The money multiplier

The practice of creating new bank deposits from thin air has large economic effects. It is important to recognize that from a practical standpoint, deposit money in demand deposits at banks is part of the money supply. It matters not if money circulates in the form of banknotes and coins or is deposited in demand deposits – demand deposits are a perfect money substitute, which is to say, they are money. We have previously commented on measures of the money supply and provided links to the various methodologies attempting to measure it in ‘Monetary conditions in the US‘, but for this article it is enough to state, money is the medium of exchange, and every form of money or money substitute that performs this function from the viewpoint of the individual actors in the economy is ipso facto money.

  moneymultyImage via Pennsylvania Lottery


We want to first look now at the extent to which fractional reserve banking can increase the supply of money from thin air. A simple assumption we can use as our starting point (it makes the calculation easier) is that banks, after observing the behavior of depositors for a while, decide that a 10% reserve is sufficient to cover all withdrawal demands in the ‘normal course of business’ (this is to say, the course of business prior to the advent of the economic crisis that the credit expansion will inevitably create).

It is important here to consider that when banks extend loans backed by a fraction of an original deposit they have received for safe-keeping, they create a new deposit. This new deposit money then will be spent by the borrower, and thereafter becomes a deposit liability either at the same bank that extended the loan, or some other bank where the recipient of the spent money has a demand deposit account (some of the deposit money may also remain unused, and thus remain at the bank). This new deposit can then once again be used to create an additional deposit, once again keeping only the 10% fraction in reserve.

This process naturally can be continued ad infinitum. If there were only one, monopolistic bank in existence, it would have an easy time of engaging in this practice, since it could rest assured that all newly created deposit money will be redeposited with it. However, the mathematical end result of fractionally reserved deposit creation is essentially the same, whether a single monopolistic bank or a system of several banks is involved (for details on this see the previously referenced ‘Money, Bank Credit and Economic Cycles’, J.H. De Soto, chapter 4, ‘The credit expansion process’). Consider now a deposit of 100,000 units of money (let us say, ‘dollars’) in a small bank, that is used to expand credit at a 10% reserve ratio. If the entire newly created money leaves the bank, it will be able to add fiduciary media of 90,000 dollars (90% of 100,000). If only 20% of these 90,000 dollars remain with the bank, it can expand deposits by 109,756 dollars (or 22% more).

This can be shown mathematically as follows:

If the reserve ratio is R, the originally deposited money D, and the remainder of newly created deposits remaining with the bank is K, then in the case of K=0, the credit expansion X would simply be given by the formula X=D (1-R). In the case of K=0,2 (i.e. 20% of the new deposit money remains with the bank), the formula for credit expansion would be: X=D(1-R)/1-K(1-R). The reserve ratio and the percentage of newly created deposit money remaining with the bank influence the bank’s credit expansion possibilities greatly – the smaller R and the bigger K, the more new credit money can be brought into existence. In the case of a monopolistic bank with K=1 (this is to say, all newly created deposit money remains with the bank or is redeposited with it), which lends out 90% of every newly created deposit (starting with the original deposit of 100,000 dollars and using a reserve ratio R of 10%), reiterating the process begun with the initial deposit again and again, a sequence of the form


D+D(1-R)+D(1-R)+D(1-R)+D(1-R)+D(1-R)…= 100,000(1+0.9+0.9+0,9+0,9+0,9…)


describes the total of the bank’s deposits that will result from the process. In short form we get


D/1-(1-R), or 100,000/1-0,9=100,000/0,1=1,000,000.


This means that in fact an original deposit of $100,000 has resulted in the creation of $900,000 in additional deposit liabilities , i.e. the amount of fiduciary media issued by the bank is exactly 9 times of the original deposit. Putting it differently, the total amount of money has increased ten-fold. It turns out that the same result is obtained in a system of banks with K= any number < 1, or a system of banks where K=0.

The formulas for the calculation change slightly, but the end result remains a ten-fold expansion of deposit money from the original deposit if the reserve ratio R is 10%. In the real world, banks tend to expand credit simultaneously, so that any reduction in cash at an individual bank from money that is flowing out, will soon be covered by the money flowing in due to the other banks engaging in the same credit expansion process.

This theoretical expansion of credit and fiduciary media is obviously highly dependent on the reserve ratio, but also on the amount of money in circulation. To the extent that deposit money is removed from the banking system in the form of bank notes circulating outside of the banks, their credit expansion will be curtailed. This curtailment effect is very large, which explains why Sweden’s banks are such eager supporters of the bureaucratic drive to eliminate cash, which we talked about in our articles on the discussion regarding a cash ban for a variety of spurious reasons in Sweden.

To demonstrate the size of this effect, if only 15% of the newly created deposit money is withdrawn in the form of currency, the putative size of the credit expansion with a 10% reserve ratio and an initial $100,000 deposit would decline from $900,000 to $261,702 (rounded). Money that leaves the banks in the form of currency therefore has an effect that is similar to increasing the reserve requirement, or a voluntary increase of bank cash reserves.


