Willem H. Buiter Works – Always The Simple Analytics Of .
Vol. 8, 2014-28 August 21, 2014 14-28The Simple Analytics of Helicopter Money: Why ItWorks – AlwaysWillem H. BuiterAbstractThe author provides a rigorous analysis of Milton Friedman’s parable of the ‘helicopter’drop of money – a permanent/irreversible increase in the nominal stock of fiat base moneyrate which respects the intertemporal budget constraint of the consolidated Central Bank andTreasury – the State. Examples are a temporary fiscal stimulus funded permanently throughan increase in the stock of base money and permanent QE – an irreversible, monetized openmarket purchase by the Central Bank of non-monetary sovereign – debt. Three conditionsmust be satisfied for helicopter money always to boost aggregate demand. First, there mustbe benefits from holding fiat base money other than its pecuniary rate of return. Second, fiatbase money is irredeemable – viewed as an asset by the holder but not as a liability by theissuer. Third, the price of money is positive. Given these three conditions, there always exists– even in a permanent liquidity trap – a combined monetary and fiscal policy action that boostsprivate demand – in principle without limit. Deflation, ‘lowflation’ and secular stagnation aretherefore unnecessary. They are policy choices.JEL E2 E4 E5 E6 H6Keywords Helicopter money; liquidity trap; seigniorage; secular stagnation; central bank;quantitative easingAuthorsWillem H. Buiter, Citigroup Global Markets Inc., 388 Greenwich Street, New York, NY10013, USA, willem.buiter@citi.comCitation Willem H. Buiter (2014). The Simple Analytics of Helicopter Money: Why It Works – Always.Economics: The Open-Access, Open-Assessment E-Journal, Vol. 8, 2014-28. 4-28Received May 21, 2014 Published as Economics Discussion Paper June 13, 2014Revised August 6, 2014 Accepted August 17, 2014 Published August 21, 2014 Author(s) 2014. Licensed under the Creative Commons License - Attribution 3.0
1Introduction“Let us suppose now that one day a helicopter flies over this communityand drops an additional 1000 in bills from the sky, . Let us supposefurther that everyone is convinced that this is a unique event which willnever be repeated,” (Friedman 1969, pp 4–5).This paper aims to provide a rigorous analysis of Milton Friedman’s famousparable of the ‘helicopter’ drop of money (Friedman 1948, 1969). A helicopterdrop of money is a permanent/irreversible increase in the nominal stock of fiatbase money with a zero nominal interest rate, which respects the intertemporalbudget constraint of the consolidated Central Bank and fiscal authority/Treasury –henceforth the State. An example would be a temporary fiscal stimulus (say a oneoff transfer payment to households, as in Friedman’s example), fundedpermanently through an increase in the stock of base money. It could also be apermanent increase in the stock of base money through an irreversible open marketpurchase by the Central Bank of non-monetary sovereign debt held by the public –that is, QE. The reason is that QE, viewed as an irreversible or permanent purchaseof non-monetary financial assets by the Central Bank funded through anirreversible or permanent increase in the stock of base money, relaxes theintertemporal budget constraint of the State. Consequently, there will have to besome combination of current and future tax cuts or current and future increases inpublic spending to ensure that the intertemporal budget constraint of the Stateremains satisfied. QE relaxes the intertemporal budget constraint of theconsolidated Central Bank and Treasury either if nominal interest rates are positiveor because fiat base money is irredeemable. In our simple model, QE is theirreversible purchase by the Central Bank of sovereign debt funded throughirreversible base money issuance. The same results would hold, however, if theCentral Bank purchased private securities outright instead of sovereign debt, orexpanded its balance sheet through collateralized lending.There are three conditions that must be satisfied for helicopter money asdefined here to always boost aggregate demand. First, there must be benefits fromholding fiat base money other than its pecuniary rate of return. Only then will basemoney be willingly held despite being dominated as a store of value by nonmonetary assets with a positive risk-free nominal interest rate. This means that in acashless economy, like the Woodford-Gali (Woodford 2003, Gali 2008) worlds inwww.economics-ejournal.org1
