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## The Velocity of Circulation

March 17, 2008

[From Money, the Market, and the State, edited by Nicholas B. Beales and L. Aubrey Drewry, Jr., Athens: University of Georgia Press, 1968, pp. 35–44.]The quantity theory of money is very old. But it has been most influential in the last half century in the form given it by Irving Fisher in The Purchasing Power of Money (1911). I shall refer to this as the Fisherine or mechanical quantity theory of money.

It would save a great deal of discussion at cross purpose if this, and only this, were referred to as the Quantity Theory of Money. A quantity theory of money (in the sense of a theory which merely acknowledges that the quantity of money is an important factor affecting the value of the monetary unit) is a quite different thing.

The Fisherine quantity theory is mechanical and mathematical. It takes no account of the psychological valuations of individuals. Under it, the existing quantity of money is the sole determinant of money's value. The value of the monetary unit is supposed to vary inversely with the quantity of money in existence. This means that the "price level" of goods and services is supposed to vary directly and proportionately with the supply of money.

From this comes the famous Fisherine equation: MV=PT. This equation is more frequently written: MV + M1V1 = PT. This second more complicated equation is simply meant to symbolize that bank deposits are counted just as much as hand-to-hand money. But we shall take this for granted hereafter and confine ourselves merely to the simpler symbols.

Now I am not primarily concerned here with refuting the Fisherine quantity theory of money. That was done magnificently by Benjamin M. Anderson in The Value of Money in 1917. But the Fisherine equation, which once dominated the field, is still found in contemporary expositions of the forces that determine the purchasing power of money. It seems to have had a wonderful longevity as a result of its apparent simplicity, its apparent mathematical precisions — and because it is easier to teach than other theories.

In my present comments I shall confine myself to a special examination of the V in this equation.

In the Fisherine equation, M stands for the quantity of money (and of demand bank deposits) in existence; V stands for the "velocity of circulation" of that money; P stands for "the average price level" of commodities and services; and T stands for the "volume of trade," or the quantity of goods and services against which money is exchanged.

Now as Anderson has pointed out, in an acute analysis, the two sides of this equation are equal only because they are identical:

The equation asserts merely that what is paid is equal to what is received. This proposition may require algebraic formulation, but to the present writer it does not seem to require any formulation at all. The contrast between the "money side" and the "goods side" of the equation is a false one. There is no goods side. Both sides of the equation are money sides.[1]

But I am concentrating here upon the meaning of V, the "velocity of circulation." Anderson, in discussing this, tells us,

The conception of the velocity of circulation as a real, unitary entity, a cause in the process of price-determination is, I suppose, almost as old as the quantity theory itself. It is an essential part of the quantity theory.[2]

In Fisher's treatment of it in The Purchasing Power of Money, V is treated as something that is fairly constant, so that when M is doubled MV is doubled, and therefore the "price level" is doubled. The quantity theory as Fisher framed it assumed that "normally" the "price level" varies directly and proportionately with the supply of money.

But when careful statistical comparisons are made, it is found that this is not so. And here is where V comes in. When the price level has not changed in direct proportion to the supply of money, the Fisherine quantity theorists assume that there has been some offsetting change in the "velocity of circulation" of money to the exact extent necessary to account for the discrepancy. If, for example, they find statistically that the quantity of money has increased by 10 percent in a given year, while the "price level," as measured by the wholesale price index or the consumers' price index, has remained unchanged, they assume that there must have been a slowing down of about 10 percent in the velocity of circulation. If the quantity of money has remained unchanged, but there has been a 10 percent increase in the "price level" in a given period, they assume that there must have been an increase in the "velocity of circulation" of money of 10 percent in that period. And so on.

Perhaps we can most clearly recognize what is wrong with this notion if we see what commonly happens in an inflation, and what the real explanation is.

What we commonly find, in going through the histories of substantial or prolonged inflations in various countries, is that, in the early stages, prices rise by less than the increase in the quantity of money; that in the middle stages they may rise in rough proportion to the increase in the quantity of money (after making due allowance for changes that may also occur in the supply of goods); but that, when an inflation has been prolonged beyond a certain point, or has shown signs of acceleration, prices rise by more than the increase in the quantity of money. Putting the matter another way, the value of the monetary unit, at the beginning of an inflation, commonly does not fall by as much as the increase in the quantity of money, whereas, in the late stage of inflation, the value of the monetary unit falls much faster than the increase in the quantity of money. As a result, the larger supply of money actually has a smaller total purchasing power than the previous lower supply of money. There are, therefore, paradoxically, complaints of a "shortage of money."

