Helicopters and the Neutrality of Money

Do not despise the lore that has come down from distant years; for oft it may chance that old wives keep in memory word of things that once were needful for the wise to know.

J.R.R. Tolkien, The Fellowship of the Ring
Money & Macro

Helicopters and the Neutrality of Money

An Essay in Loanable Fundamentalism


This paper is also available on SSRN as a PDF. The description and results of the agent-based model can be found there; the model itself can be downloaded below.

In 1969, Milton Friedman first used the famous “helicopter” metaphor for monetary policy. Granting that changes in the money stock are neutral with respect to relative prices in the long run, he argued, we can ignore relative price disturbances in the short-run too if we assume that new money balances are distributed directly to agents via helicopter. Bernanke (2002) gave Friedman’s simplifying assumption new life as a semi-tongue-in-cheek policy proposal for avoiding deflation at the zero lower bound. Since then, the idea has persisted on the inner fringes of macroeconomic discourse,1 especially in the aftermath of nearly a decade of sluggish post-recession growth worldwide.

Since that time, the truism that money is neutral in the long run but disturbing in the short run has been mostly papered over. Such effects may exist in principle, the conventional wisdom goes, but they are more or less quantitatively irrelevant, except perhaps in the case of a major inflation.

The conventional wisdom, of course, is conventional for a reason. There has been little evidence of cash-induced relative price distortions causing any major inefficiency in a reasonably well-managed monetary regime. However, this fact is no reason to be sanguine on the prospects of helicopter money. Indeed, real life “helicopter drops” are likely to be significantly distortive; up to this point, monetary expansions have been more or less neutral in practice precisely because they are not helicopter drops.

This feature of stable currencies has been relatively underappreciated in economic theory. Milton Friedman (1969), for example, famously argued for an optimal behavior of the money stock on the assumption that changes would be distributed directly to agents via helicopter. On the other hand, those who do appreciate the significance of the banking system in originating and distributing changes in the money stock tend to lament the fact (e.g. Hayek [1933] 2008, ch. 4).

In order to explore the relative merits of the two broad channels of monetary expansion, this paper sets up a stylized two-agent model in order to highlight the relevant feature of Friedman’s model that results in monetary neutrality: not the helicopter drop at all, but the representative agent construction. To relax this construction, we then formalize and implement an agent-based model with heterogeneity in the demand for cash balances, subject to random shocks either to cash demand or to the nominal money supply. To the extent that the distribution of demand for cash balances is not totally orthogonal to the distribution of demand for different types of goods, a helicopter drop will in fact be less neutral than traditional open-market operations, with newly created money flowing into the economy through the banking system.

I. Equilibrating Adjustments

The centrality of banking to stable currencies has been relatively underappreciated in economic theory. Indeed Friedman’s helicopter thought experiment exists for the explicit purpose of ignoring the banking system, a tendency followed by many subsequent monetarists. On the other hand, those who do appreciate the significance of the banking system in originating and distributing changes in the money stock tend to lament the fact (e.g. Hayek [1933] 2008, ch. 4; see also Burns & Harwick [2016] for a historical survey of opposition to bank money).

Changes in the money supply, whether stabilizing or not in practice, have – with few and mostly seigniorage-driven exceptions – always entered through or originated in the market of financial intermediaries.2 Very little monetary expansion across the world consists in the literal printing of money. It is not insignificant that the supplies of official currencies everywhere in the world are managed by central banks.

In order to evaluate the relative efficiency of the two mechanisms for adjustment, we will consider each in the case of an equilibrating, and a disequilibrating adjustment – respectively, an expansion in response to an exogenous cash demand shock, and an exogenous expansion beginning from equilibrium. In both cases, open market operations come out substantially more neutral than helicopter drops, albeit with a caveat in the latter case.

Imagine, then, a small country unexpectedly winning a war. As fighting winds down, taxation relents, and confidence revives, the demand to hold the central bank’s issues increases. In order to prevent downward pressure on prices (let us assume it successfully avoided inflationary finance during the war), the central bank must expand its issues. Supposing that the central bank is somehow able to calculate the exact magnitude of the quantity adjustment necessary to stabilize nominal spending, the question we will pose to the bank’s director is this: should he continue the traditional course of open market operations and inject the new money into the banking system, or would it be wiser to employ a squadron of newly idle helicopters to distribute the cash more “equitably”?