which something called ‘money’ serves as a numéraire but either has no existenceas a store of value (currency, an account with the Central Bank or e-money) oryields no non-pecuniary benefits, earns the same pecuniary rate of return as bondsand is not irredeemable, helicopter money is ineffective. Second, fiat base moneyis irredeemable: it is view as an asset by the holder but not as a liability by theissuer. This is necessary for helicopter money to work even in a permanentliquidity trap, with risk-free nominal interest rates at zero for all maturities. Third,the price of money is positive.The paper shows that, when the State can issue unbacked, irredeemable fiatmoney or base money with a zero nominal interest rate, which can be produced atzero marginal cost and is held in positive amounts by households and other privateagents despite the availability of risk-free securities carrying a positive nominalinterest rate, there always exists a combined monetary and fiscal policy action thatboosts private demand – in principle without limit. Deflation, inflation belowtarget, ‘lowflation’, ‘subflation’ and the deficient demand-driven version ofsecular stagnation are therefore unnecessary. 1 They are policy choices. Thiseffectiveness result holds when the economy is away from the zero lower bound(ZLB), at the ZLB for a limited time period or at the ZLB forever.The feature of irredeemable base money that is key for this paper is that theacceptance of payment in base money by the government to a private agentconstitutes a final settlement between that private agent (and any other privateagent with whom he exchanges that base money) and the government. It leaves theprivate agent without any further claim on the government, now or in the future.The helicopter money drop effectiveness issue is closely related to the questionas to whether State-issued fiat money is net wealth for the private sector, despitebeing technically an ‘inside asset’, where for every creditor that holds the assetthere is a debtor who owes a claim of equal value (see Patinkin 1965, Gurley and1 The term ‘lowflation’ is, I believe, due to Moghadam et al. (2014). The term ‘subflation’ has beenaround the blogosphere for a while. I use it to refer to an inflation rate below the target level orlower than is optimal. ‘Secular stagnation’ theories go back to Alvin Hansen (1939). I refer here tothe Keynesian variant, which holds that there will be long-term stagnation of employment andeconomic activity without government demand-side intervention. There also is a long-term supplyside variant, associated e.g. with Robert Gordon (2014), which focuses on faltering innovation andproductivity growth. Larry Summers (2013) marries the demand-side and supply-side secularstagnation approaches by invoking a number of hysteresis mechanisms. For a formal model seeEggertsson and Mehrotra (2014).www.economics-ejournal.org2
Shaw 1960 and Pesek and Saving 1967), Weil (1991). The discussions in Hall(1983), Stockman (1983), King (1983), Fama (1983), Helpman (1983), Sargentand Wallace (1984), Sargent (1987) and Weil (1991) of outside money, privatemoney and the payment of interest on money ask some of the same questions asthis paper, but do not offer the same answer, because they don’t address theirredeemability of fiat base money. Krugman (1998), Sims (2001, 2004), Buiter(2003a, 2004) and Eggertsson and Woodford (2003, 2006) all stress that to boostdemand in a liquidity trap, base money increases should not be, or expected to be,reversed. None of these papers recognized that even a permanent increase in thestock of base money will not have an expansionary wealth effect in a permanentliquidity trap unless money is irredeemable in the sense developed here; withoutthis, there is no wealth effect or real balance effect from irreversible base moneyissuance in a permanent liquidity trap. Ben Bernanke spent years living down themoniker “helicopter Ben” which he acquired following a (non-technical)discussion of helicopter money (Bernanke 2003). The issue has also been revisitedby Buiter (2003b, 2007) and, in an informal manner, by Turner (2013), byReichlin et al. (2013).The paper shows that, because of its irredeemability, state-issued fiat money isindeed net wealth to the private sector, in a very precise way: the initial stock ofbase money plus the present discounted value of all future net base moneyissuance is net wealth, an ‘outside’ asset to the private sector, even after theintertemporal budget constraint of the State (which includes the Central Bank) hasbeen consolidated with that of the household sector.This irredeemability of base money and the resulting asymmetric treatment ofbase money in the solvency constraints of households and of the state accounts forour base money expansion/QE effectiveness at the zero lower bound (ZLB), whenEggertsson and Woodford (2003) (henceforth EW) established the existence of aself-fulfilling deflationary trap at the ZLB and ineffective base money issuance orQE. In most of the EW paper, base money is treated symmetrically in the solvencyconstraints of the State and the household sector. When, towards the end of theEW paper, a fiscal rule is introduced that effectively imposes asymmetrictreatment of base money in the solvency constraints of the State and the householdsector identical to what we assume, QE effectiveness at the ZLB is present, even inthe EW model.www.economics-ejournal.org3
