What really is money supply?
It is impossible to buy a good or a service except with currency or a check (which is merely a representation of a demand deposit). Yet M1, which is the sum of currency and demand deposits, does not correlate well with real economic activity. The following paper resolves this apparent contradiction. By using Murray Rothbard's arguments but along different lines it shows that not all demand deposits bear the same character, and that the definition of money supply is therefore erroneous. When the error is removed the resulting monetary aggregate (which is different from the Austrian "true money supply") is seen to closely correlate to changes in the economy and that too without a significant time lag.
In the late sixties and seventies of the 20th century money supply was the main issue which divided economists. Pitched battles were fought between Keynesians and monetarists  on the subject. The mid- and late-seventies were the heyday of monetarism with the highpoint being reached when Paul Volcker as the Federal Reserve chairman decided to focus on monetary aggregates instead of interest rates. The experiment was successful. But then, as suddenly as it had come into the limelight, money supply ceased to matter very much so that now neither Keynesians nor the former monetarists consider it of significance. The official view today is that it is of peripheral importance.
Almost the only people who talk these days of money supply are economists belonging to the Austrian school. And this is significant because the Austrian view of money supply on the one hand is different from that of monetarists and Keynesians on the other. For monetarists following in the tradition of Milton Friedman money is an asset, one of many alternative assets. For Keynesians too, following in the tradition of James Tobin or even earlier, of Keynes as revealed in the idea of liquidity preference, money is one of many (for Keynes, two) assets. The similarity between Keynesian and monetarist economics has occurrred to more than one observer, e.g. Don Patinkin and Peter Drucker. For economists of the Austrian school, however, money is a medium of exchange, as exemplified in Ludwig von Mises or Murray Rothbard. The difference is important, and crucial to our analysis.
ROTHBARD'S ANALYSIS OF MONEY
In Austrian Definitions of Money Supply Rothbard noted: ".. Ludwig von Mises set forth the essentials of the concept of money supply in his Theory of Money and Credit, but no Austrian has developed the concept since then, and unsettled questions remain (e.g. are savings deposits properly to be included in the money supply?) And since the concept of the supply of money is vital both for the theory and for applied historical analysis of such consequences as inflation and business cycles, it becomes vitally important to try to settle these questions, and to demarcate the supply of money in the modern world."
Rothbard's arguments on why savings deposits should be included in the money supply are worth considering at length. Remember that these arguments were put forward in 1978, and that some of the characteristics of savings deposits have changed since then. Rothbard mentions, among others, two arguments for not including savings deposits in the money supply. (1) they are not redeemable on demand, the bank being legally able to force the depositors to wait a certain amont of time (usually 30 days) before paying cash; (2) they cannot be used directly for payment; checks can be drawn on demand deposits, but savings deposits must first be redeemed in cash upon presentation of a passbook.
The first argument, he says, fails from focusing on the legalities rather than on the economic realities of the situation; in particular the objection fails to focus on the subjective estimates of the situation on the part of the depositors. In reality, the power to enforce a thirty-day notice on savings depositors is never enforced; hence the depositor invariably thinks of his savings account as redeemable in cash on demand. He adds that "objection (2) fails as well, when we consider that, even within the stock of standard money, some part of one's cash will be traded more actively or directly than others. Thus, suppose someone holds part of his supply of cash in his wallet, and another part buried under the floorboards. The cash in the wallet will be exchanged and turned over rapidly; the floorboard money might not be used for decades. But surely no one would deny that the person's floorboard hoard is just as much part of his money stock as the cash in his wallet. So that mere lack of activity of part of the money stock in no way negates its inclusion as part of his supply of money."
The Austrian "true money supply", drawing upon Rothbard's arguments, consists of the following: currency component of M1, total checkable deposits, savings deposits, US government demand deposits and note balances, demand deposits due to foreign commercial banks, and demand deposits due to foreign official institutions. 
The graph in Fig 1 shows True Money Supply from 2001 to 2009. We would expect an accurate measure of money supply to mirror at least important changes in the economy. Unfortunately, as Fig 1 shows, "true money supply" does not yield any insights.
In what follows we go over Rothbard's arguments once again, because no other economist has set forth so clearly the reasons for or against including a certain class of deposits in the money supply.
