The riddle of money, finally solved

Schools, like people, are subject to hardening of the arteries. Students learn the embalmed truth from their teachers and sacred textbooks, and the imperfections in the orthodox doctrines are ignored as unimportant.
— From 'Economics' by Paul A. Samuelson & William Nordhaus


For nearly a century the progress of macroeconomics has been stalled by a single error, an error so silly that generations to come will scarcely believe that it could have persisted for as long as it has done. It is an error that has been committed by John Maynard Keynes and Milton Friedman, John Hicks and James Tobin, Franco Modigliani and Ludwig von Mises, Murray Rothbard and Paul Krugman, and continues to be taught to every economics undergraduate today.

The error has blinded economists so that, like the seven men of Hindostan, they have mistaken the partial reality that has come within their groping grasp for the whole of reality. And this in turn has divided them into warring sects, looking very little like practitioners of a science and a lot like religious fundamentalists. Keynesian has poked fun at monetarist. Monetarist has ridiculed Keynesian. And both have mocked Austrian and been mocked in return.

Thanks to the error Keynesians have been unable to appreciate the importance of money, monetarists have arrived at a wholly misconceived notion of money, and Austrian economists, although they have occasionally stumbled towards the truth, have fallen far short of it. Worst of all, central banks have been forced to direct monetary policy without a measure of money to guide them, a situation one would have thought hilarious if it had not had such terrible consequences. Were an energy authority to attempt to control energy without having some way to measure energy, it would have been laughed out of town. But modern economists seem perfectly comfortable with the idea of a monetary policy without money.


The error we are talking about is the error of regarding money as cash balances, and the demand for money as the demand for cash balances. The idea dates back to the early part of the 20th century in Cambridge, UK, and has appeared so obvious it has held unquestioning sway over all schools of economics.

To view it in practice let us look at how Friedman, for example, used it. For Friedman money was an asset, one of many alternative assets, such as stocks, bonds, durable consumer goods, or even human capital. To determine the demand for money one had to compare it with the demand for those alternative assets. If Paul wishes to hold more stocks and bonds it follows that his demand for money and therefore his cash balances will come down. Put another way, when the expected return on stocks and bonds goes up compared with the return on money, the demand for money falls. Given such a view of money it must not have seemed unusual to Friedman when his and Anna Schwartz's calculations showed that just before the 1929 crash, when stock prices were soaring, money supply growth was not unusually high. To the rest of us it seems just a bit odd. After all, money is needed to buy stocks and when stock prices are growing at a manic rate one would expect to need a hugely greater amount of money than before. Be that as it may the theory indicated otherwise, so Friedman and Schwartz were not only not surprised when their calculations showed that money supply growth was not high, it must have seemed a confirmation of their theory. The Great Depression was indeed caused by a contraction in money, but there was no unseemly growth of money before it.

One is not sure what is more egregious - Friedman's error or its passing unnoticed for half a century, a fact that hardly paints economists or indeed economics itself in glowing colours. To see why, consider that Paul decides to hold fewer bonds than he did, preferring instead to hold more money. In Friedman's analysis his demand for money has gone up. But the only way that Paul can reduce his holding of bonds is to sell some to Peter. So Peter's holding of bonds goes up and his demand for money goes down. Although Peter and Paul can change their individual stocks of bonds and money, their combined stock of bonds or combined stock of money cannot change. And the same holds for the economy as a whole. By trading in financial assets the stock of money in the economy cannot be changed one whit. Friedman had fallen into what is known as the fallacy of composition. He assumed that his argument was inductive when it was not.

Exactly the same error can be seen in the Keynesian idea of liquidity preference. The argument goes somewhat like this. When interest rates are very low, everyone expects interest rates to rise and therefore bond prices to fall. Therefore everyone gets out of bonds and prefers to hold cash, whence the phrase 'liquidity preference'. But it is impossible for any one individual to exit bonds and accumulate a larger cash balance without at the same time increasing someone else's supply of bonds and reducing his cash balance. The economy as a whole cannot change its liquidity preference by disposing of bonds.

For both Friedman and Keynes money is primarily an asset. The Austrians on the other hand are vehement that money is not an asset, but a medium of exchange. But like the Keynesians and monetarists they too cling to the idea of cash balances, so that for them too in practice money is mostly an asset, not a medium of exchange, or at best some kind of mongrel hybrid.