The paper also demonstrates that fiat base money issuance is effective inboosting household demand regardless of whether there is Ricardian equivalence(debt neutrality).Finally, the effectiveness of helicopter money requires that there is a rate-ofreturn dominated (except at the ZLB) store of value that is willingly held by theprivate sector and that is irredeemable. Base money must be rate-of-returndominated (equivalently, base money must yield non-pecuniary benefits to theholder) if helicopter money is to have wealth effects away from the ZLB or if theeconomy is at the ZLB temporarily. Irredeemability of base money is required forhelicopter money to have wealth effects even if the economy is at the ZLB forever.In a cashless economy, where ‘money’ exists only as a numéraire, the wealtheffect of helicopter money drops cannot exist either at or away from the ZLB andit is not possible do discuss the topic of helicopter money. In the Woodford (2003)cashless world, where there is a security issued by the government called moneywhich serves as the numéraire, yields the same pecuniary rate of return as nonmonetary securities and yields no other (non-pecuniary) benefits, there can be noeffective helicopter money drops away from the ZLB or if the economy is at theZLB temporarily. If Woodford’s money were irredeemable (his specification ofthe solvency constraint of the State suggests it is not) there could be effectivenessof helicopter money drops if the economy were at the ZLB forever.2The modelAll important aspects of how helicopter money drops work and what makeshelicopter money unique can be established without the need for a completedynamic general (dis)equilibrium model. All that is needed is a completespecification of the choice process of the household sector in a monetary economy,the period budget identity and solvency constraint of the consolidated generalgovernment/Treasury and Central Bank – the State – and the no-arbitrageconditions equating (in principle risk-adjusted) returns on all non-monetary storesof value and constraining the instantaneous nominal interest rate to be nonnegative.www.economics-ejournal.org4
I shall show that, as long as the price of money is positive, the issuance of fiatbase money can boost household consumption demand by any amount, given theinherited stocks of financial and real assets, given current and future wages andprices, and given current and future values of public spending on goods andservices. Whether such helicopter money drops change asset prices and interestrates, goods prices, wages and/or output and employment depends on thespecification of the rest of the model of the economy – including, in more generalmodels, the behavior of the financial sector and of non-financial businesses indriving investment demand, production and labor demand, the rest of the ‘supplyside’ of the economy and the rest of the world, if the economy is open. The pointof this paper is to show that, whatever the equilibrium configuration we start from,helicopter money drops will boost household demand and must disturb thatequilibrium. What ‘gives’ ultimately, in a fully articulated dynamic generalequilibrium model nominal prices and wages, employment or output, is not ourconcern here.The model of household behavior I use is as stripped-down and simple as I canmake it without raising concerns that the key results will not carry over to moregeneral and intricate models. The continuous-time Yaari-Blanchard version of theOLG model is used to characterize household behavior (see Yaari 1965, Blanchard1985, Buiter 1988 and Weil 1989). This model with its easy aggregation and itsclosed-form aggregate consumption function includes the conventional (infinitelived) representative agent model as a special case (when the birth rate is zero).With a positive birth rate, there is no Ricardian equivalence or debt neutrality inthe Yaari-Blanchard model. With a zero birth rate there is Ricardian equivalence.This permits me to show that helicopter money drops boost household demandregardless of whether there is Ricardian equivalence or not. Apart from theuncertain lifetime that characterized households in the Yaari-Blanchard model(which plays no role either in Ricardian equivalence or the effectiveness ofhelicopter money drops), the model has no uncertainty. To save on notation Iconsider a closed economy.www.economics-ejournal.org5
2.1The household sectorWe consider the household and government sectors of a simple closed economy.The holding of intrinsically worthless fiat base money is motivated through a‘money-in-the-direct utility function’ approach, but alternative approaches tomaking money essential (cash-in-advance, legal restrictions, money-in-thetransactions-function or money-in-the production function, say) would work also.For expository simplicity, there is only private capital. The helicopter money wediscuss could, however, be used equally well to fund government investmentprograms as tax cuts or transfer payments that benefit households, or boost tocurrent exhaustive public spending.2.1.1Individual household behaviorAt each time t 0, a household born at time s t maximizes the following utilityfunctional:α 1 α m ( s , v ) θ ( v t )max Et eln c ( s, v ) dv P ( v ) t (1){c ( s, v ), m( s, v ), b ( s, v ), k ( s, v ); s t , v t}c( s, v ), m( s, v ) 0,θ 0,0 α 1where Et is the conditional expectation operator at time t, θ 0 is the pure rate oftime preference, c ( s, v ) is consumption at time v by a household born at time s,m( s, v ) , b ( s, v ) and k ( s, v ) are, respectively, the stocks of nominal base money,nominal risk-free constant market value bonds and real capital held at time v by ahousehold born at time s, and P ( v ) 0 is the general price level at time v. 2 Thecashless economy where money only serves as a numéraire is the special case ofthis model when α 0 .Each household faces a constant (age-independent) instantaneous probabilityof death, λ 0 . The remaining expected life time λ 1 is therefore also age2 If a unit of real capital is interpreted as an ownership claim to a unit of capital (equity), thenbe negative, zero or positive. If it is interpreted as a unit of physical capital itself,negative.www.economics-ejournal.orgk cank has to be non-6
independent and constant. The randomness of the timing of one’s demise in theonly source of uncertainty in the model. It follows that the objective functional in(1) can be re-written as:α 1 α m ( s , v ) max eln c ( s, v ) dv P ( v ) t{c ( s, v ), m( s, v ), b ( s, v ), k ( s, v ); v t} (θ λ )( v t )(2)Households act competitively in all markets in which they operate, and assetmarkets are complete and efficient, with free entry. In particular, there existactuarially fair annuities markets that offer a household an instantaneous rate ofreturn of λ on each unit of non-financial wealth it owns for as long as it lives, inexchange for the annuity-issuing entity claiming the entire stock of financialwealth owned by the household at the time of its death.The household has three stores of value: fiat base money, which carries a zeronominal rate of interest and is an irredeemable financial instrument issued by theState (the consolidated general government and Central Bank, in this note),nominal instantaneous bonds with an instantaneous nominal interest rate i andreal capital yielding an instantaneous gross real rate of return ρ . 3 Capital goodsand consumption goods consist of the same physical stuff and can be costlesslyand instantaneously transformed into each other. Capital depreciates at theconstant instantaneous rate δ 0 . The real wage earned at time v by a householdborn at time s is denoted w( s, v ) and the real value of the lump-sum tax paid to theTreasury (lump-sum transfer payment received if negative) at time v by ahousehold born at time s is τ ( s, v ) . The nominal value of the helicopter moneydrop received at time v by a household born at time s is d ( s, v ) . This can beviewed as a lump-sum transfer payment from the Central Bank (which is part ofour consolidated State) to the household sector. Labor supply is inelastic andscaled to 1.Competition ensures that pecuniary rates of return on bonds and capital areequalized. With money yielding positive utility, there can be no equilibrium with a3 In Sections 3.5, 3.6 and 3.7 we interpret ‘bonds’ as ‘bonds net of loans’. Bonds and loans areassumed to be perfect substitutes as stores of value.www.economics-ejournal.org7
negative nominal interest rate. Let r (t ) be the instantaneous risk-free real interestP (t )the instantaneous rate of inflation. It follows thatrate and π (t ) P (t )(3)i (t ) 0ρ (t ) δ (t ) r (t ) i (t ) π (t )(4)The instantaneous budget identity of a household born at time s t that hassurvived till period t is: 4m ( s, v ) b ( s, v )b ( s, v )m( s, v )k ( s, v ) ( ρ ( v ) δ λ ) k ( s, v ) ( i ( t ) λ ) λP(v )P(v )P(v )(5)d ( s, v ) w( s , v ) τ ( s , v ) c ( s, v )P(v )The real value of total non-human wealth (or financial wealth) at time v of ahousehold born at time s isa ( s, v ) k ( s, v ) m( s, v ) b ( s, v )P(v )(6)The flow budget identity (5) can, using (4) and (6) be written as:m( s, v )d ( s, v )a ( s, v ) ( r ( v ) λ ) a ( s, v ) i ( v ) w( s, v ) τ ( s, v ) c ( s, v )P(v )P(v )(7)The no-Ponzi finance solvency constraint for the household is that the presentdiscounted value of its terminal financial wealth be non-negative in the limit as thetime horizon goes to infinity:v( r ( u ) λ )dulim a ( s, v )e t 0 v 4 The notational convention is thatwww.economics-ejournal.org k ( s, v ).k ( s, v ) v8
Because the instantaneous utility function is increasing in both consumptionand the stock of real money balances, the solvency constraint will bind:v ( r ( u ) λ )dulim a ( s, v )e t 0(8)v
The Simple Analytics of Helicopter Money: Why It Works – Always Willem H. Buiter Abstract The author provides a rigorous analysis of Milton Friedman’s parable of the ‘helicopter’ drop of money – a permanent/irre
The Open-Access, Open-Assessment E-Journal, May 2017. 76. "Government Deficits in Large Open Economies: The Problem of Too Little Public Debt", Willem H. Buiter and Anne C. Sibert, Ɛconomics, The Open-Access, Open-Assessment E-Journal, No. 2016-2, January 18, 2016. Website. 75. " The Simple
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