What is the real explanation of this? It is perfectly true, to begin with, that the quantity of money affects the value of the monetary unit, just as the quantity of wheat, say, affects the value of an individual bushel of wheat. In both cases, an increase of supply, other things being equal, reduces the value of a given unit, and a reduction of supply increases the value of a given unit. But no one assumes, in the case of wheat or of any other commodity, that the reduction in value of a unit is exactly proportional to the increase in the total supply (or an increase in value exactly proportional to a reduction in the total supply). And neither should we assume that there will be an exactly inverse proportional variation between the value of a unit of money and the supply of money.

The value of a unit of money is determined, like the value of a unit of a commodity, primarily by psychological factors, and not merely by mechanical or mathematical factors. As with commodities, the value of money is influenced not merely by the present quantity, but by expectations concerning the future quantity as well as the future quality. At the beginning of an inflation, many prices and wages remain as they are through habit and custom, and also because, even when the increase in the money supply is noticed, it is assumed to be purely a past event that is now over. Confidence in a sort of fixed value of the monetary unit remains high. Of course an increase in the supply of money will probably raise some prices, though the average of prices will not necessarily rise as much as the monetary increase.

In the middle stage of an inflation, prices may respond rather directly to an increase in the supply of money. But as the inflation goes on, or perhaps becomes accelerative, fears begin to spread that the inflation will continue into the future, and that the value of the monetary unit will fall further. These fears for the future are reflected in the present. There is a flight from money and a flight into goods. People fear that prices are going to rise even further, and that the value of the monetary unit is going to fall even further. Their own fears and actions help to produce that very consequence.

Now when such developments are called to the attention of, or noticed by, the adherents of a rigid quantity theory, these adherents have a ready answer. The discrepancy, they say, is accounted for by changes in V, the "velocity of circulation." And they state or assume that these changes in the velocity of circulation are of the exact mathematical extent necessary to account for the discrepancies between the increase in the supply of money and the increase in the price level.

They do not offer any mathematical proof of this. As we shall see, such mathematical proof does not and cannot exist. Let us look at some of the reasons why.

To begin with, the "velocity of circulation" of money is a misnomer. It is simply a figure of speech, a metaphor — and a misleading one. Strictly speaking, money does not "circulate"; it is exchanged against goods. Money is said to "circulate" because it changes hands, or, more precisely, changes ownership. But when a house, say, frequently changes ownership we do not say that it "circulates." If we are to apply the metaphor of circulation to money, then we should also logically apply it to goods. For money (except in borrowing or in paying off debts) is always exchanged against goods (or services). Therefore the "velocity of circulation" of money can never be any greater than the "velocity of circulation" of goods.

In the Fisherine equation of exchange, V is commonly treated as an independent variable. In other words, V is treated as something that can change independently of any change in T, or the volume of trade. An increase in the velocity of circulation is treated as being equivalent to the same percentage increase in the volume of money. Money is thought of as something that has a certain "amount of work to do." If the velocity of circulation of money is doubled, then one dollar is said to do "the work" previously done by two. According to this theory, if merely the velocity of money doubled, with no change in the quantity of money, the price level would double.

A common classroom illustration runs something like this: A owes B a dollar, who owes C a dollar, who owes D a dollar, who owes E a dollar, who owes A a dollar. If they sit around a table, and each pays the dollar he owes to the other, then the dollar "circulates," and one dollar "does the work of" five dollars. Two things may be noticed about this illustration. First, in the situation described, no actual dollar would have to change hands at all: debts could be cancelled out by mere bookkeeping transactions. This mutual cancellation of debts occurs in actual practice every day, and on a large scale, in bank clearing houses, or institutions that act as clearing houses. Secondly, the illustration, in fact, applies only to borrowing, or to paying off previously incurred debts.

But what we have to deal with, in the so-called circulation of money, is the exchange of money against goods. Therefore V and T cannot be separated. Insofar as there is a causal relation, it is the volume of trade which determines the velocity of circulation of money rather than the other way around.

What the mathematical quantity theorists seem to forget is that money is not exchanged against a vacuum, nor against other money (except in bank clearings and foreign exchange), but against goods. Hence the velocity of circulation of money is, so to speak, merely the velocity of circulation of goods and services looked at from the other side. If the volume of trade increases, the velocity of circulation of money, other things being equal, must increase, and vice versa.