Helicopter Drop

Suppose the helicopter drop increases each agent’s money holdings in proportion to his existing holdings.3 By assumption, the increase in money supply is such in the aggregate as to exactly compensate for the increase in the demand for money. In the long run, therefore, no prices change. Our benchmark – monetary neutrality – is that no prices change in the short run either.4

For this to be true, it is necessary that the increase in the demand for cash balances that triggered the expansion be absolutely uniform across all people. Only in this case will spending habits – and thus the structure of prices – remain undisturbed.

In Friedman’s story, the helicopter drop is neutral precisely because his economy is a representative individual economy (p. 5). Everyone in his hypothetical economy has a uniform demand for cash balances expressed in terms of weeks of income. Once he drops this assumption (p. 6), he is forced to concede “initial distribution effects” which preclude instantaneous and price-neutral equilibration.

To illustrate the significance of these effects, imagine our economy is composed of one half hobbits and one half dwarves, each group holding equal wealth in the aggregate. We will provisionally assume that helicopters are necessary because there is no banking sector, so the demand for money consists entirely of the demand for cash balances, and we have a mint rather than a central bank. Hobbits, of course, are creatures of habit and essentially fixed in their spending habits, so following the defeat of Mordor, the revival of confidence causes only the dwarves to increase their demand for money.

In response to the change, the mint’s helicopters distribute half of the demanded increase to the dwarves themselves, and half to the hobbits. Because the dwarves constitute the entirety of the increased demand but only receive half the balances necessary to satisfy it, they continue trying to build up their money holdings, while the hobbits enjoy a windfall. In the short run, then, pickaxes continue to fall in price, and tobacco and raspberry jam rise in price.

These price changes are, of course, disequilibrium phenomena. As the new money works its way through the economy, the dwarves will eventually succeed in building up their money holdings, and the hobbits will eventually spend off their windfall. As each group’s spending returns to its previous pattern, the price of pickaxes must rise, and the price of tobacco and raspberry jam must fall. In the meantime, however, the jam industry has been able to bid away resources from the pickaxe industry, resources which must eventually be reincorporated at a cost into the production of pickaxes.

This illustrates our general principle: when the distribution of the monetary increase does not match the distribution of the change in demand for cash balances, some people whose demand has not increased will receive a windfall, while some whose demand has increased will remain unsatisfied. This holds whether the increase is distributed proportionally, as a lump sum, or in toto to some favored group. Whether or not the overall price index is disturbed, the initial changes must eventually reverse themselves. Even if the mint knows the precise quantity of the changes in cash balances, unless it also knows the pattern of those changes, it cannot avoid the misdirection of resources associated with money-induced relative price changes.5

Open Market Operations

Fortunately, there is generally no need for the central bank to know where the change in money demand originates. However, introducing a banking sector to our economy complicates the analysis somewhat, as the demand for money may be met by a number of assets varying in liquidity, and exchangeable one for another at a fixed price. Let us first of all limit our discussion to two generic types of money assets: base money and bank liabilities, the latter being issued on a fractional reserve basis, and (therefore) the former being more liquid. For concreteness and to match the current regime of fiat monies, I will refer to cash balances and deposit balances, respectively, with the qualification that this identity will be misleading for other monetary regimes.

In addition, we must distinguish between the transactions demand for money, for which cash and deposits are (by hypothesis) perfect substitutes, and liquidity demand, for which they are not substitutes. In a well-functioning banking regime, an increase in transactions demand is typically accommodated by an expansion in bank money (Selgin 1988, ch. 5). By this account, a lower gross volume of clearings allows the bank to safely expand loans and issues to the point of satisfying the new excess demand. If banks are not prevented from doing so, there is no need for central bank action at all, and no relative prices need be disturbed. We therefore leave aside the case of an increase in transactions demand.