We begin with the "floorboards" argument. According to Rothbard, if a person holds part of his money in his wallet and part under the floorboards, we would still consider the under-floorboards hoard as part of his money stock. Consider an economy with 100 pieces of gold currency. The manufacturers pay workers 100 gold pieces in wages. The workers spend 95 pieces and save 5 pieces, which they bury under their floorboards. According to Rothbard, we should still consider the system as having 100 gold pieces in money stock. But the fact is that the system now has only 95 gold pieces to use as a medium of exchange. In subsequent cycles, if workers continue to save 5% of their income, and bury it under their floorboards, the amount of gold available to serve as a medium of exchange in the economy would steadily diminish. From the subjective viewpoint of somone other than the workers, the 5 pieces buried under their floorboards are still money because they can be used as a medium of exchange. What matters, however, is the subjective estimate of the workers themselves for, as the owners of the 5 gold pieces, only they know the character of the gold pieces they have buried under the floorboards. The 5 pieces can be used as a medium of exchange theoretically; but the workers know that they will not be used as a medium of exchange, because by definition, savings are what is not spent. The 5 gold pieces are asset money but they are not medium-of-exchange money, and therefore cannot be included in money supply.
Carrying the argument a step further it makes no difference if the 5 gold pieces, instead of being placed under the floorboards, are put into banks as a savings deposit. From the standpoint of the savers, the 5 gold pieces are not intended to be used as a medium of exchange. The bank can of course lend the 5 gold pieces in which case they will again be used as a medium of exchange, but this time by the borrowers of the 5 gold pieces. In the case of a modern bank the saver has a savings deposit and the borrower has a demand deposit. But to obtain the money supply, only the demand deposits that stand in the name of borrowers should be added up, not the savings deposits.
But if savings deposits are not included in the money supply we are basically left again with the sum of currency and demand deposits, which is M1, and what we know of the behavior of M1 is that it rises during expansions and rises during recessions, which is hardly what we expect of a measure of money supply that acts as a medium of exchange. So where is the flaw? For that we turn to Rothbard's discussion of demand deposits.
ROTHBARD ON DEMAND DEPOSITS
Rothbard observes that "no contemporary economist excludes demand deposits from his definition of money. But it is useful to consider exactly why this should be so. When Mises wrote The Theory of Money and Credit in 1912, the inclusion of demand deposits in the money supply was not yet a settled question in economic thought."
After elaborating von Mises' arguments for including demand deposits in the money supply, Rothbard says, "It is important to recognise that demand deposits are not automatically part of the money supply by virtue of their very existence; they continue as equivalent to money only so long as the subjective estimates of the sellers of goods on the market think that they are so equivalent and accept them as such in exchange."
Now consider a person who is paid a monthly salary of $1,000 which comes into his demand deposit on the first of each month. During the course of the month he spends $950 and saves $50, so that on the first of the next month he has $1,050 in his demand deposit. From the viewpoint of the seller of goods the entire $1,050 is money supply because all of it can be used as a medium of exchange. But the correct subjective viewpoint to be considered here is that of the owner of the demand deposit, and he knows that he only intends to use $950 of the demand deposit as a medium of exchange, the rest being savings. Now it is highly likely that a person earning $1,000 a month will be content to leave just a buffer of $50 or $100 in his bank account. To meet exigencies he is likely to leave much more. If he receives a constant salary each month, and saves a constant sum of $50 each month, then if he has $1,000 as a buffer it means that he has 20-months-savings in his demand deposit, which he has no intention of using as a medium of exchange except in dire emergencies. Since this amount is not intended to be used as a medium of exchange it must not be included in the money supply.
If every person saved at a constant rate and maintained a constant buffer in his demand deposit the part of the demand deposits that are savings would not have a significant effect. It would just raise the money supply curve by a constant amount at all times. But people do not save at a constant rate. During an expansion they tend to save less and during recessions they tend to save more. So in just adding up demand deposits the money supply is underestimated during expansions and overestimated during recessions.
But how do we calculate this savings part of the demand deposits? It is of course impossible to go about asking the owner of every demand deposit what the extent of savings in his demand deposit is. Fortunately, there is an easier way of estimating it using some simple assumptions.
ESTIMATING THE AMOUNT OF SAVINGS IN DEMAND DEPOSITS
Note that the total amount of demand deposits is the sum of demand deposits that are savings and other demand deposits (loans, loans in the process of being spent, non-M1 deposits that were converted to demand deposits etc).
DDTotal = DDS + DDO (1)
where the subscript S stands for savings and O for others
When we divide both sides of (1) by DDS we get
DDTotal/DDS = 1 + DDO/DDS (2)
If we plot a graph of DDTotal/DDS against time for the correct DDS we would expect to find that during recessions, when the quantum of loans and spending falls and the quantum of savings rises, the second term on the right hand side of eqn (2) would grow smaller and smaller and the left hand side of eqn (2) would approach a value closer and closer 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. Fig 2 shows four graphs for four different values of DDS: 6-month savings, 10-month savings, 11-month savings, and 12-month savings.
We observe that the minimum in the 6-month savings graph is much above 1, and that in the 12-month savings graph it falls below 1. The graph in which the minimum ratio is closest to 1 is the one in which savings is equal to 10 months savings. Assuming therefore that people maintain a buffer equal to 10-months-savings at all times, we can calculate the corrected money supply Mc as equal to M1 minus the sum of 10-months savings. Fig 3 shows the graph of Mc and M1 for the period from January 2001 to the present.