To cut a sad story short, the error of confusing cash balances with money means that such elegant concepts as liquidity preference and the liquidity trap, very nearly the whole of Milton Friedman's analysis of money, such elegant constructs as the IS-LM diagram, and a series of classic papers dealing with money by economists of the stature of James Tobin and William Baumol are wholly erroneous.

What is interesting is that although no one unequivocally proved that the IS-LM diagram was wrong, that Friedman's conception of money was erroneous, or that the Tobin analysis of money was incorrect, these ideas have simply passed out of economics. Even when wrong ideas are not proven wrong; they tend to wither away, perhaps a case of truth by attrition.


We begin with the money multiplier, a concept that Keynesians, monetarists and Austrians all agree with. In its simplest form, this is how the money multiplier works. The central bank buys $100 worth of, say, government bonds, from a bond dealer. The dealer deposits the $100 in a commercial bank. Assuming that the reserve ratio is 20%, the bank has to retain $20 as a reserve; so it lends out $80. Assuming this is deposited in another bank, the second bank now has to retain 20% of this $80 as a reserve i.e. $16 and can lend out $64, which in turn is deposited in a third bank. By adding up the entire chain of new deposits it can be shown that the $100 created by the central bank's initial purchase of a bond for $100 will result in the creation of $500 of new money, under some standard assumptions.

The model above is silent on how much time it takes for this to happen. Textbooks also often attempt to relate the money multiplier (5 in the above example) to the reserve ratio and other variables. Since we do not know exactly how much time this takes we dispense with these calculations and show the money multiplier in a simple diagram as below.

Fig 1: The money multiplier

In the diagram the purchase of a bond for M dollars by the central bank results in the creation of new money equal to mM dollars, where m is the money multiplier which we do not attempt to relate to the reserve ratio or other variables, since we are not in a position to say how much time has elapsed.

So far, Keynesians, monetarists and Austrians will all be in agreement with us. Curiously none of them seems ever to have asked: What happens when this newly created money mM is spent? We now ask the question by drawing the figure below.

Fig 2: The money multiplier integrated with the economy

And having asked the question we are immediately confronted by a problem. At A the central bank injects M dollars into the system. The banking system, through a series of loans and deposits, converts it into mM dollars at B. When this money returns to A, it is then converted by means of the multiplier to a value of m2M at B. In the next cycle this becomes m3M at B, and on on in an ever-increasing spiral. Equilibrium, it would seem, is impossible.

To salvage the situation we have to resort to a sort of deus ex machina. In order that equilibrium be maintained in the system the money created while moving from A to B must be destroyed in the movement from B to A, so that it again becomes M at A. We answer one objection immediately. Why isn't the entire mM dollars created at B spent? That is to say, why is M dollars retained unspent at A while moving from B to A? The answer is quite simple: in the money multiplication process described at the start of this section, when 500 dollars of new money is created, 100 dollars has to be retained by all the banks together as reserve. In other words M must be retained unlent and unspent in the system; it is simply the total reserves in the example. If it is not, which happens for example when the central bank sells back the bonds, the entire process of money creation described in the example will unravel.

The answer to the second question may be a little more difficult to appreciate. How is the amount of money mM at B destroyed so that it becomes M at A? The answer is that the destruction happens through the mechanism of saving. Each person who receives money spends some of it while saving a little and withdrawing it from the system. The total of this saving must be exactly equal to the net money created mM-M for equilibrium to be maintained. But people do not hide their savings under their mattresses. Because they are assured that the central bank will not allow the disorderly failure of banks they place their savings in the bank. We draw the result as in Fig 3 below.

Fig 3: Savings and money creation in the economy

To sum up the process an injection of money M by the central bank is, through repeated lending by banks, increased to an amount mM. Part of this money is paid out to other firms to buy inputs, a process that leaves money unchanged. The rest is paid out to individuals as wages, interest, rent, dividends and so on. Individuals save part of their receipts and place them in banks which again lend them out. Simple (or even simplistic) as it looks this is the correct model of money, which has eluded economists to this day. The demand for money has nothing to do with cash balances. The demand for money is the demand for loans, and money is equal to loaned funds.

