B h is (non-moneary claims on he Treasury held by he priae secor, B denoes Treasury deb held by he Cenral Bank and L Cenral Bank (non-moneary) financial claims on he priae secor. All non-moneary financial claims are nominally denominaed and earn he risk-free insananeous ineres rae i. T is he real alue of axes paid by he priae secor o he Treasury, T is he real alue of paymens made by he Cenral Bank o he Treasury. The Treasury spends G g in real erms on consumpion goods and serices and he Cenral Bank spends G. For exposiional simpliciy, Treasury and Cenral Bank capial expendiure are ignored. Because we are considering a closed economy, he Cenral Bank does no hold any foreign exchange reseres. Noe ha: h B B L (35) g G G G + (36) h h B () + B () B () + B () g i() + G () T() T () P () P () h B () + B () g r( u) T ( ) + T () G () e d P () h B ( ) + B () + lim e P ( ) r( u) h B ( ) + B () r( u) lim e 0 P ( ) M () B () L () D () B () + L () G () + + T () i () P () P () P () (37) (38) (39) (40) 37

39 M() B () L() D() M( ) r( u) G ( ) T ( ) i( ) e d P () + P () P ( ) (41) M( ) B ( ) L( ) r( u) + lim e P ( ) B ( ) + L ( ) r( u) lim e 0 P ( ) (42) The Treasury s ineremporal budge ideniy and solency consrain imply he Treasury s ineremporal budge consrain: h B () + B () g r( u) ( T ( ) + T () G () ) e d P () (43) The Cenral Bank s ineremporal budge ideniy and solency consrain, which recognizes he irredeemabiliy of fia base money, imply he Cenral Bank s ineremporal budge consrain: M() B () L() M( ) r( u) lim e d P () P ( ) (44) D ( ) M ( ) r( u) + G ( ) T ( ) i ( ) e + P ( ) P ( ) Assume ha he Treasury, as he beneficial owner of he Cenral Bank, receies all he profis or cash flows of he Cenral Bank. Defining Cenral Bank profis as he Cenral Bank s financial surplus, ha is, he excess of Cenral Bank ineres income oer Cenral Bank consumpion expendiures, inesmen expendiures and helicoper drops, his implies: B () + L () D () T () = i () G () P () P () (45) This in urn implies ha M () = B () + L () (46) 38

40 Under his sric inerpreaion of he Treasury appropriaing all Cenral Bank profis, he Cenral Bank runs a balanced budge coninuously hus keeping is conenionally defined Ne Worh or Equiy - he excess of he alue of is financial asses oer he alue of is financial liabiliies - consan (excep for capial gains and losses no considered here). For he equialence of he Cenral Bank cancelling a gien amoun of soereign deb or holding i permanenly (rolling i oer as i maures) a coninuous budge balancing hrough paymens o (ransfers from) he Treasury is no necessary. All ha is required is ha he presen discouned alue (NPV) of he ne paymens made by he Cenral Bank o he Treasury be he same as he NPV of he paymens sream ha balances he Cenral Bank s budge coninuously. Equaions (44) and (45) imply ha i( u) M( ) B ( ) L( ) ( i( ) ( M( ) B ( ) L( ) )) e d (47) i( u) + lim M( e ) Briefly, i does no maer wheher he Cenral Bank oday cancels an amoun B () of deb owed o i by he Treasury and as a resul does no pay ou as profis o he Treasury an infinie fuure sream of Cenral Bank profis { ib ( ) ( ), } (whose NPV is, of course, B () ), or wheher i keeps is exising holdings of Treasury deb on is books and pays ou as profis o he Treasury an infinie sream of fuure profis ha is larger a each poin of ime by an amoun ib ( ) ( ),. 13 { } 3.6 Helicoper money drops and he ECB Maers are slighly more complicaed for he ECB, whose equiy is held by he naional Cenral Banks (NCBs) of he member Saes ha are par of he euro area. Each NCB has is naional Treasury as is beneficial owner. Cancelling an amoun B i () of soereign deb of euro area member Sae i (which has an equiy sake η i 13 i( u) i( ) B () e d = B () 39