An increase in V may come about through greater eagerness to buy goods. But the velocity of circulation of money cannot be speeded up to anything like the extent commonly assumed by the mathematical quantity theory. This particularly applies to spending for consumption. There is a customary (and even a maximum) rate of consumption of food, for example, which is not speeded up even in a hyperinflation. People who are paid weekly may buy their entire week's stock of food (or whatever part of it will keep) on the day they get their weekly paycheck rather than buy their needs each day. But this will not increase the weekly V. In a hyperinflation, people may stock up much sooner than otherwise in their purchase of durable goods — housing, automobiles, appliances, clothing, jewelry, works of art, etc. But even this will not increase V over a prolonged period, unless the rate of production is correspondingly speeded up. After any buying spree of durable goods, there is likely to be, other things being equal, a less than normal rate of V for such durable goods — partly because nearly everybody will be "loaded up" with them, partly because retailers' stocks will be exhausted or low, unless output can be equally speeded up.

These "hurryings" and "waitings" (to use the vocabulary of L. Albert Hahn[3]) are part of the business cycle.

As money is exchanged against goods, and as the rate of consumption can change only within comparatively minor limits, we must look elsewhere to find the reason for the variations in V that we actually do encounter. This reason is found in speculation. This can be shown inductively as well as deductively. There are no reliable statistics, of course, on the "velocity of circulation" of hand-to-hand currency. But we have figures on the annual rate of turnover of demand bank deposits, and as bank deposits in the United States cover nearly nine-tenths of the media of payment, these figures are a very important index. (In August of 1966, bank deposits, both time and demand, totaled \$288 billion as against \$38 billion representing currency outside of banks.)

What is most striking, when we examine the figures, is first of all the wide discrepancy that we find between the rate of turnover of demand deposits in the big cities, especially New York, and the rate that we find in 218 other reporting centers. In August of 1966, the annual rate of turnover of demand deposits in these 218 small centers was 34.1. In six large reporting centers outside of New York City, it was 52.2.When we come to New York City itself, the rate of turnover was 112.7. In other words, the rate of turnover of demand deposits in New York City was more than three times as great as it was in small towns and country districts.

This does not mean that people in New York City were furiously spending their money at three times the rate of people in the small centers. (We must always remember that each individual can spend his dollar income only once.) The difference is accounted for by the fact that New York, with the New York Stock Exchange, the American Stock Exchange, the stock brokers and bond houses, and a myriad of speculative markets for commodities, is the great center of speculation in the United States. This fact is further emphasized by comparisons over a period of years. For example, in 1943, the turnover of demand deposits in New York was only a little greater than in other reporting centers. But it has kept increasing since then, in relation to other centers. This increase had corresponded broadly with the measurable increase in speculation during the same period.

Though the velocity of circulation of money increases with speculation, speculation itself does not indefinitely increase. In order for speculation to increase, willingness to part with commodities must increase just as fast as eagerness to buy them. It is rapidly changing ideas of commodity values — not only differences of opinion between buyer and seller, but fluctuating opinions on the part of individual speculators — that are necessary to increase volume of speculation. But an increase of V does not necessarily mean increased commodity prices, let alone proportionately increased commodity prices. There may be violently active falling markets as well as violently active rising markets.

We may get much closer to the truth of this situation if we take what has come to be known as the "cash holdings" approach. This has been admirably presented in the works of Ludwig von Mises.[4] I quote at length from his views as given in a letter to me:

The service that money renders does not consist in its turnover. It consists in its being ready in cash holdings for any future use.

Money is never "idle." It always renders to somebody the only service that it can render, namely being a part of a man's cash holdings.

Cash holdings are sometimes greater and sometimes smaller with the same individual. But nobody ever has cash holdings greater than he wants to have. If he thinks that his cash holding are excessive, he invests the surplus either by buying (producers' or consumers' goods) or by lending it. (Time deposits are one method of lending money.) It is a judgment of value to call somebody's cash holding "hoarding." The individual concerned believes that under the given state of affairs, the best policy (let us say: the minor evil) is to increase his cash holdings. It does not matter whether I approve of his behavior or not. His behavior — not my subjective opinion about its expediency — is a factor influencing the formation of market prices.

It is futile to distinguish between "circulating" money and "idle" money. Money changes hands without being ownerless for any fraction of time. Money may be in the process of transportation, traveling in railroad cars or in other means of transportation. But it is, even from the legal point of view, always in somebody's possession.

In a changing world everybody is under the necessity of keeping an amount of ready cash on hand. This desire creates the demand for money and makes people willing to sell goods and services in exchange for money. A realistic theory of the value and the purchasing power of money must therefore start from a recognition of these desires. The changes in the purchasing power of the monetary unit are brought about by changes arising in the relation between the demand for money, i.e., the demand for money for cash holding, and the supply of money.

