The fiat money quantity FMQ

Sep 27, 2013·Alasdair Macleod

This paper seeks to establish a measure of currency quantity that helps economists identify and estimate the risk that confidence in fiat currencies might be significantly eroded or even vanish altogether. It is this phenomenon that was referred to in the great European currency inflations of the 1920s as Katastrophenhausse, or a crack-up boom, when ordinary people lose all confidence in a fiat currency, disposing of it as rapidly as possible instead preferring ownership of goods.

This is essentially a modern phenomenon, with all except one fiat currency collapse recorded occurring since the First World War[1]. The Austrian economist Ludwig von Mises experienced this at first hand, initially in his native Austria and then in Germany. It is clear from both aprioristic economic theory and contemporary accounts that loss of confidence in a fiat currency involves both an abandonment of all rights of conversion into gold and a significant expansion in the quantity of the unbacked currency. While Von Mises explained the phenomenon giving us a theoretical understanding of it, few economists seem to be aware that we face these dangers on a global scale today.

The first condition, the abandonment of gold convertibility has been entirely satisfied with no fiat currencies offering gold conversion. The second condition is in progress led by the US dollar, which is the international currency standard to which all others refer. It is the risk from the US dollar’s rapid quantitative expansion we shall attempt to assess by constructing a new monetary measure for the purpose, referred to herein as the fiat money quantity, or the FMQ, for the US dollar.


Most central banks record several versions of the quantity of money issued, ranging from cash or near-cash usually termed M0 or M1, to broader measures that include bank-generated credit, variously termed M2, M3 or even M4. Monetarists, who try to link changes in the quantity of money to changes in the general level of prices are unable to agree which measure is appropriate for the management of monetary policy, sometimes selecting one then another on empirical grounds or even whimsy.

Monitoring and managing money supply in a fiat currency system as a means of achieving a price-inflation outcome is a forlorn hope. Under a gold standard, where paper money acted as freely exchangeable money-substitutes there was an approximate relationship between changes in the quantity of money and prices, albeit temporally deferred as changes in the gold or gold-substitute quantity took time to be fully absorbed into economic activity. This truth is still assumed by many to hold true for fiat currencies. However, in a fiat currency regime there is an overriding confidence factor not present under a gold standard, due to the absence of any underlying intrinsic value in government-issued currency. This means that the purchasing-power of a fiat currency can alter independently from conventionally understood supply and demand factors simply due to changes in the level of confidence vested in the government, the national banking system and the currency itself. While the relationship between the quantity of money and prices was approximate under a gold standard, this cannot be said to be true for modern currencies. If this was not the case, substantial and rapid changes in currency purchasing power, such as the dramatic collapse of the Icelandic krona on 8 October 2008 could not occur.

Once this point is grasped, we can dismiss central banks’ attempts to fine-tune monetary policy for a desired price-inflation outcome and offer a realistic purpose for money supply statistics in the context of today’s fiat currency regime. Instead of looking for some relationship between the quantity of money and prices, it must be to form a conceptual idea of the dollar’s potential instability compared with sound money, i.e. gold. We can therefore aim to ascertain at what point monetary policy is getting out of control, leading in turn to an escalating risk of a collapse of its purchasing power.

The sound money standpoint

The comparison with gold dictates the approach we should take. Before the existence of central banks, a bank was required to hold enough gold to meet withdrawals in gold coin (we shall ignore silver for the purpose of this paper). Withdrawals could either occur through the redemption of the bank’s own banknotes by members of the public or through cheques drawn upon it and presented through the banking system.  Therefore, each bank maintained a stock of physical gold whose size relative to deposits depended on an individual bank’s decision on the quantity of deposit liabilities not covered by gold coin, a practice which has come to be known as fractional reserve banking. This decision was based on a bank’s estimate of its customers’ gold requirements, and likely settlement demands from other banks. As central banks became established and acquired a note-issuing monopoly, the gold originally deposited by the public in local banks was transferred to the central banks. Central banks, backed by governments and protective legislation, were able to expand the quantity of bank notes even further while progressively restricting conversion rights, until all rights of conversion into gold were finally abandoned by President Nixon in August 1971.

Therefore unwinding the historic move from full gold convertibility to today’s fiat currency system forms the basis of comparison between sound money and government fiat currency, specifically all cash, coin and deposits. It is in accordance with John Exter’s[2] inverted pyramid, which described how paper liabilities were built up on a small base of gold; but FMQ is more specific focusing on deposit money and cash.