The common endeavor in testing a measure of money supply is to compare it with GDP. But this idea has no logical basis, and amounts to a misunderstanding of money. GDP measures goods and services produced in the current year. But money is not spent on just current goods and services; it is also spent on second-hand cars, second-hand houses, and, most important of all, financial assets. An increase in money supply is thus partitioned among an increase in GDP, inflation, and an increase in spending on financial assets (which could be houses, stocks, bonds), and it is not possible to predict in advance how the partitioning will occur.
Fig 3 shows just that. From January 2001 to the end of 2002 Mc rose rapidly. This was during a period when the US economy went through a recession and the stockmarket fell. But it was also a period when housing prices began to rise rapidly. The fall in Mc during 2002 coincides with a fall in the stockmarket, but a rise in GDP and a rise in the housing market. From around October 2002 to December 2005, Mc rose steeply, at an annual average of around 12%, during which the GDP expanded and the stockmarket and housing prices rose to stratospheric heights. From January 1, 2005 to December 1, 2005, when M1 was almost flat, Mc rose more than 16%. Thereafter it began to fall drastically, although the economy was still purring along and there were few signs of the impending disaster except for the collapse of the housing market.  What the graph tell us thereafter is even more interesting. In the absence of a monetary aggregate to steer by the Fed had no idea there was anything wrong. During Federal Open Market Committee (FOMC) meetings in both June and August 2007 it maintained the Federal Funds Rate and moved to lower it only in September 2007. But what is surprising is that the graph of Mc shows that the recovery had by then already begun on its own; it can of course be argued that the problems caused by the collapse in money supply were just hidden and would surface only a little later.
In Fig 4 the graph of Mc shows the recession under Volcker, the stockmarket recovery from 1982 to 1984, the fall in the stockmarket in 1984, and thereafter the steady rise in money supply (most of it under Volcker's watch) until the collapse of the stockmarket in 1987 and the recovery thereafter. The pattern seen here occurs repeatedly: push up money supply so that an asset bubble is set up, then when the asset bubble collapses pump in even more money to recover from the consequences.
In Fig 5 there is a steep increase in Mc from 1991 to the end of 1993 but after that through a series of interest rate increases, Mc is squeezed. The sharp fall in 1998, leading among other things to the collapse of Long Term Capital Management, can be clearly seen. Thereafter, Mc rises steeply over a period of a little more than a year leading to the collapse of the stockmarket in 2000 and the subsequent recession.
WHY M1 FAILED AFTER 1981
Now that we have established how to measure money supply we can answer the question: Why did M1 which was a relatively good indicator of economic changes before 1981 fail as a metric after that? That question is easily answered: Since M1 was wrongly defined it was bound to fail. But that is not the right question. We need to stand that question on its head to obtain the right question, which is: Given that M1 was a wrong measure of money supply how did it perform relatively well as an indicator before 1981?
The reason is that before 1981 checking accounts did not pay interest; NOW accounts (which paid interest and counted as M1) were introduced in 1981. So individuals tended to maintain as low a buffer as possible in their demand deposits (which counted as M1) and moved money to a savings deposit which paid interest and did not count as M1. In other words, the M1 which economists used as a metric automatically came with part of the savings subtracted from it; individuals were doing it by physically moving their savings to savings deposits. That can also be seen from the graphs in Fig 2. The demand deposit series before 1981 and the demand deposit series after 1981 are two completely unrelated sets; before 1981 the ratio of total demand deposits to savings does not fall towards 1 during recessions. However, we can also observe that in Fig 2 (in the total deposits to 10-month savings graph), the minimum to which the ratio of total deposits to savings falls at each recession goes down, from about 5 in the 1960 recession to about 2 in the 1973-75 recession, and falls even further after that. The explanation for this seems to be that gradually rising prices forced people to keep larger buffers in their demand deposits.
Thus M1 worked as an indicator in the seventies not because the definition was right, but because savers who moved their savings out of M1 were automatically carrying out part of the correction, which I have carried out by subtracting 10-month savings (obtained from national accounting) from the sum of demand deposits plus currency. In retrospect, it is not a surprise that the highpoint of monetarism came in the seventies, and that monetarist predictions worked so well then. They worked well despite the wrong definition of money supply and for reasons that monetarists did not recognise. When it ceased to work monetarists did not understand why because they had not understood in the first place why it had worked in the seventies. The movement of savings from checking accounts also explains the "missing money" phenomenon observed in the seventies when econometric estimates of money demand began to break down, and actual growth of M1 fell below estimates.
