Journal Article
No. 2014-28 | August 21, 2014 (Version 2: August 23, 2016)
The Simple Analytics of Helicopter Money: Why It Works — Always


The paper offers a rigorous analysis of Milton Friedman’s parable of the ‘helicopter’ drop of money – a temporary fiscal stimulus funded through an increase in the stock of fiat base money that is never completely reversed in present discounted value (PDV) terms.  A monetized fiscal stimulus is more expansionary than a debt-financed one because a monetized expansion of the Central Bank balance sheet is profitable: it relaxes the intertemporal budget constraint of the State – it creates fiscal space.  It is up to the fiscal authority to make appropriate use of this fiscal space.

Four conditions must be satisfied for a helicopter money drop to boost aggregate demand. First, it must not be reversed fully in PDV terms.  Second, there must be benefits from holding fiat base money other than its pecuniary rate of return: that is, the interest rate on any additional base money issued is below the rate of return on the Central Bank’s assets. Third, fiat base money is irredeemable – an asset to the holder but not a liability to the issuer. Fourth, the price of money is positive. Given these conditions, there always exists – even in a permanent liquidity trap – a combination of monetary and fiscal policy actions that boosts private and/or public demand demand) – in principle without limit. Deflation, ‘lowflation’ and secular stagnation are therefore policy choices.

Other conclusions are: (1) the increase in the monetary base need not be permanent for helicopter money to be effective; (2) Treasury debt cancellation by the Central Bank or the purchase by the Central Bank of perpetuities (with zero, negative or positive coupons) rather than finite maturity debt are fundamentally irrelevant policy actions. At most they have signaling value; (3) dropping perishable helicopter money will make it more effective if households are liquidity-constrained.


JEL Classification:

E2, E4, E5, E6, H6


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Cite As

Willem H. Buiter (2016). The Simple Analytics of Helicopter Money: Why It Works — Always. Economics: The Open-Access, Open-Assessment E-Journal, 8 (2014-28): 1—45 (Version 2).

Comments and Questions

Boris Petkov - They (money) would work always, but only if stamped
August 22, 2014 - 15:03

Pls see the pdf file attached below.

Willem H. Buiter - Comment to version 2
September 03, 2015 - 11:20

During the past week I have revised the first article version slightly to rebut an uninformed and misleading, but apparently quite widely circulated, Bank of England Blog post by one of the Bank of England’s Economists (Cumming, Fergus (2015), “Helicopter money: setting the tale straight”, Bank Underground Blog, 5 ...[more]