Identifying deposit money as the basis for comparison with sound money accords with a depositor’s point of view. He regards a bank deposit as his own property, even though fractional reserve banking denies him this belief. A banking system aligned with complete monetary stability, that is when the ratio of gold to gold substitutes is one-for-one, would treat deposits as money held in custody for customers against which cheque and settlement facilities may be provided. The investment of savings where ownership of money is clearly transferred from the saver to another party must not be confused with the deposit function.[3]

Austrian or True Money Supply (TMS)

Much of the work to accurately count the currency quantity has been done for us through the compilation of the True Money Supply by adherents of the Austrian school of economics. The theoretical approach behind TMS is an attempt to construct a useful monetary statistic. Essentially TMS seeks to extract from the various monetary statistics cash and instant-access bank balances, including savings deposits that may not be theoretically instantly accessible, but in practice can be regarded as available[4].

This was the basis behind the calculation of TMS, originally put forward by Professors Rothbard and Salerno[5]. Salerno concluded that the following statistics should be extracted from the US banking system to construct US dollar TMS:

  • Currency component of M1,
  • Total Checkable Deposits,
  • Savings Deposits,
  • U.S. Government Demand Deposits and Note Balances,
  • Demand Deposits Due to Foreign Commercial Banks, and
  • Demand Deposits Due to Foreign Official Institutions.

Professor Salerno’s paper was published in 1987, and Professor Frank Shostak wrote a follow-up paper in 2000[6]. Our task is similar but different. Salerno and Rothbard sought to “provide a statistical measure of money that is consistent with the theoretical definition of money as the general medium of exchange in society”. We are now trying to define with FMQ a fiat currency quantity that assumes the unwinding of the history of its evolution from its original role as a freely convertible money-substitute for gold.

Reserves held at the Fed

The question arises as to whether required and excess reserves, shown as deposit liabilities in favour of Depository Financial Institutions (defined as commercial banks, savings banks, savings and loans institutions and credit unions) on the Fed’s balance sheet, should be included in the FMQ. Required reserves are set by the Fed and can be varied by it; excess reserves are the excess over required reserves.

In normal times excess reserves are kept at a minimum, because the Fed does not monetise large amounts of assets through purchases leading to the creation of these reserves, and banks have been keen to maximise their profitability by expanding their balance sheets, moving excess reserves onto their own balance sheets and to the required reserve category. These historical norms changed in the wake of the 2008 banking crisis, because the Fed rapidly expanded its balance sheet by monetising assets and banks were also reluctant to lend, wishing to appear more liquid. Furthermore the Fed started paying interest at 0.25% on excess reserves to control their monetisation by the banks.

The dramatic expansion of excess reserves is shown in Chart 1. They increased a thousand-fold from $1.9bn in August 2008 to $1,969bn in June 2013.

Excess reserves held 

Required reserves are shown in Chart 2.

Reserves balances required 

Required reserves are comprised of vault cash (currency on hand) or balances at the Fed, and were originally intended to be highly liquid and available to meet customer withdrawals – the role fulfilled by gold before it was demonetised. To avoid double-counting, vault cash, which is already reflected in M1 cash as a component of TMS, must be subtracted from required reserves to arrive at FMQ.

A further reason not to distinguish between required and excess reserves is the split between them is a matter of policy judgement by the Fed; otherwise there is no monetary difference between the two.

It is not entirely clear why reserves held at the Fed, should not have been included in TMS, beyond the convention of drawing a line between deposits held within depository institutions and those held at the central bank. It is however normal for an individual bank to draw freely on its excess reserves to increase its lending or to balance its own books, or even to reorganise its balance sheet funding so as to minimise deposited required reserves.

In normal times bank reserves have expanded and contracted as the counterpart of the Fed’s control of interest rates through money market operations. After the banking crisis the Fed’s assets expanded rapidly as a result of quantitative easing, whereby the Fed bought assets from both the banks and also newly-issued government stock from the primary dealers. The Fed’s liabilities in the form of bank reserve deposits expanded accordingly, and it is presumably intended by reversing this process that these reserves will be eventually reduced.

Therefore excess reserves at the Fed are a counterpart to asset purchases. Typically the Fed buys Treasuries from the primary dealers, crediting the primary dealers’ banks’ deposits at the Fed, increasing total reserves. The primary dealers are simultaneously credited with matching deposits by their banks. Some Fed-watchers argue that reserves at the Fed cannot be part of the money supply, because asset purchases through primary dealers result in matching deposits at their banks, and would be double-counted if included in TMS.

This argument ignores the ability of a primary dealer to draw down his deposit from his bank, independently from the bank’s deposit at the Fed. His bank might respond by funding the loss of the primary dealer’s deposit either by finding other depositors, through interbank funding, drawing down its excess reserves at the Fed, or by reducing its own assets. If someone has a deposit he regards it as his property, and this is also true of a bank with a deposit at the central bank, irrespective of how it was created. The underlying point is that it is a mistake to establish an explicit connection between a deposit at the Fed with a particular deposit in the banking system, and to claim the deposit is being counted twice.

Our task in constructing FMQ is to replicate the theoretical reversal of the process of replacing physical gold initially with money-substitutes, and then unbacked currency after the Nixon Shock when all convertibility was finally suspended. It is clear that deposits at the Fed shown as bank reserves are the property of the depository financial institutions concerned, and must be considered as part of that reversal process.