It has been a common complaint that money supply has long ceased to correlate well with other macroeconomic variables. In this paper I have showed that this is not the case by retracing Rothbard's arguments about the nature of money, differing with him only in one fundamental respect. Where he looked at money from the viewpoint of the seller of goods, I have looked at money from the viewpoint of the owner of a savings deposit or demand deposit, since only he is aware to what extent the asset money he holds is also a medium of exchange. As is proper to a money measure that is a medium of exchange, the three graphs of Mc from 1976 to 2010 correlate well with events in the real economy, and without any significant time lag. It is hoped that this paper will put money supply back at the centre of monetary economics where it rightfully belongs.
Footnotes. Robert Solow's quote: "Everything reminds Milton Friedman of the money supply. Everything reminds me of sex, but I try to keep it out of my papers" more or less summed up the differences. For the monetarists everything hinged on money supply; for the Keynesians it was at best a side issue.
. Ben Bernanke summarised it in 2006 as follows: "Although a heavy reliance on monetary aggregates as a guide to policy would seem to be unwise in the U.S. context, money growth may still contain important information about future economic developments. Attention to money growth is thus sensible as part of the eclectic modeling and forecasting framework used by the U.S. central bank."
. In Monetary Studies of the National Bureau Friedman wrote: "It will help put our work in proper perspective to distinguish at the outset between different senses in which the word 'money' is used. In popular parlance, there are three main senses - as in pocket money, money market, and making money. In the first sense, money refers to a class of assets of wealthholders; in the second, to credit; in the third, to income. Our work has been concerned with money in the first sense."
. "Liquidity preference theory takes as given the choices determining how much wealth is to be invested in monetary assets and concerns itself with the allocation of these amounts among cash and alternative monetary assets" in Liquidity Preference as Behavior Towards Risk.
. "..the conceptual framework of a portfolio demand for money that Friedman denotes as the 'quantity theory' is actually that of Keynesian economics" in Friedman on the Quantity Theory and Keynesian Economics.
. Drucker describes Friedman's monetarism as a "desperate attempt to patch up the Keynesian system of equilibrium economics" in Modern Prophets: Schumpeter or Keynes?
. "Money is nothing but a medium of exchange" in Preface to Money and Credit.
. "Money is the uniquely liquid asset because money is the final payment, the medium of exchange used in virtually all transactions to purchase goods or services. Other non-monetary assets, no matter how liquid-and they have different degrees of liquidity-are simply goods to be sold for money" in The Mystery of Banking.
. The 'true' money supply: A Measure of the Supply of the Medium of Exchange in the US Economy by Joseph T. Salerno.
. The mystery of the money supply definition by Frank Shostak differs from the usual Austrian definition of money by excluding savings deposits.
. In Mystery of Banking Rothbard notes, "Oddly enough, it was in the United States, then considered a backwater of economic theory, that economists first insisted that bank deposits, like bank notes, were part of the money supply. Condy Raguet, of Philadelphia, first made this point in 1820. But English economists of the day paid scant attention to their American colleagues."
. On December 19, 2006 The Economist said, "Having grown at an annual rate of 3.2% per head since 2000, the world economy is over halfway towards notching up its best decade ever. If it keeps going at this clip, it will beat both the supposedly idyllic 1950s and the 1960s. Market capitalism, the engine that runs most of the world economy, seems to be doing its job well."
. The graphs plot the ratio of total demand deposits to the part of demand deposits that are savings. Since people are moving part of their savings to deposits that pay interest, the numerator and denominator of the ratio are reduced by equal amounts. It is easy to prove that if a > b >c > 0, then (a-c)/(b-c) is greater than a/b.
BibliographyBernanke, Ben S. Monetary Aggregates and Monetary Policy at the Federal Reserve: A Historical Perspective, Speech at the Fourth ECB Central Banking Conference, Frankfurt, Germany, November 10, 2006 Drucker, Peter. "Modern Prophets: Schumpeter or Keynes?" in The Frontiers of Management, 1986 Friedman, Milton. The Optimum Quantity of Money, 1969 Mises, Ludwig von. The Theory of Money and Credit, 1912 Patinkin, Don. "Friedman on the Quantity Theory and Keynesian Economics", The Journal of Political Economy, September-October 1972 Rothbard, Murray N. "Austrian Definitions of the Supply of Money" in New Directions in Austrian Economics (1978) Rothbard, Murray N. The Mystery of Banking, 1983 Salerno, Joseph T. The "True" Money Supply: A Measure of the Supply of the Medium of Exchange in the US Economy, Austrian Economics Newsletter, The Ludwig von Mises Institute, Spring 1987 Shostak, Frank. "The Mystery of the Money Supply Definition", The Quarterly Journal of Austrian Economics, Winter 2000 Tobin, James. "Liquidity Preference as Behavior Towards Risk", The Review of Economic Studies, February 1958