Let us see what the model implies. First of all, Fig 3 tells us: If an injection of money into the banking system by a central bank is multiplied through a process of bank lending, then to sustain the creation of that new money the economy must produce an equal amount of savings AND those savings must be relent by the banking system. If the economy does not produce that quantity of savings or if those savings are not relent, the central bank has to repeatedly inject money into the economy to maintain the money supply. If these repeated injections do not take place the newly created money is destroyed. (That explains, for instance, why QE1 had to be followed by QE2 and so on.)

This is of course what the Austrians have been asserting all these years, or close to what they have been asserting, but have been unable to prove.

What happens when the creation of money runs ahead of savings? In Fig 4 below we have plotted the ratio of M1 to the sum of 12 months savings for the period from 2001 to January 2011. We show later on that M1 is not an accurate measure of money. The sum of 12-months' savings is likewise an arbitrary measure of savings although we show later that it is not quite as arbitrary as we assume here.

Fig 4: The ratio of M1 to 12-months savings

Nevertheless the figure shows clearly that whenever money creation runs far ahead of savings, the result must inevitably be a crash. Seen from this viewpoint it is clear what a recession is: The destruction of unsustainable money until it reaches sustainable levels.

The money model in Fig 3 can be used to throw light on many controversies in economics. Looking at it again, we see that bank lending creates a certain amount of money and that the net money created must be equal to total savings at equilibrium.

S = mM-M (1)

If the savings rate is s, it follows that the total income

Y = (mM-M)/s (2)

and total expenditure

E = (mM-M) (1-s) /s (3)

So income is proportional to money. Now consider the LM curve of the famous IS-LM diagram of Hicks. It is a schedule showing how interest rates change with income given a constant money supply. But as Eqn (2) shows it is impossible for income to increase without an increase in money. The LM curve, in other words, is an impossibility. In hindsight it is surprising that Friedman did not catch this. After all he was the author of the resurrected quantity theory of money. The problem was of course that Friedman's quantity theory was not quite a quantity theory. Witness, for instance, his statement, in an article co-authored with Schwartz, that "the outstanding cyclical fact about the stock of money is that it has tended to rise during both cyclical expansions and cyclical contractions." In practice Friedman's quantity theory of money was the rate of change of quantity of money theory.

In what follows we explore briefly how the money model works in practice.

Fig 5: The Keynesian case

a. The Keynesian case: In Fig 5 the economy is in equilibrium with all expenditure being on current goods and services, no asset bubbles in formation, and no speculative expenditure. An injection of 100 units of money by the central bank is turned into 500 units by the banking system thanks to a multiplier of 5. From equation (1) the Total Savings of the system is 400 units of money and this is spent on investment goods. If we assume a savings rate of 10% the total expenditure resulting from the injection of 100 units of money is, from equation (3), nine times 400 or 3600 units of money.

Fig 6: The speculative case

b. The speculative case: In Fig 6, the central bank decides to loosen monetary policy and accommodate the demand for money by reducing the reserve ratio. The multiplier rises to 6 resulting in the creation of 600 units of money. Now the Total Savings of the system must go up to 500 units. Assume that thanks to the pressure of imports from China, there is no inflation. As in the Keynesian case, 400 units are lent to firms producing real goods and services, and continue to be spent on investment goods. The additional savings of 100 units is borrowed by speculators and spent in the stockmarket, pushing up the prices of shares, and starting an asset bubble. The new expenditure is 4500 units, consisting of 3600 units on real current goods and services as before and 900 units (the multiplier is 9 because of the savings rate of 10%) on stocks. Both the monetary economy and the real economy are in equilibrium, inflation is under check, and the central bank is happy. True, there is some irrational exuberance. But overall things seem to be in control.

Fig 7: The bursting of the asset bubble

c. The bursting of the asset bubble: The central bank decides it's time to rationalise stockmarket exuberance. It calls for banks to cut lending and raises the reserve ratio. The idea is to curb the stockmarket while allowing the real sector to chug along at its current pace. Unfortunately, the plans don't pan out. With money supply squeezed the stockmarket crashes. Banks that have lent heavily to stock punters find themselves with a large hole blown in their assets and capital. They are forced to cut lending. The multiplier falls, not to 5 as intended, but 4. Total savings fall to 300 units. At this level it is not only speculative borrowers who suffer but firms manufacturing real goods and services as well. Total expenditure falls to 2700 units. A recession set off by the bursting of the asset bubble is in full swing.

