Journal Article

No. 2014-28 | August 21, 2014
The Simple Analytics of Helicopter Money: Why It Works — Always PDF Icon


The paper offers 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 money which respects the intertemporal budget constraints of the Central Bank, the Treasury and the consolidated State. One example is a temporary fiscal stimulus funded permanently through an increase in the stock of base money. Another one is permanent QE – an irreversible, monetized open market purchase by the Central Bank of Treasury debt or private debt, when it is recognised that this permanent up-front open market purchase will have to be followed sooner or later by public spending increases or tax cuts, to ensure that the intertemporal budget constraints of the Central Bank and the Treasury remain satisfied. Three conditions must be satisfied for a helicopter money drop always to boost aggregate demand. First, 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: central banking, and specifically Central Bank balance sheet expansion, is profitable. Second, fiat base money is irredeemable – viewed as an asset by the holder but not as a liability by the issuer. Third, the price of money is positive. Given these three conditions, there always exists – even in a permanent liquidity trap – a combined (set of) monetary and fiscal policy action(s) that boosts private demand (or public demand) – in principle without limit. Under these conditions, a helicopter money drop will not cause ‘policy insolvency’: the Central Bank does not lose control of the size of its balance sheet or of the inflation rate. Deflation, ‘lowflation’ and secular stagnation are therefore policy choices.

JEL Classification

E2 E4 E5 E6 H6



Willem H. Buiter (2015). The Simple Analytics of Helicopter Money: Why It Works — Always. Economics: The Open-Access, Open-Assessment E-Journal, 8 (2014-28): 1—38.


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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.