41 in he ECB), represens ulimaely a wealh ransfer of (1 ηi) Bi ( ) o he Treasury of member Sae i from he Treasuries of all oher member Saes. Holding Bi () indefiniely on he balance shee of he ECB would resul in an infinie sream of profis { i ( ) η ibi ( ), } o he NCB of counry i, and hus ulimaely o he Treasury of counry i, and { i ( )(1 η ) i Bi ( ), } o he NCBs of he remaining euro area member Saes and hus ulimaely o heir naional Treasuries. This real-world implemenaion of helicoper money drops is legal and easily implemened eerywhere excep in he euro area. Aricle of he Treay on he Funcioning of he European Union Saes: Oerdraf faciliies or any oher ype of credi faciliy wih he European Cenral Bank or wih he Cenral Banks of he Member Saes (hereinafer referred o as naional Cenral Banks ) in faour of Union insiuions, bodies, offices or agencies, cenral goernmens, regional, local or oher public auhoriies, oher bodies goerned by public law, or public underakings of Member Saes shall be prohibied, as shall he purchase direcly from hem by he European Cenral Bank or naional Cenral Banks of deb insrumens. 14 This clause has commonly been inerpreed as ruling ou he financing of goernmen deficis in he euro area hrough goernmen deb sales o he ECB (or o he naional Cenral Banks (NCBs) of he Eurosysem) and heir moneizaion by he Eurosysem. Unless his can be fudged by he Eurosysem purchasing he soereign deb in he secondary markes (as i did under he Securiies Markes Programme and proposes o do under he Ourigh Moneary Transacions programme (should i eer be aciaed)), Aricle depries he euro area of he one policy insrumen a emporary fiscal simulus permanenly funded by and moneized by he Cenral Bank ha is guaraneed o preen or cure deflaion, lowflaion or secular sagnaion. I is ime for Aricle 123 o be scrapped in is enirey if he euro area does no wish o face he unnecessary risk of falling ino any of hese raps. 14 hp:// 40

42 3.7 How can he Cenral Bank, echnically, do helicoper money drops on is own? Consider again he case where he Treasury, as he beneficial owner of he Cenral Bank, receies all he profis or cash flows of he Cenral Bank as in equaions (45) and (46). 15 From (45) i follows ha if he Cenral Bank increases is flow of helicoper money drops (D()), oher hings ( G ) being equal, i will rece one-for-one he amoun of profis i remis o he Treasury ( T ). If nohing else changes in he Treasury s budge consrain (oher han T ) and if he Cenral Bank does no increase is ne lending o he priae secor ( L ), he Treasury will increase is B sales of Treasury deb o he Cenral Bank ( ) by he same amoun as he P recion in T and he increase in D. The increase in he change in he P moneary base, M herefore equals he increase in he rae of helicoper money drops, D. If he axaion by he Treasury of he profis of he Cenral Bank were less asphyxiaing han assumed in (45), for insance in he case where T is gien exogenously, he Cenral Bank can, in principle, engage in helicoper money drops wihou purchasing Treasury securiies or indeed engaging in any kind of open marke purchases or sales of financial asses (or changing he socks of ousanding non-moneary Cenral Bank liabiliies no considered in his simple model). Consider he period budge ideniy of he Cenral Bank in (40). Assume he Cenral bank increases is helicoper money drops, holding eeryhing else consan (securiies purchases from he Treasury, lending o he priae secor, Cenral Bank consumpion, Cenral Bank inesmen and axes paid o he Treasury), and mainains such a policy for some finie period of ime. Thus for < we hae: 0 1 M () D () (48) 15 This sub-secion owes much o he insighful commens of Norber Häring on an earlier ersion of his paper. He is quie correc ha, echnically/legally, he Treay does no prohibi helicoper money drops when he ECB signs he checks. My reseraions relae o legiimacy consideraion raher han legal ones. 41