An increase in the demand for liquidity, however, is a more difficult case. In our hypothetical banked economy, banks issue liabilities redeemable for cash on a fractional-reserve basis. An increase in the demand for cash balances will contract the banks’ balance sheets, making them less liquid and (assuming binding reserve requirements) forcing them to contract loans, effecting a contraction in deposit balances larger than the increased demand for cash balances – a problem variously referred to as multiple contraction or the perverse elasticity of credit.6

Liquidity runs are for this reason among the more disastrous events that can befall a modern financial system. If the run cannot be averted, the only market mechanism for returning to monetary equilibrium is a deflationary recession.

Most discussion of the problem, for this reason, has focused either on central bank responses to a liquidity run, or on prophylactic measures. So keeping (for now) the assumption that the central bank can respond with an injection of liquidity of the appropriate size, let us compare the central bank’s response to an increase in the demand for cash balances (and not deposits – i.e. an increase in liquidity demand) with its response in the helicopter scenario.

Suppose, then, that following a liquidity run the Bank of Gondor ignores the idle helicopters and instead expands the money supply the traditional way by buying assets from banks on the open market. Any long-run windfall accrues to the originator of the asset as seigniorage – to the government in the case of treasury bills, or to the bank in the case of bank liabilities – which is able to issue debt at a lower interest rate. The financial system has not necessarily received a windfall, but it has become more liquid – i.e. it is able to more readily exchange (illiquid) interest-bearing assets which its customers will not accept for non-interest-bearing assets (cash) which its customers will accept, without incurring “fire-sale” losses.

This “shoring up” obviates the necessity of contracting the bank’s issues: if the central bank is able to inject just enough liquidity into the banks to offset the increase in the demand for cash balances, no changes in the banks’ portfolios, in the pattern of consumer spending, and (therefore) in relative prices, need occur. Those whose demand has increased withdraw cash from their banks, and these banks in turn will bid more for liquidity from the central bank. The banks which would have been forced to restrict their lending by raising their interest rates now find it unnecessary to do so.7 The central bank, for its part, is relieved of the necessity of matching the pattern of the change in demand: that task is taken care of by the banks themselves.

Finally, it should be noted that the existence of a banking sector does not essentially change the story in the previous subsection if the central bank decides to use helicopters after all. If the dwarves initially register their demand for cash balances by withdrawing deposits from their banks, the banks will again be forced to contract their loan portfolios. In this case, the demand is simply transformed into a demand for liquidity on the part of the banks. The new money still constitutes a one-time redistribution, and must still find its way circuitously back to the banks, effecting price changes as it goes.

II. Disequilibrating Adjustments

Clearly it is a heroic assumption that the central bank can respond to a change in the demand for liquidity with an injection of the proper size and at the proper time. This assumption is a necessary (but not sufficient) macroeconomic condition of monetary neutrality in the face of such changes. It may be, however, that changes in the money stock beyond what is necessary to compensate for changes in money demand will be more harmful than those distributed by helicopter. This is what skeptics of monetary adjustment through financial markets seem to aver. Mises (1966, p. 556), for example, claims that “the gross market rate of interest is the more violently affected, the sooner the inflowing additional supply of money or fiduciary media reaches the loan market.”

Let us rehash the last analysis then, on the assumption that the demand for money has not changed. But facing pressure from mithril-mining unions, the Bank of Gondor nevertheless wishes to expand the money stock, with the same choice of instruments at its disposal.

The helicopter story, in this case, does not essentially change. An increase in proportion to existing cash holdings will not affect spending habits equally, and thus relative prices must be disarranged in the transition. The only difference is that, at the end of the process, the overall level of prices must be higher. This is the situation analyzed by Friedman (1969, sect. III) in his original use of the helicopter metaphor.

Likewise, banks can intermediate additional liquidity to those whose demand at the margin is highest. Thus we will still expect to see less purely monetary disarrangement of relative prices based on idiosyncratic spending habits. Prices must rise more uniformly when inflation is carried on through financial markets than by helicopter drop.8

However, in addition to the general increase in prices, the additional liquidity in the banking system can only be distributed at a lower interest rate – the “liquidity effect”. Thus, rather than a monetary disequilibrium, we have an intertemporal disequilibrium. Whatever may be thought of the specifics of the canonical Austrian Business Cycle story, monetary pressure on the interest rate can be expected to result in serious dislocations of investment resources, dislocations of a different character than those resulting from ordinary monetary disequilibrium.