The failure of the centrally planned monetary system

A large increase in bank cash reserves can in fact be observed as a result of the 2008 crisis that would have absent a central bank and state-guarantees of ‘toxic’ bank assets led to the obliteration of a large number of the de facto insolvent fractionally reserved banks (see the chart below). This explains why the Federal Reserve is so eager to expand the money supply by cutting the administered overnight interest rate to zero and engaging in practices such as ‘quantitative easing’, i.e. the monetization of both government and mortgage debt securities. If not for these measures, the biggest deflationary contraction of the money supply since the Great Depression would have undoubtedly occurred by now.

As it is, the Fed’s modus operandi of pumping money into the commercial banking system which then hoards these excess reserves by depositing them back at the central bank, does little to stimulate inflationary bank credit, at least not yet.


Excess Reserves held by commercial banks at the Fed – previously, during the boom and incessant credit expansion, these were held as close to zero as possible. Now the banks have become careful and are keeping these reserves at hand as their assets deteriorate in value and they are concerned about the concomitant decline in their capital ratios. The Federal Reserve also has begun to pay interest on bank reserves held with it , which gives banks an extra incentive to park such large amounts of reserves with the Fed. You could call the above chart ‘the echo of a deflationary crash’. At the same time, it represents the ‘seeds of the next inflationary credit expansion’ – click to enlarge.


It needs to be noted here that the formulas above merely serve to illustrate how much credit expansion is possible, given a certain amount of original deposits and a certain reserve ratio.

Looking back at the acceleration of the credit boom from the mid 90’s onward, we know that the introduction of sweeps (see: ‘Inflationary Deception’ by Charles T. Hatch, pdf) dramatically reduced effective reserve requirements and gave the creation of additional fiduciary media a shot in the arm it certainly didn’t need. This is also why there was an enormous amount of monetary inflation while bank reserves held at the Fed effectively stagnated.

The financial system became ever more creative in keeping the credit boom going. After the Federal Reserve and the ECB dropped their administered interest rate to an artificially low level during the 2001-2002 recession, keeping them low for a prolonged period of time, the banks began to explore ever more avenues for profiting from the spread between short and long term interest rates. Securitization of loans made it possible to extend more and more credit to an increasingly less creditworthy pool of borrowers.

Special purpose vehicles were set up that financed themselves in the commercial paper markets and in turn held CDO’s containing mortgage-backed securities. Such securities in SPVs were held off bank balance sheets so as to not have a detrimental effect on the regulatory capital ratios of the banks sponsoring them. However, in order to make it possible for these SPVs to attract funding in the CP market, the banks furnished ‘liquidity guarantees’ to the vehicles, thereby increasing their risk profile to the same extent that would have pertained had the securities held by the SPVs remained on the bank’s balance sheet in the first place.

If we look at the behavior of money TMS over the long boom, we see that every short term crisis was met with an even bigger expansion of credit.


The growth of the true money supply during the great boom – as can be seen, the inevitable crises of the fractionally reserved banking system have been met with ever greater expansions of money and credit. Note especially the expansion of money following the 1990-1991 and 2001-2002 recessions and the most recent bust beginning in 2008 – click to enlarge.


Ludwig von Mises‘ assertion that


“The boom can last only as long as the credit expansion progresses at an ever-accelerated pace. The boom comes to an end as soon as additional quantities of fiduciary media are no longer thrown upon the loan market.”


(Human Action, p.552, ch. XX, 5 , ‘The Effects of Changes in the Money Relation’) has been confirmed by what has actually happened. The credit expansion indeed accelerated ever more, with every short term bust met with additional credit creation, thus creating a giant boom that went through several stages as the newly created money percolated through the economy. It came to an end once short term interest rates rose back to the level they had been at prior to the credit expansion, with the yield curve inverting and making the ‘borrow short, lend long’ trade unprofitable.

Mises further states (ibid.):


“But it [the boom] could not last forever even if inflation and credit expansion were to go on endlessly. It would then encounter the barriers which prevent the boundless expansion of circulation credit. It would lead to the crack-up boom and the breakdown of the whole monetary system.”


Ludwig von Mises: “The wavelike movement affecting the economic system, the recurrence of periods of boom which are followed by periods of depression, is the unavoidable outcome of the attempts, repeated again and again, to lower the gross market rate of interest by means of credit expansion. There is no means of avoiding the final collapse of a boom brought about by credit expansion. The alternative is only whether the crisis should come sooner as the result of a voluntary abandonment of further credit expansion, or later as a final and total catastrophe of the currency system involved.” (Human Action, p. 570).