43 Here sands for he difference relaie o some benchmark sequence. The implicaions of such unilaeral helicoper money drops by he Cenral Bank could worry hose accusomed o analyzing he conenionally defined Cenral Bank balance shee, consising of he Cenral Bank s financial asses and liabiliies (Table 1). Here NW sands for conenionally defined ne worh or equiy, he excess of he alue of conenional asses oer conenional liabiliies. NW B + L M (49) I is clear ha if he Cenral Bank engages in moneized helicoper money drops iself (as in (48)), i follows from Table 1 ha, if he moneary base expands (expands a a faser rae) because of helicoper money drops (a faser rae of helicoper money drops) and he financial asses of he Cenral Bank remain consan, he equiy or conenionally defined ne worh of he Cenral Bank falls (falls faser). I could become negaie. Does his maer? Consider he ineremporal budge consrain of he Cenral Bank, equaion (44) in Table 2 as he Comprehensie Balance Shee of he Cenral Bank. Here * NW sands for he comprehensie ne worh of he Cenral Bank. Compared o he conenional balance shee in Table 1, he comprehensie balance shee ads wo asses, i( u) i( ) M ( ) e i( u) d and lim M( e ) and hree liabiliies, i( u) P( ) G ( ) e i( u) d, De ( ) r( u) dand P( ) T ( ) e d. Table 1: Sylized Conenional Cenral Bank Balance Shee B L Asses M NW Liabiliies 42

44 Table 2: Comprehensie Cenral Bank Balance Shee Asses Liabiliies B M L i( u) i( ) M ( ) e lim M( e ) i( u) d P( )G ( ) e d De ( ) i( u) i( u) r( u) d P( ) T ( ) e d * NW Solency of he Cenral Bank only requires, from equaion (44), ha is comprehensie ne worh is non-negaie. This is perfecly consisen wih is conenional ne worh being negaie: * i( u) i( u) NW = NW i( ) M ( ) e d lim M ( ) e i( u) i( u) r( u) + PG ( ) ( e ) d+ De ( ) d+ PT ( ) ( e ) d In Buier and Rahbari (2012) and Buier (2012) we hae esimaed he NPV of fuure currency issuance 16 by he ECB/Eurosysem (and oher Cenral Banks) a he arge rae of inflaion (assumed o be 2 percen) and making a range of assumpions abou he oher driers of real currency demand (assumed o be nominal ineres raes and real GDP). I was no difficul, in he case of he Eurosysem o come up wih wha we labelled he Non-Inflaionary Loss 16 From equaion (26) his is gien by i( u) ( ) ( ) ( ) i u i u M e d im ( ) ( e ) = d+ lim M( e ) M ( ) (50) 43

45 Absorpion Capaciy (NILAC) of around 3 rillion. This number of course is an underesimae of he rue NILAC as i only considers fuure issuance of currency. The oher componen of he moneary base, commercial bank deposis wih he Cenral Bank are effeciely assumed no o be a source of profi o he Cenral Bank (hey pay he marke rae of ineres). 3.8 The legaliy and legiimacy of unilaeral helicoper money drops by he Cenral Bank Can a Cenral Bank ac openly as a fiscal principal, engaging in public expendiure on real goods and serices oer and aboe wha is required for he fulfillmen of is mandaed asks, making ransfer paymens o he priae secor (such as helicoper drops of money) and imposing axes on he priae secor? I is clear ha Cenral Banks can and do ac as quasi-fiscal acors on a large scale. Resere requiremens ha don pay he marke rae of ineres are equialen o a ax on banks. During he financial crisis many Cenral Banks paid implici subsidies o he banks hey deal wih by lending on erms ha were beer han was warraned by he crediworhiness of he borrowing banks and by he qualiy of he collaeral ha hey offered. No Cenral Bank I know of does, howeer, engage in open fiscal acions as a principal. They do no ley axes and explici ransfer paymens are de minimis chariable conribuions ec. In some counries he power o ax and o use public resources o fund ransfer programs and oher public spending programs are consiuionally or legally resered for he legislaure. In he US Consiuion, Aricle 1, Secion 8. Clause 1 (hp:// saes: The Congress shall hae Power o lay and collec Taxes, Duies, Imposs and Excises, o pay he Debs and proide for he common Defence and general Welfare of he Unied Saes; bu all Duies, Imposs and Excises shall be uniform hroughou he Unied Saes. If one inerpres The Congress as Only he Congress hen he Fed can only engage in (explici) ax and spend acions wih he approal of and as an agen of he Congress. We hae no been able o find a comparable clause in he European Treaies (TEU and TFEU). Howeer, as regards explici axaion, he widely acceped 44