Whether the monetary or the intertemporal disequilibrium is likely to be more severe will depend on how quickly equilibrating forces may be brought to bear. For a purely monetary disequilibrium, these forces are the diffusion of the additional funds throughout the economy and the re-establishment of an equilibrium structure of relative prices. For an intertemporal disequilibrium, these forces are disappointing returns on investment, which must occur after the investments have come to fruition.

For expansions of equal magnitude, it is impossible to say generally which of the two disequilibria will be resolved more quickly and with the least dislocation of resources. However, the particular errors of intertemporal disequilibrium are more systematic than the idiosyncratic relative price disarrangements resulting from monetary disequilibrium. Continued helicopter drops may induce further disarrangements, but they cannot prolong the existing pattern of distortions. Continued credit expansion, on the other hand, will entrench and prolong the particular disequilibrium investments, preventing their disappointment and thus their correction.

We may say, therefore, that the peculiar danger of monetary expansion through financial markets is political rather than economic. The systematic nature of the disequilibrium investments resulting from intertemporal disequilibrium makes it easier to marshall political support for continued expansion. On the other hand, the group which gained from the distortions resulting from a helicopter drop, even if it could be identified and organized, could not expect ex ante to gain from further drops.

The agent-based model instantiating the stylized economy described above is formalized in the PDF available on SSRN, and can be downloaded at the top of this page.

III. Discussion

The Costs of Fiscal Policy

To the extent that the helicopter drop represents a policy proposal rather than a simplifying assumption, it is usually used as a metaphor either for the monetization of fiscal policy or for the transfer of newly created base money directly to consumers. From the standpoint of this paper, both proposals are similar in the sense of increasing spending by giving some group – a subset of consumers, or the government – a windfall to be spent off, in a way that fails to match the pattern of money demand on the margin.

The idea has an intuitive appeal. If the problem is lax consumer spending, the banking system seems like an unnecessary interposition. Especially if banks are reluctant to lend, why not skip the middleman entirely and give the money directly to the people we’d like to spend it?

There exist a great number of arguments for and against fiscal stimulus and direct-to-consumer monetary stimulus, involving both political economy and welfare economics considerations. Economic inefficiency arising from relative price distortions are unlikely to be the decisive consideration in any particular helicopter drop proposal. However, as a heretofore underappreciated cost, it should discourage such programs at least on the margin, if not on the whole.


In addition to the use of so-called helicopters as an anti-deflationary tool, the comparison developed in this paper also has direct relevance to the recent development of crypto-currencies, which provide something like a small, open, and unbanked economy, in which money supply adjustments must be distributed by a fixed rule rather than through a banking system.9

To date, and despite a great deal of innovation around the problem, there are no circulating assets leveraged on top of a cryptocurrency base. There is thus no way to accommodate shifts in currency demand except by a change in the value of the currency – hence a tremendously volatile exchange rate. The daily change in the BTC/USD exchange rate has reached nearly 50% in both directions on multiple occasions – the EUR/USD rate, by contrast, never changed by more than 2% in a day. For this reason, exchange rate stability by management of the money supply has become something of a holy grail for crypto-currency protocol design.

Because the protocol constituting the currency is also the means of transaction, the velocity of money is available as a parameter to the protocol, and the money supply can respond to shifts in money demand automatically and with a precision unavailable to central banks. Our apparently unrealistic assumption in Section I that the total quantity of helicopter money necessary to compensate a fall in spending could be precisely determined could, therefore, in principle, be overcome programmatically by a well-designed cryptocurrency. Other creative solutions have also been offered to fix the exchange rate to (for example) the Dollar.