The model clearly shows how an asset bubble ultimately results in a recession. It agrees with what our common sense tell us, that asset bubbles grow when there is large monetary expansion. When you stop thinking in terms of cash balances everything begins to make more sense.

If we seem to have set up a totally unrealistic example, showing money growth having no impact on inflation, it is only a case of bendng the stick backwards. For all schools of economics without exception seem to have a touching belief that money affects only real goods and services, not financial assets.

Thus Keynes, although he likened the capitalist system to a casino, conducted his entire analysis in terms of investment, savings and aggregate demand for real goods and services.

Friedman said: "To the best of my knowledge there is no instance in which a substantial change in the stock of money per unit of output has occurred without a substantial change in the level of prices in the same direction." Thus the fact that there was no inflation in the period before the 1929 crash was for Friedman proof that there was no substantial increase in the supply of money.

Even the Austrians, who hold that the growth of money supply causes a rise in the price of financial assets, have drawn up an elaborate theory of how a growth in money leads to entrepreneurs investing in longer processes of production, and thus a shift from consumer goods to investment goods, which is unsustainable. This is one possibility and will certainly occur, but more often it is the rise in prices of financial assets which is of greater importance.

In our own time John Taylor's eponymous rule seeks to relate the interest rate with the rate of growth of GDP and inflation, with prices of financial assets not entering anywhere into the equation.

The truth of course is different. In general, it can be said that an increase in money supply will result in an increase in nominal output and an increase in the price of financial assets, and it is impossible to predict how the partitioning will take place.

Fig 3 incidentally shows that Keynes was right in thinking that during a recession monetary policy alone is impotent. For money supply to rise, two conditions must be met: there must be a willing lender and there must be a willing borrower. After a crash like the recent one, banks that have been crippled by the loss of capital are hardly likely to start lending again. But by the same logic, Keynesians are wrong in thinking that keeping interest rates low will get entrepreneurs investing again. Keeping the price of wheat very low may seem very attractive from the viewpoint of the buyer of wheat and certain to keep people from starving, but it is more likely to discourage farmers from growing any wheat and thus to cause the very starvation it seeks to prevent. When interest rates are very low, it may not be profitable for banks to lend to businesses, especially when the risk of the loan not being returned is taken into consideration; it is more tempting to earn higher profits by speculation or by lending to speculators. What else can explain the situation today when unemployment in the US is still high at the same time that the stockmarket is back to its old highs.

Other controversial issues can be analysed with the money model of Fig 3 but since we do not wish to turn this article into a treatise, we move on to a subject on which we have been silent so far.


Paul brings an apple to me for safekeeping. I write in my ledger: Paul, 1 apple, meaning thereby that I owe one apple to Paul. Some time later, Peter comes to me asking for an apple and I give him the apple given to me by Paul. I write in my ledger: Peter, 1 apple, meaning thereby that Peter owes me one apple. There are two apple entries in my ledger, but of course in reality there is only one apple.

Paul brings 100 dollars of his savings to me in currency notes. I write in my ledger: Paul, 100 dollars, meaning that I owe Paul 100 dollars. Some time later, Peter comes to me asking for a loan of 100 dollars and I give him the 100 dollars given to me by Paul. I write in my ledger: Peter, 100 dollars, meaning thereby that Peter owes me 100 dollars. There are two 100 dollar entries in my ledger, but of course in reality there are only 100 dollars in existence.

Paul deposits a cheque of 100 dollars of his savings in the bank that I run. I open a deposit in his name and write in my ledger: Paul, 100 dollars. Some time later, Peter comes to me asking for a loan of 100 dollars. I lend him the money by opening a deposit in his name for 100 dollars. So now the total amount of deposits is 200 dollars, but of course in reality there are only 100 dollars in existence. If Paul insists on being paid back his 100 dollars I have no option but to take back the loan from Peter.

The point of all the above is to show that to calculate the amount of money in existence it is incorrect to add all the deposits in existence. I must subtract from them the total amount of savings present in those deposits. So without any further ado we can state categorically that both the Friedmanian and the Austrian definitions of money are incorrect because they both include savings deposits.