46 principle of no axaion wihou represenaion would seem o make i implausible ha he ECB, as an uneleced, appoined echnocraic body could impose axes on euro area (EA) ciizens or residens. The lack of poliical legiimacy of axaion by he Cenral Bank would doom he effor and probably also he Cenral Bank engaged in i. Wha abou public spending ransfer paymens o EA residens/ciizens or spending on consumpion (healh or ecaion, say) or inesmen (EA infrasrucure)? Again, alhough we hae no been able o find clauses in he Treaies prohibiing helicoper money drops by he ECB, oher good deeds or infrasrucure spending beyond is own organizaional needs, he poliical legiimacy of such acions would appear o be quesionable. Cenral Bank resources are public resources ax-payers money. An uneleced body like he ECB would appear o lack he inpu legiimacy o decide how o spend public resources oer and aboe wha is necessary o implemen is mandae. Here, howeer, here is a bridge oer he legiimacy chasm. The primary objecie of he ECB is price sabiliy, operaionally defined as an inflaion rae (on he HIPC measure) below bu close o wo percen per annum in he medium erm. If he only way o pursue his primary objecie of price sabiliy is o engage in helicoper money drops, and if Aricle 123 of he TFEU is deemed o rule ou a join moneary-fiscal policy simulus by he ECB and 18 (in 2014, 19 from January 1, 2015, when Lihuania joins he EA) naional fiscal auhoriies, hen one could argue ha he Treay no only permis bu demands helicoper money drops from he ECB. Oupu legiimacy may rump he lack of inpu legiimacy. While he argumen in he preious paragraph may appear persuasie in he case where inflaion is below he leel deemed consisen wih price sabiliy he case where a helicoper money drop is called for -, i fails o conince when he inflaion rae is aboe arge and he helicoper would hae o acuum up money held by priae agens. Such reerse helicoper money drops or acuum cleaner money grabs - which would hae he Cenral Bank send a bill o each eligible residen in is jurisdicion, would definiely be me wih cries of axaion wihou represenaion. A combined Cenral Bank-Treasury operaion wih he Treasury sending he demands for paymen would likely no be me wih such oucry and resisance. Boh pracically and concepually, here appears o be an asymmery in he direc helicoper money drop procere. 45