Reverse repurchase agreements (reverse repos)

Having made the case for reserves held at the central bank to be included in FMQ, we must now consider reverse repos. From the St Louis Fed’s FRED website, so far as the central bank is concerned these are defined as follows:

“Reverse repurchase agreements are transactions in which securities are sold to primary dealers or foreign central banks under an agreement to buy them back from the same party on a specified date at the same price plus interest. Reverse repurchase agreements absorb reserve balances from the banking system for the length of the agreement. They are typically collateralized using Treasury bills. As with repurchase agreements, the naming convention used here reflects the transaction from the dealers' perspective; the Federal Reserve receives cash in a reverse repurchase agreement and provides collateral to the dealers.”[7]

The relevance to FMQ is that reverse repos are a means of temporary replacement of bank deposits (reserves) at the Fed. All reverse repos are closed at the end of a defined period, at which point they are replaced with reserves. Importantly, by increasing the quantity of reverse repos the Fed can reduce excess reserves, giving the appearance of a reduction in them. Therefore, on both these grounds they should be considered to be part of FMQ.

Putting it all together

We can now calculate our measure of fiat currency, the FMQ, which is the sum of TMS and total reserves less vault cash plus reverse repos. The cumulative growth of the major FMQ components is shown in Chart 3. (US Government Demand Deposits, Demand Deposits due to Foreign Commercial Banks, Demand Deposits Due to Foreign Institutions, required reserves less vault cash and reverse repos are all currently too small to register on the chart – all data from St Louis Fed).

Major FMQ components 

Reserves less vault cash in particular have in recent years added dramatically to the FMQ making an accelerating rate of deposit inflation significantly worse. We can now measure its progress against an established exponential growth rate as shown in Chart 4.

Fiat money 

The pecked line is the exponential compound growth rate for the FMQ; in other words its long-term average percentage rate of increase.

Significant deviations from this rate of increase can be expected to have material consequences. The dot-com bubble ran out of monetary fuel, followed by the expansionary monetary policies of 2003-2005. Before the banking crisis in 2008 the FMQ again lagged the long-term exponential rate, suggesting that the asset inflation noticeable at the time in off-balance sheet securitisations had insufficient monetary fuel to continue. This was realised by the banking crisis which provoked the Fed’s exceptional monetary response. Since then the FMQ has increased at a significantly faster rate, signalling a developing hyperinflation of dollar deposits. The consequences of this exceptional monetary expansion are also likely to be proportionately significant.

One test as to whether or not the growth in the currency quantity can be brought under control by policies designed to revert the rate of expansion back to the exponential mean is to assess what monetary policies are required. In August 2013 it would require measures to reduce the gap in Chart 4 by withdrawing currency and bank credit so that deposits would contract by about $3.7 trillion, 31% of FMQ, of which $2.1 trillion is required and excess reserves, less vault cash. Alternatively FMQ would have to remain unchanged for over five years to allow the original exponential trend to catch up.


In the FMQ we have constructed a measurement of currency-quantity that gives a better understanding of the risks to which a currency may be exposed from loss of confidence. In the case of the US dollar, this risk increased significantly at after the banking crisis in 2008 and has continued to escalate since.

Importantly the acceleration of the rate of growth of FMQ is now too great to return to its exponential trend without economic consequences considerably more serious than those that followed the collapse of both the dot-com bubble, and the asset securitisation bubble six years later. And given the lack of intrinsic value as discussed above, there is an increasing danger that underlying confidence in the US dollar’s purchasing power and its suitability as a medium of exchange for goods and services will be tested.

There is therefore also a risk of a global fiat money collapse, due the US dollar’s role as the leading international settlement medium. Nearly all other countries manage their currency rates vis-à-vis the dollar, and there is at the same time a similar and unprecedented monetary expansion in both the Japanese yen and British pound. Therefore a loss of confidence in the US dollar would be unlikely to be an isolated event.

The dangers emanating from monetary policy since the banking crisis are not readily recognised nor fully understood by economists and observers who rely on conventional measures of fiat currency quantities. The FMQ clearly identifies this risk.

[1] 56 episodes of currency hyperinflation have been identified, the first being the French mandat in 1795-6, according to criteria set by Professors Hanke and Krus. See Hanke & Krus, Cato Working Paper August 15 2012.

[2] Exter was an eminent central banker and economist. See .

[3] For more on the subject of natural law and banking practice see de Soto, Money, Bank Credit and Economic Cycles.

[4] It is common practice for US banks to allow customers to immediately draw down term savings with no more than an interest rate penalty. According to G L Harrison, Governor of the New York Fed who testified in 1931, any attempt to enforce the official 30-day notice for redemption would probably cause the appropriate authority to close the bank immediately (quoted in Mystery of Banking by Murray Rothbard, pp241).

[5] See (accessed September 2013)

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