(Photo credit: Wikimedia Commons)


The latter quote explains the ‘counter-cyclical policy’ behavior of the central bank, which attempts to counter-act budding ‘inflation expectations’, this is to say a realization by the public that the inflationary policy is permanent. Were the public to realize that the purchasing power of the money unit is condemned to fall ever more swiftly, it would lower its demand for money and flee into hard assets, trying to get rid of cash balances as quickly as possible.

Modern ‘independent’ central banks are supposed to counter-act this tendency of a credit expansion to turn into a crack-up boom and total collapse of the monetary system by ‘tapping the brakes’ at opportune moments, this is to say, before the public becomes worried enough about the declining purchasing power of money that it begins to reject the money the central bank issues.

The frog is to be boiled slowly in other words – in this endeavor, the central bank directed fiat money system has been quite successful in e.g. the US, where the US dollar has lost roughly 97% of its purchasing power since the third central bank was established in 1913, with a complete repudiation of the currency not having occurred as of yet.

This decline in the dollar’s purchasing power is by the way an indication of the size of the excess profits that the fractionally reserved banking system and the ‘invisible tax’ the State have diverted to themselves in the course of the central bank’s operations.

Given that the financial crisis of 2008 and the subsequent economic contraction have been recognized as the biggest bust of the entire post WW2 period, which is to say the biggest bust since the Great Depression, it has become evident that the central bank – directed centrally planned financial system has in fact failed. Note that central banks were ostensibly established in order to prevent economic cycles, by guaranteeing the liquidity of the fractionally reserved banks during crises and by steering the volume of money issuance in a ‘scientific manner’ according to the precepts of the ‘price stability policy’.

When the crisis of 2008 broke out, supporters of statist doctrines were quick to denounce the crisis as a ‘market failure’ and a ‘failure of deregulation and liberalization of economic activity’, a view which we have already criticized in ‘A Failure of Capitalism?‘ and ‘Greenspan is shocked‘.

It should be self-evident that given the fact that we have a central bank and a highly regulated, centrally planned financial system that has been erected under the pretense that it would be able to avert economic downturns and keep the boom going forever, that the system has failed by its own standards.

The notion that the centrally planned money system would be able to deliver this mythical ‘eternal boom’ was indeed a widespread belief, as evidenced by the late Rudi Dornbusch , a Monetarist (i.e., Keynesian-in-drag) economics professor at the MIT, naively asserting in 1998: ‘We won’t have a recession because the Fed doesn’t want one’). Here are a few of Dornbusch’s pertinent quotes from his 1998 essay ‘US recession? No , thank you’:


“Not to worry, this expansion will run forever; the US economy will not see a recession for years to come. We don’t want one, we don’t need one and therefore we won’t have one. The reason is never mind how the expansion is threatened, we have the tools to keep it going.”

[….] “None of the postwar expansions died of natural causes, they were all be murdered by the Fed.”

[….] “The situation today, deep into the second longest expansion, is quite different in two respects: First, there is no inflation and hence natural causes of death rather than the Fed will have to bring the economy to a stand still. Second, the government’s coffers are overflowing with budget surpluses. Thus, monetary and fiscal are there to keep the party going in a way we have not seen for ages. Our current policy team believes in their potency and they won’t hesitate to bring them into the battle for continued expansion.”


The late MIT economics professor Rudiger Dornbusch: believer in the eternal boom, just as long as the central bank doesn’t ‘murder it’.

(Photo credit: MIT)


This corresponds to the erroneous Keynesian belief that artificial credit booms can be sustained in perpetuity by an interventionist state, and the equally wrong belief that one of the effects of inflation – the decline in the money unit’s purchasing power – is the correct definition of inflation. However, inflation is the increase in the supply of fiduciary media, and its most pernicious effect is not necessarily only the loss of the money unit’s purchasing power more generally, but the distortion it imparts to relative prices along the economy’s production structure.

Furthermore, during economic cycles such as those observed in the 1920’s and 1990’s, when strong productivity growth would normally lead to sharp declines in the general price level, the debilitating effect of inflationary policy on the money unit’s purchasing power is simply masked – the policy of ‘price stability’ is in reality a policy of massive inflation during such time periods. In any case, the system has evidently failed to avert the collapse of the boom – just as the Austrians – alone among all economic schools of thought – predicted would eventually happen.

The question then becomes, why were Austrian economists able to predict this failure while the large bulk of mainstream economists failed to do so?


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One Response to “The Problem of Fractional Reserve Banking, Part 2”

  • Andrew Judd:

    Mises was working at a time of a gold standard so some of his comments about certain collapse seem wrong to me today in an era where prices over time are controllable by the state by having interest rates on average too low with the resulting accompanying debt monetization.

    As far as I can see the misean view is that there should be no state intervention? With our current system if there was no state intervention prices would surely roll backwards to even perhaps medieval times in the biggest deflationary collapse of all time and most of our lives would be totally ruined where only a few elite survived?

    So fundamentally you guys seem to be working with a gold standard model when today there is no gold standard? But you might also be saying gold is the real money?

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