47 4 Conclusion 4.1 The wo funding adanages of fia base money: zero nominal ineres rae and irredeemabiliy The fia base money analyzed in his paper, which can be proced a zero marginal cos by he Sae (much like paper currency or bank reseres wih he Cenral Bank in he real world), and which households are willing o hold a a zero nominal ineres rae een when alernaie sores of alue wih posiie nominal ineres raes are aailable, has wo hings going for i as a funding insrumen for he Sae, compared o ineres-bearing non-moneary deb. Firs, he Sae saes each period (insan in he coninuous ime model) he ineres bill i would hae paid had i issued bonds insead of money. Second, een if he nominal ineres rae is zero and een if i is confidenly expeced o be zero foreer, money is a more aracie funding insrumen for he Sae because i is irredeemable. Fia base money is ne wealh o he priae secor in he sense ha is curren sock plus he NPV of ne fuure issuance is a componen of he comprehensie wealh of he household secor. 4.2 Helicoper money drops always boos demand A permanen helicoper drop of irredeemable fia base money booss demand boh when Ricardian equialence does no hold and when i holds. I makes he deficien demand ersion of secular sagnaion a policy choice, no somehing drien by circumsances beyond naional policy makers conrol. I booss demand when nominal risk-free ineres raes are posiie and when hey are zero and een in a pure liquidiy rap when nominal ineres raes are zero foreer. A helicoper money drop always booss demand when he price of money is posiie. 17 If he Cenral Bank has he legal righ and he poliical legiimacy o send checks o hose liing in is jurisdicion, i can implemen helicoper money drops on is own. Oherwise cooperaion beween he Cenral Bank and he 17 In dynamic general equilibrium wih flexible nominal prices, here always exiss an equilibrium wih a zero price of money in all periods and all Saes of naure he barer equilibrium or nonmoneary equilibrium. Obiously, helicoper money drops won boos demand in such an equilibrium. 46

48 naional Treasury (Treasuries in he euro area) is necessary o implemen helicoper money drops. Acknowledgemen The iews and opinions expressed are hose of he auhor alone and should no be aribued o Ciigroup or o any oher organizaion he auhor is associaed wih. I would like o hank Larry Summers from prodding me o wrie a shor(ish) noe seing ou he essence of he helicoper money argumen, and Norber Häring for insighful commens on an earlier ersion of his paper. Two anonymous referees proided excepionally helpful commens on an earlier ersion of his paper. 47

49 References Bernanke, Ben (2003). Some Thoughs on Moneary Policy in Japan, speech, Tokyo, May. hp:// Blanchard, Oliier J. (1985). Deb, Deficis and Finie Horizons. Journal of Poliical Economy 93(2): hp://ideas.repec.org/a/ucp/jpolec/93y1985i2p hml Buier, Willem H. (1988). Deah, Birh, Prociiy Growh and Deb Neuraliy. Economic Journal 98 (June): hp://ideas.repec.org/a/ecj/econjl/98y1988i391p hml Buier, Willem H. (2003a). Deflaion; Preenion and Cure, 2003 McKenna Lecure on Inernaional Trade and Economics; Perspecie on he Economy. NBER Working Paper 9623, April hp://willembuier.com/mckenna.pdf Buier, Willem H. (2003b). Helicoper Money: Irredeemable Fia Money and he Liquidiy Trap. NBER Working Paper No. W10163, Dec. hp:// Buier, Willem H. (2004). Two Naked Emperors? Concerns abou he Sabiliy and Growh Pac & Second Thoughs abou Cenral Bank Independence. Fiscal sudies 25(3): hp://eprins.lse.ac.uk/846/1/ifs_25%283%29.pdf Buier, Willem H. (2007). Seigniorage. Economics: The Open-Access, Open-Assessmen E- Journal 1( ): hp://dx.doi.org/ /economics-ejournal.ja Buier, Willem H. (2012). The Role of Cenral Banks in Financial Sabiliy: How Has i Changed?, in World Scienific Sudies in Inernaional Economics: Volume 30, edied by Douglas D Eanoff, Cornelia Holhausen, George G Kaufman and Manfred Kremer. hp://willembuier.com/chicago.pdf Buier, Willem H. and Ebrahim Rahbari (2012). Looking ino he Deep Pockes of he ECB. Cii Economics, Global Economics View, 27 February. hp://blogs.r.fdaa.co.uk/money-supply/files/2012/02/cii-looking-ino-he-deep- Pockes-of-he-ECB.pdf Buier, Willem H., Ebrahim Rahbari and Joseph Seydl (2014). Secular Sagnaion: Only If We Really Ask for I. Cii Research, Economics, Global, Global Economics View, 13 January. hps://ir.cii.com/shp9jqos7%2bilayopq%2f8xauzl6isyjm8qgwyxyk64oj 5eO3Iz86d9D2CS%2BlgKn2 48