But measuring money is far more difficult than just excluding savings deposits. That would give us M1, and we know that M1 does not correlate well with other macroeconomic variables. To measure money accurately, we also need to measure the amount of savings contained in M1, and subtract the savings from M1. When banks (or shadow banks) lend money to a firm it shows up immediately as a demand deposit. When the firm uses that deposit to buy a good or service from another firm the money in the demand deposit changes hands but because it appears in the demand deposit of some other firm it still counts as money. When the firm uses the money in the demand deposit to pay a wage, rent, interest or dividend to Paul the demand deposit in Paul's name increases by an identical amount. Say, the firm pays $1000 as salary to Paul. If his saving rate is 10% he will spend $900 and $100 will be the extent of savings in the demand deposit (we assume that firms are net dissavers). This $100 must be subtracted from the value of demand deposits to derive the value of money. But it is unlikely that Paul goes about the business of life with just $100 in spare money in his demand deposit. If, apart from the $1000 he is paid at the start of the month, he has $500 in his account, it means that he has 5 months of savings in his deposit and this has to be subtracted from the sum of all demand deposits to arrive at the correct value of money.

We cannot go around asking every Peter and Paul how much savings he has in his demand deposit. We have to estimate it by other means. Now, all that we have said upto the beginning of this section is analysis; it is true at all times and at all places. But in estimating the quantum of money we have to dirty our hands and resort to empirical means. In what follows we demonstrate one such method. But it is perfectly possible that there are better and more refined methods to estimate money.

The total amount of demand deposits is the sum of demand deposits that are savings and the demand deposits that are loans.

DDT = DDS + DDL (4)

where T stands for Total, S for Savings, and L for Loans

When we divide both sides of (4) by DDS we get

DDT/DDS = 1 + DDL/DDS (5)

Now, during recessions, two things happen. First, people save more. Second, because interest rates are close to zero, they are more tardy in moving their savings to some other kind of deposits that yield more interest. Therefore, during a recession we would find that the second term in (5) approaches close to zero, and the ratio DDT/DDS approaches close to 1. We use this expected result to find the correct value of DDS. For identifying the correct DDS we use the sum of n-month savings where n=1, 2, 3 etc and examine whether the resulting graph tends towards 1 during severe recessions; the assumption is that at all times demand deposits contain a constant number of months of savings.

Fig 8: Total Deposits to 12 months' savings 1991 to 2010

We have omitted showing all the graphs (of 1-month, 2-month etc savings) but observe that the sum of 12-month savings approaches closely to 1 during the recession of 2008-09. We use this fact to calculate Mc or Corrected Money Supply by deducting 12-months-savings from M1. Our assumption that people keep a constant number of months savings in their demand deposits may not be correct. But it is still a huge improvement over M1 which does not correct for savings at all. Note that the fact that people keep savings in their demand deposits does not increase or decrease money because money is only determined by lending and borrowing, but it affects our MEASUREMENT of money.

Fig 9 plots M1 for the period from 2001 to 2011.

Fig 9: M1 from January 2001 to January 2011

M1 shows a more or less secular rise throughout the period and in 2008, when the liquidity crunch was most intense, shows a sharp rise, whereas from 2004 to 2006 it remains almost flat.

Fig 10 below shows Mc or Corrected money supply during the same period.

The graph of Mc shows clearly the rise in money supply from 2003 right till the peak in money supply at the beginning of 2006, the fall thereafter, and the unsteady attempts by the Fed to push up money supply. Where the difference is most stark is during 2008 when M1 shows a steep rise at a time when the recession was at its peak. This was of course because the amount of savings in demand deposits went up sharply during this period and was miscounted as money. It also explains why Friedman's calculations did not show a sharp rise in money before the crash of 1929. By adding up demand deposits we miss the extent to which savings are falling during an expansion at the same time that money is being borrowed to frantically push up the prices of financial assets. Only towards the latter part of 2009 does corrected money supply finally begin to rise permanently, which is when the recession ended.

We may mention in passing the implications of our calculations for a favourite Austrian recommendation: 100% reserves. Implementing the recommendation would have disastrous effects, because it would mean that the 12 months of savings contained in demand deposits would not be lent out. Without the use of the money model we have developed, ideas like 100% reserve banking are just an opinion, the war-cry of one tribe of economists against another. With the new model the idea can be analysed rationally.

In conclusion, the reader will note that we have upset the existing notion of money and replaced it with a more plausible one, without resorting to any Advanced Mathematical Economics Nonsense.


For all our calculations we have used data from the web site of the Federal Reserve Bank of St Louis at the beginning of March 2011

4 April 2011

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