The main deficiency of the velocity of circulation concept is that it does not start from the actions of individuals but looks at the problem from the angle of the whole economic system. This concept in itself is a vicious mode of approaching the problem of prices and purchasing power. It is assumed that, other things being equal, prices must change in proportion to the changes occurring in the total supply of money available. This is not true.

It is true that in periods of falling money value, when money is expected to fall further, people will try to reduce their cash holdings to a minimum. But as a universal thing this will be impossible. The total quantity of money remaining the same, or even increasing, somebody must hold it, and the average per capita holding will not decrease. The faster consumers seek to get rid of money, the faster tradesmen must take it in. The average individual cash holding must always be the total supply of money outstanding divided by the population.

What causes prices to go up and down, therefore, is not changes in the average cash holding, but changes in the valuations that people put on the monetary unit. V is not a cause but a result, or even a mere side effect. People who are more eager to buy goods, or more eager to get rid of money, will buy faster or sooner. But this will mean that V increases, when it does increase, because the relative value of money is falling or is expected to fall. It will not mean that the value of money is falling, or prices of goods rising, because V has increased.

When people value money less and goods more, they will offer more money for goods, and may increase "velocity of circulation." But it is not the mechanical increase in velocity of circulation that causes any subsequent price rise, let alone any proportional price rise. It is the changed valuation by individuals of either goods or money or both that causes the increased velocity of circulation as well as the price rise. The increased velocity of circulation, in other words, is largely a passive factor in the situation.

To go further: There is no necessary relation whatever between velocity of circulation and the value or purchasing power of the monetary unit. We can see this clearly if we return to the analogy with other commodities (considering money, for the moment, as it was in its origin, merely one commodity exchanged against others). The relative value of a unit of wheat, or eggs, or potatoes (if we take quality and use for granted), depends mainly on the total relative quantities in existence of these commodities. When any one of them is in short supply, the price per unit goes up; when it is in excessive supply, the price per unit goes down.

These rises or falls may or may not be accompanied by an unusual volume of speculative transactions. But the volume of speculative transactions merely reflects the extent of differences of opinion or changes of opinion among traders in the market; it has no functional relation with either rises or declines of value. Thus a falling wheat market or stock market may be more active than a steady wheat market or stock market. But so may a rising wheat market or stock market.

Similarly, when we turn to money, increased exchanges (i.e., an increased V) may accompany a decline in the value or purchasing power of money. But there will be no necessary relation between the change in velocity of circulation and the extent of the decline in the monetary unit's purchasing power. In fact (though this happens less often), an increase in the velocity of circulation of money may be accompanied by an increase in the purchasing power of money, i.e., by a fall in prices. This can happen in a speculative collapse, as, say, in late 1929.

This bears repetition in slightly different words. Increased velocity of circulation is not, in itself, even a contributing cause of higher commodity prices. It is not even a link in the chain of causation. Increased velocity of circulation and higher commodity prices are joint results of a change in the value of money in relation to the value of goods. When people value money less in relation to goods, they offer more money for goods; when they value it more in relation to goods, they offer less money for goods. Any change in velocity of circulation is likely to be a result of these changed value decisions: it is not itself a cause of the change in value. The value of money does not decline because its velocity of circulation has increased, though the velocity of circulation may increase, when it does so, because the value of money in relation to goods has declined.

\$14

To sum up:

1. Velocity of circulation is a result, not a cause. It is commonly a passive resultant of changes in people's relative valuations of money and goods.
2. Velocity of circulation cannot fluctuate for long beyond a comparatively narrow range, because it is closely tied (except for speculation) to the rate of consumption and production.
3. V does vary with the volume of speculation, but an increased volume of speculation may accompany either rising or falling prices.
4. V is never an independent factor on the side of money, because the transfer of goods must speed up, other things being equal, to an equal amount. It is just as valid to think of the velocity of circulation of money being caused by what happens on the side of goods as by what happens on the side of money.
5. Actually it is psychological factors — desire to buy and sell, produce and consume — that determine V.
6. Monetary theory would gain immensely if the concept of an independent or causal velocity of circulation were completely abandoned. The valuation approach, and the cash holdings approach, are sufficient to explain the problems involved.

Notes

[1] Benjamin M. Anderson, The Value of Money (New York: Macmillan Company, 1917), p. 161.

[2] Ibid., p. 204.

[3] L. Albert Hahn, Common Sense Economics (New York: Abelard-Schuman, Limited, 1956).

[4] Ludwig von Mises, Human Action (New Haven: Yale University Press, 1949), and The Theory of Money and Credit (London: Jonathan Cape, Limited, 1934, and New Haven: Yale University Press, 1953).

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