Without a banking system, a crypto-currency protocol must specify two monetary rules: 1) a rule by which the quantity of money is determined, and 2) a rule by which changes made necessary by the first rule are distributed. Both types have been discussed, though the macroeconomic effects of the latter have so far been much neglected; the case for one rule over another usually hinges on technical or fairness considerations. Possible distributive rules include the following, any of which can in principle be joined to a quantity rule that stabilizes the flow of nominal spending:

  1. Distributing new coins in toto to miners as a reward for verifying transactions. This is a natural extension of the Bitcoin protocol. Decreases in the money stock must in this case be borne elsewhere, so mandatory transaction fees which are then destroyed (as in Peercoin) have been proposed.
  2. A variant of this, based on the proof-of-stake paradigm, is to distribute coins in proportion to the product of coin balances and time on the network, again as a reward for verifying transactions.
  3. A protocol-level democratic mechanism by which users vote on the direction of new funds (Lee 2014).
  4. Finally, there is “rebasing”, in which nominal coin balances are scaled up and down automatically in order to stabilize the purchasing power in terms of some other currency or a basket of goods.

The last is closest to what we had in mind by helicopter drops, but the essential point does not change regardless of the distributive rule.

It follows from the foregoing analysis that none of these norms can in fact mitigate relative price distortions arising from changes in the monetary base, even assuming the necessary magnitude of that change can be perfectly calculated.10 Without a banking system, the automatic behavior of the money stock comes only at the expense of the automatic distribution of liquidity to those who demand it. To introduce elasticity to the supply of crypto-currency will not, in fact, reduce monetary disequilibrium, purchasing power volatility, or exchange rate volatility from the high levels thus far observed in Bitcoin and other cryptocurrencies.11

Implications for Monetary Regimes

The analysis of this paper also suggests sensible reforms for central banks. In the first place, while an increase in the demand for cash balances is equivalent to an increase in the demand for liquidity in the current monetary regime, this is not necessarily true across monetary regimes. While cash is the only base money readily usable for transactions by the public, deposits may be a poor substitute for cash in some cases for reasons other than the latter’s higher liquidity. There are, in addition, important physical characteristics such as anonymity and physical transferability.

Nevertheless, if more liquid monies are the only way to satisfy the demand for such characteristics, the total money supply will be subject to needless shocks.

A rise in [the demand for cash balances] is a routine occurrence which does not involve any loss of confidence in banks; it can in theory be satisfied by a circulating form of [bank liabilities]. In contrast, a rise in [base] money demand means a demand to exchange [bank liabilities] for [base] money, the ultimate money of redemption. In a closed system this implies either a loss of confidence in banks issuing [liabilities] or a failure of the banking system to provide enough [bank liabilities] for use as currency. (Selgin 1988, p. 108)12

With the only circulating currency serving as base money, as is the case in modern fiat money systems, an increase in the demand for cash balances triggers an even larger contraction in the stock of deposit balances. The ability for banks to issue circulating banknotes as liabilities leveraged on top of the base money, rather than just deposits, would make it a matter of indifference whether the public holds its money balances as deposits or currency. The central bank would be absolved of the responsibility of adjusting to changes in the composition of money balances, and be tasked only with adjusting to changes in the velocity of spending – a task which, though still perhaps herculean, carries with it far less room for catastrophic error.

At that point, it is true, the tradeoff becomes more rigid. Once shifts in the form of money demand do not initiate changes in the economy’s liquidity structure, once such changes are initiated only by shifts in demand for liquidity, strict automaticity of the money supply must be traded off against automaticity of the distribution of liquidity. But for now, our current system lies well within the institutional possibilities frontier.

IV. Conclusion

The significance of relative price distortions arising from monetary expansions has been mostly ignored since Friedman’s thought experiment in which the expansion was distributed directly to consumers via helicopter drop. What began as a move for analytical convenience was solidified due to lack of evidence that such distortions were quantitatively relevant, even if they necessarily existed in principle. Even if helicopter drops weren’t a good description of the mechanics of monetary expansion, relative price neutrality seemed to be a passable description of the effects.

This paper has subsumed that result into a wider framework in which monetary expansions are approximately neutral only to the extent that they are distributed through a banking system. The conventional wisdom, while correct in practice, is reversed in principle: significant allocative inefficiency does not in fact arise from expansion through the banking system, but is likely to do so in any expansion that bypasses the banking system.