50 Eggersson, Gaui and Michael Woodford (2003). The Zero Bound on Ineres Raes and Opimal Moneary Policy. Brookings Papers on Economic Aciiy 34(1): hp:// Eggersson, Gaui and Michael Woodford (2006). Opimal Moneary and Fiscal Policy in a Liquidiy Trap, edied by Richard H. Clarida, Jeffrey Frankel, Francesco Giaazzi and Kenneh D. Wes, ediors NBER Inernaional Seminar on Macroeconomics 2004, NBER book, pp Eggersson, Gaui and Paul Krugman (2012). Deb, Deleeraging and he Liquidiy Trap: A Fisher-Minsky-Koo Approach, Quarerly Journal of Economics, 127(3), Eggersson, Gaui and Neil Mehrora (2014). A Model of Secular Sagnaion. Discussion Paper, July 4. hp:// Fama, Eugene F. (1983). Financial Inermediaion and Price Leel Conrol. Journal of Moneary Economics, 12(1): Helpman, Elahanan (1983). Commens on: Financial Inermediaion and Price Leel Conrol by Eugene F. Fama. Journal of Moneary Economics 12(1): hp:// Friedman, Milon (1948). A Moneary and Fiscal Framework for Economic Sabiliy. The American Economic Reiew 38 (3): hp:// redireced Friedman, Milon (1969). The Opimum Quaniy of Money, in Milon Friedman, The Opimum Quaniy of Money and Oher Essays, Chaper 1. Adline Publishing Company, Chicago. Gali, Jordi (2008). Moneary Policy, Inflaion and he Business Cycle: An Inrocion o he New Keynesian Framework, Princeon Uniersiy Press. Gordon, Rober J. (2014). The Demise of U. S. Economic Growh: Resaemen, Rebual, and Reflecions. NBER Working Paper 19895, February. hp://econpapers.repec.org/paper/nbrnberwo/19895.hm Gurley, John G. and Edward S. Shaw (1960). Money in a Theory of Finance. The Brookings Insiuion, Washingon D.C. Hall, Rober E. (1983). Opimal Ficiary Moneary Sysems. Journal of Moneary Economics 12(1): hp://web.sanford.e/~rehall/opimal_ficiary_moneary_sysems.pdf 49

51 Hansen, Alin (1939). Economic Progress and Declining Populaion Growh. American Economic Reiew 29(1, Par 1) hp:// Kareken, John and Neil Wallace (1981). On he Indeerminacy of Equilibrium Exchange Raes. The Quarerly Journal of Economics, 96(2): hp://qje.oxfordjournals.org/conen/96/2/207.full.pdf King, Rober G. (1983). On he Economics of Priae Money. Journal of Moneary Economics 12(1): hp:// Krugman, Paul R. (1998). I s Baaack: Japan s Slump and he Reurn of he Liquidiy Trap. Brookings Papers on Economic Aciiy 2: hp:// ominquez_rogoff.pdf Leeper, Eric (1991). Equilibria under Acie or Passie Moneary and Fiscal Policy. Journal of Moneary Economics 27(1): hp:// Lenza, M, Pill, H and Reichlin L (2010). Moneary policy in excepional imes Economic Policy 25, hp://ideas.repec.org/a/bla/ecpoli/25y2010ip hml Moghadam, Reza, Ranji Teja and Pelin Berkmen (2014). Euro Area Deflaion Versus Lowflaion. IMFdirec, The inernaional Moneary Fund s global economy forum, March 4. hp://blog-imfdirec.imf.org/2014/03/04/euro-area-deflaion-ersus-lowflaion/. Nickelsburg, Gerald (1984). Dynamic Exchange Rae Equilibria wih Uncerain Goernmen Policy. Reiew of Economic Sudies 51(3): hp://resud.oxfordjournals.org/conen/51/3/509.absrac Painkin, Don (1965). Money, Ineres and Prices; An Inegraion of Moneary and Value Theory. Second Ediion, Harper & Row, Publishers, New York. Pesek, Boris P., and Thomas R. Saing (1967). Saing, Money, Wealh, and Economic Theory. New York: The Macmillan Company,. Reichlin, Lucrezia, Adair Turner and Michael Woodford (2013). Helicoper money as a policy opion. VoxEU, 20 May 2013, hp:// Sargen, Thomas. J. (1987). Dynamic Macroeconomic Theory, Cambridge Massachuses: Harard Uniersiy Press. Sargen, Thomas J. and Neil Wallace (1984). Ineres on Reseres. Journal of Moneary Economics 15(3): hp://ideas.repec.org/a/eee/moneco/15y1985i3p hml 50