... August 2015, Cumming conjures up a central bank that (despite having no foreign currency liabilities of note) can become insolvent or borderline-insolvent. In the latter case survival means loss of control of the size of the central bank’s balance sheet and of future inflation. Cancelling Treasury debt held by the central bank – a substantively meaningless accounting exercise - likewise can lead to ‘policy insolvency’ for the central bank. In the original version of the Helicopter Money paper I assumed, in the body of the paper, that the interest rate on base money was zero. This was to economize on notation in what was already a notationally top-heavy paper. In a few footnotes I indicated the modifications required to handle any interest rate on base money. In the current version I have dragged a (possibly non-zero) interest rate on base money into the body of the paper. This makes it (even) clear(er) that Cumming’s analysis yields the above-mentioned surprising results because it violates the most important of the three conditions my original paper gives for Helicopter Money Drops effectiveness: that base money is ‘pecuniary-rate-of-return-dominated’ by the central bank’s assets: the interest rate on base money is required to be less or equal to the safe interest rate on non-monetary assets. In the normal case, where the interest rate on base money is strictly less than the safe rate of return on non-monetary financial instruments, that’s what makes central banking profitable and in particular makes central bank balance sheet expansions profitable. Drop that assumption and strange things happen: the central bank goes insolvent, or loses control of the size of its balance sheet and/or of the rate of inflation – so-called 'policy insolvency'. Fortunately for the UK Treasury and the US Treasury, the Bank of England and the Fed are highly profitable ventures. Some central banks do indeed make losses. For instance, the SNB made large marked-to-market losses on its gold holdings and, more recently, on its holdings of mainly euro-denominated foreign exchange reserves, when it lost its nerves on January 15, 2015 and threw away a 'money machine' by sharply appreciating the external value of the Swiss Franc. Other central banks have been forced by their political masters or by flawed logic into highly risky investments in private securities/loans or in the debt issued by near-insolvent sovereigns (the ECB is an example). But any reasonably competently managed central bank is bound to be profitable, thanks to the unique liquidity and creditworthiness characteristics of its monetary liabilities. Clearly, as pointed out in the many references attached to both the original and the revised version of this paper, even if the interest rate on base money is below the interest rate on the bank’s assets, if the central bank does make strange investments in gold, other commodities or highly risky financial instruments, it can suffer losses so large, that its solvency can only be preserved (absent recapitalisation by some third party) through the issuance of new base money in quantities that undermine the inflation target. But that is a far cry from Cumming’s ‘policy insolvency’ proposition. The revised paper makes it even clearer how the counter-intuitive propositions of Cumming require the peculiar assumption – highly unlikely to be hold in the real world for any length of time – that central banks borrow at a an interest rate greater than or equal to the interests rate they earn get on their assets. Even if the rate of interest on base money is equal to the interest rate on non-monetary financial instruments, Cumming’s policy insolvency results fail because his analysis does not allow for the irredeemability of base money –which ensures that helicopter money drops are effective in boosting demand even if the interest rate on central bank base money equals the rate of return on its assets. I am pleased to be able to re-issue this slightly expanded paper and to circulate it among the academics, technical research-oriented central bankers and other researchers at whom this is directed. It is rather techy, like the orginal, and drowning in probably unnecessary math.

Willem H. Buiter - Comment to version 3
August 23, 2016 - 09:44

The reason for doing a second revision of The Simple Analytics of Helicopter Money: Why It Works - Always, is that, since I published the first revision in September 2015, there has been a veritable avalanche of comments on and assertions concerning ‘Helicopter Money’, virtually all of which were analytically ...[more]

... incorrect, misleading or incomplete. The issues raised include the following:

(1) Helicopter money refers to a temporary fiscal stimulus that is monetized. Does the increase in the monetary base have to be permanent for a monetized temporary fiscal stimulus to have a larger impact on aggregate demand than the same temporary fiscal stimulus funded with sovereign debt and never monetized? Answer: no.
(2) What is the relationship between QE and helicopter money? Answer: central banking (strictly speaking, a monetized expansion in the size of the central bank’s balance sheet) is profitable for two reasons. First, most of the time base money is pecuniary-rate-of-return dominated by non-monetary risk-free financial instruments. Second, even if all non-monetary financial instruments’ yields are at the ELB at all maturities, base money is irredeemable.
(3) Does it help the effectiveness of helicopter money if the central bank cancels (forgives) the sovereign debt it buys? Answer: no, unless such a cancellation (debt forgiveness) is viewed as a credible signal not to reverse the increase in the monetary base. A credible signal has to be costly to the signaler. This looks like cheap talk.
(4) Does it help the effectiveness of helicopter money if the central bank buys perpetuities from the government? Does it make a difference whether the perpetuities have a negative, zero or positive coupon? Answer: no, unless this has signaling value, which is implausible.
(5) Does helicopter money become more effective if the central bank gives the Treasury a credit line, overdraft facility or loan on concessional terms? Answer: no, unless this has signaling value, which is implausible.
(6) Is helicopter money more effective if a touch of ‘Gesell’ is added: the base money increase funds a ‘perishable’ transfer to households (say by taking the form of the transfer of an instrument with a negative interest rate or of a limited-duration voucher that expires after a short interval) that provides an incentive to spend the transfer rather than save it? Answer: only if these perishable transfers go to liquidity-constrained or debt-constrained households.

All these issues are now addressed in the revised version of the Helicopter Money paper, using the integrated analytical framework developed in the earlier versions of the paper.

Romar Correa - Comment to version 3
August 29, 2016 - 10:43

see attached file

Willem H. Buiter - Reply to Romar Correa
September 06, 2016 - 12:56

see attached file