Monetary expansion has typically been conducted through traditional open-market operations. Even recent unconventional expansion through quantitative easing has mainly centered on the banking system. For this reason, any allocative distortion arising from the spread of new money through the economy has been minimal. Should monetary policy turn in an even more unconventional direction, however, we should expect a great deal of nonneutrality in the future, for reasons well understood since the beginning of monetary economics.


  1. Among unconventional monetary policy proposals, it ranks perhaps less serious than forward guidance, but more serious than the trillion-dollar-coin.
  2. In fact, even under the classical gold standard, and despite the analytical predominance of the price-specie flow mechanism at the time, specie flow was relatively unimportant compared to, and largely obviated by, changes in the supply of bank money (Eichengreen 1995, p. 47).
  3. Other patterns of distribution – for example uniformly dividing the sum among agents regardless of their current balances – do not change the basic result. See below.
  4. The change in the demand for cash balances will itself have real effects, but they are for our purposes unimportant and would needlessly complicate the analysis. The reader is welcome to interpret “undisturbed price structure” henceforth as “adjustment to new data, unhampered by further monetary disturbances”.
  5. This echoes the discussion in Mises (1966, p. 412): “We may, if we like, assume that every member gets a share of the additional money right at the moment of its inflow into the system . . . The result will be that changes . . . never affect the prices of the various commodities and services to the same extent and at the same date.” He also considers countervailing changes like those we are considering now, that leave purchasing power unchanged but nevertheless disarrange prices, at least temporarily (his example is the productivity of gold mining increasing in lockstep with money demand). Later (p. 793) he discusses credit expansion. Unfortunately the explicit comparison of the two does not appear to have been made.
  6. In the real world this problem is even more severe, as there exist assets leveraged on top of bank deposits and other financial assets that will be forced to contract in the event of a liquidity run.
  7. The seigniorage may disarrange relative prices as it is spent off, but this quantity is small compared to the expansion effected (or the contraction avoided) in the broader money supply, so its effect should be relatively minor.
  8. It is worth distinguishing the potentially complementary Austrian and New Keynesian explanations for price stickiness. In the former, the signal to raise prices reaches some merchants sooner than others. In the latter, the signal reaches everyone at once, but some merchants still fail to respond with the appropriate price change. Without venturing a guess as to which is quantitatively more important, a banking system mitigates the Austrian fear, but not the New Keynesian fear. If the latter predominates, then there will be little advantage to overexpansion through a banking system as opposed to helicopters.
  9. This section draws on and expands the argument in Harwick (2016).
  10. It will be not do to apportion the changes among finer classes according to their pattern of spending, either. The protocol must know ex ante how many groups to divide the users into, and must have a rule placing each user in a definite group. Under free and anonymous registration, it is difficult to imagine the ecosystem avoiding collapse under the weight of rent-seeking for new funds. In fact, if rational expectations means agents have the “true” model of the economy in mind when forming expectations, an open-source codebase will imply strongly rational expectations, which in turn implies that such a protocol could never get off the ground in the first place.
  11. One caveat on the application to cryptocurrency bears mention. The relative price and capital allocation effects will not be immediately evident in a currency that does not serve as a unit of account. Most Bitcoin transactions, for example, are priced in Dollars and converted to Bitcoin at the point of sale. Because prices are perfectly flexible, monetary disequilibrium comes through fully and immediately in the exchange rate. In addition, because relative prices are pinned down by a far larger volume of Dollar-denominated activity, no mispricing or capital misallocation need occur. In other words, cryptocurrencies can avoid the most severe consequences of monetary disequilibrium only so long as they remain niche currencies. As soon as they begin to take on unit of account functions, the stakes of monetary disequilibrium become much higher, and real economic distortions must result.
  12. I have replaced some equivalent terms for the sake of terminological consistency with the rest of this paper.


Agent-Based Model, Banking, Bitcoin, Money, F.A. Hayek, George Selgin, Ludwig Von Mises, Milton Friedman


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Hi, I'm C. Harwick, an economics PhD candidate in Virginia with an interest in monetary theory, institutional evolution, and folk music.

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