52 Sims, Chrisopher A. (2001). Fiscal Aspecs of Cenral Bank Independence. CESifo Working Paper Series No hp://ideas.repec.org/p/ces/ceswps/_547.hml Sims, Chrisopher A. (2004). Limis o inflaion argeing, in Ben S. Bernanke and Michael Woodford eds. The Inflaion-Targeing Debae, NBER Books, Naional Bureau of Economic Research, Inc, number bern04-1, July. hp://ideas.repec.org/b/nbr/nberbk/bern04-1.hml Sockman, Alan C. (1983). Commens; Opimal Ficiary Moneary Sysems by Rober E. Hall. Journal of Moneary Economics,12(1): hp:// Summers, Lawrence (2013). IMF 14h Annual Research Conference in Honor of Sanley Fisher, Inernaional Moneary Fund, Noember 8. hp://larrysummers.com/imf-foureenh-annual-research-conference-in-honor-ofsanley-fischer/ Turner, A (2013). Deb, Money and Mephisopheles, speech a Cass Business School, 6 February, hp:// Wallace, Neil (1981). A Modigliani-Miller heorem for open marke operaions. American Economic Reiew 71(3): hp://ideas.repec.org/a/aea/aecre/71y1981i3p hml Wallace, Neil (1990). A suggesion for oersimplifying he heory of money. Federal Resere Bank of Minneapolis Quarerly Reiew 13(1): hp://ideas.repec.org/a/fip/fedmqr/y1990iwinp19-26n.14no.1.hml Weil, Philippe (1989). Oerlapping Families of Infiniely-lied Agens. Journal of Public Economics 38(2): hp://ideas.repec.org/a/eee/pubeco/38y1989i2p hml Weil, Philippe (1991). Is Money Ne Wealh? Inernaional Economic Reiew 32(1, February): hp://ideas.repec.org/a/ier/iecre/32y1991i1p37-53.hml Woodford, Michael (2003). Ineres and Prices A Foundaion of a Theory of Moneary Policy. Princeon, New Jersey: Princeon Uniersiy Press. Woodford, M (2012). Mehods of Policy Accommodaion a he Ineres-Rae Lower Bound. Proceedings Economic Policy Symposium Jackson Hole: hp://ideas.repec.org/a/fip/fedkpr/y2012p hml Yaari, M. E. (1965). Uncerain Lifeime, Life Insurance and he Theory of he Consumer. Reiew of Economic Sudies 32(2): hp://resud.oxfordjournals.org/conen/32/2/137.exrac 51

53 Please noe: You are mos sincerely encouraged o paricipae in he open assessmen of his aricle. You can do so by eiher recommending he aricle or by posing your commens. Please go o: hp://dx.doi.org/ /economics-ejournal.ja The Edior Auhor(s) Licensed under he Creaie Commons License Aribuion 3.0.