Published by
VOL. XV
No. 2
ECONOMIC
EDUCATION
BULLETIN
February
AMERICAN INSTITUTE
for
ECONOMIC RESEARCH
1975
Great Harrington, Massachusetts
01230
VELOCITY OF MONEY
For many decades economists have been developing
theories that take into consideration the velocity, or rate
of turnover, of money. The various refinements of these
theories have been extensive, and some purport to
account for a general increase or decrease in prices as
being attributable, at least in part, to changes in the
velocity of money as differentiated from increases or
decreases in the quantity of money. In view of the many
misunderstandings that have been widely accepted, a
review of what actually happens under specified circumstances is in order.
Most of the discussions begin with a simple equation:
MV = PT
which is mathematical shorthand for the phrase: during
any period such as a week, month or year, the quantity
of money, M, times its rate of turnover or velocity, V, is
equal to the average price, P, per unit exchanged times, T,
the number of transactions. A modification of this
equation is:
MV + M'V = PT + P T '
thereby allowing specifically for M representing currency
passed from hand to hand and for M' representing the
checking accounts (demand deposits) in use. Other more
complicated equations have been developed to include the
turnover of time deposits and even other so-called money
substitutes.
For the purposes of this discussion we shall focus only
on the simple equation, MV = PT, and shall use the M to
represent what is now widely called Mj , that is, the total
of currency plus demand deposits (checking accounts) in
use.
The customary procedure has been to consider M, V, P,
and T as four variables in a typical mathematical
equation. Then these conclusions are drawn:
a. If M is increased, P will increase unless there are
offsetting changes in V or T or both.
b. If V is increased, P will increase unless there are
offsetting changes in M or T or both.
c. If M and T remain constant, P will increase if V
increases, and P will decrease if V decreases. These
relationships are said to be self-evident from the logical
connections in any equation, and indeed they are if V
and T are independent or substantially independent
variables.
However, what if V and T are not two independent
variables, but there is only one variable designated by
them; i.e., what if they designate two aspects of only one
variable? This is not apparent when the mathematical
equation is separated from or isolated from the real
world. What actually does happen in every situation
where V and T are applicable?
Every purchase involves a sale and every sale involves a
purchase. These are names for the two inseparable aspects
of an exchange in any market anywhere. One cannot have
a sale that does not involve a purchase, nor can one have
a purchase in real life without a sale. We may talk about
purchasers and sellers separately, but neither can exist as
such without the other, neither is an independent variable
capable of performing alone without the other. Necessarily, they have a one-to-one relationship.
In precisely the same manner V and T are aspects of
market exchanges. One cannot have a turnover of money
in any of the multitude of exchanges (purchase and sale)
without simultaneously having the T or transaction aspect
as measured for that exchange. This may be stated in
mathematical shorthand as V/T = 1, or T/V = 1.
Referring now to the original simple equation MV =
PT, this obviously can be transposed to read M/P = T/V,
or = 1 as indicated above. From this it follows that M =
P, or prices generally vary with the quantity of money.
The reader may object that what has been said is
clearly not true. During World War II, the total
purchasing media (currency and checking accounts)
increased greatly, but prices did not increase anywhere
near proportionately until long after the war. Moreover,
some have argued, the velocity or rate of turnover of the
available money supply decreased greatly, and this
accounted for the failure of prices to rise as rapidly as did
M. Anyone offering this argument would be correct, but
this does not disprove the preceding discussion about the
equation, MV = PT.
The equation refers to what happens during a specified
period, whatever that period may be. Obviously, the
equation must be shorthand for: The quantity of money
actually used during the specified period times the rate of
turnover equals the average price paid times the total
number of transactions. If some money were available but
were not used for exchanges during the period, that
portion of the money cannot be included in the standard
equation of exchange. Its velocity would be zero, and any
finite number multiplied by zero gives zero, that is,
nothing to be included in the equation.
During World War II, those working in wartime industrial
plants hoarded substantial portions of their earnings. While
currency was thus hoarded, it could not properly be included in a typical monetary equation. Also during the war
years, many individuals and corporations accumulated idle
checking accounts. They could not buy what they wanted
such as new cars, new houses, or new plant and equipment,
and interest rates on short-term investments were forced so
low by the Federal Reserve System in order to help finance
the war that many individuals and businesses did not bother
to invest idle funds in short-term Government issues.* Such
idle deposits cannot properly be included in any equation
of exchange during the period that they are not used in the
usual manner.
This raises the question: what is the usual manner or rate
of use of currency and checking accounts, and how do
departures from that usual manner or rate of use occur?
For any individual, income can be spent only once during what may be called his income period. For weekly
wages, this period in one week; for monthly salaries, one
month; quarterly, etc. For businesses also, income can be
spent only once per typical accounting period. This period
varies from one day for a supermarket's cash receipts to one
month for businesses that customarily receive payments
from debtors based on monthly billings, and so on. The
variety of income and expenditure periods is great but for
the most part is established by procedures that have
become customary according to the type of business and
that do not change markedly in short periods of time.
Nevertheless, great variations in the turnover of
checking accounts are indicated if debits during any
period, say one month, are divided by the total of average
balances for that period. In the last few years, for
example, the turnover of demand deposits in New York
City banks has reached an unprecedented rate, on the
order of once a day or even more often in some
instances. If velocity or rate of turnover could account
for a general increase in prices, many prices of things
involved in the transfers reflected in the velocity of
money in New York should be sky high; but no such
great increases in prices are observable. A major portion
of the transactions in New York involve purchases and
sales on the stock exchange, but for nearly all of 1973
and 1974 prices of most stocks were declining markedly.
The situation today contrasts greatly with that in
1928-29, when the velocity of demand deposits in New
York approached but did not reach the extremely high
rates reported recently. Then the stock market was rising
rapidly with an increasing volume of trading. Speculation
in common stocks was the outstanding economic feature
of those years. There is no doubt that the great
speculation in the stock market resulted in numerous very
large debits to demand deposits, especially in New York
City, but to some extent elsewhere as well. That the
increasing velocity or rate of turnover of demand deposits
did not result in a corresponding rise in commodity prices
is clearly apparent. Such prices remained below the 1925
peak and then declined sharply late in 1929. But in 1973
and 1974 commodity prices rose rapidly, in fact increased
about 40 percent.
The facts described in the preceding two paragraphs
suggest additional conjectures (hypotheses) concerning the
causes and consequences of increases in the velocity of
money.
First Conjecture:
a. Whenever speculation becomes extreme in some
aspect of economic activity, money in the form usually of
checks drawn on demand deposits moves rapidly from
one speculator to another. Sometimes clearing procedures,
* Discussions of idle purchasing media were presented some years
ago in the Institute s weekly publication, Research Reports,
including the issues for November 15, 1948, May 14, 1956, and
August 24, 1964.
as for the New York Stock Exchange between brokerage
firms, reduce the amount of cash to be transferred, but
the turnover of deposits thus used nevertheless is great.
Examples have been provided during the commodity
speculation of 1919-20, the Florida land boom of the
mid-1920's, the stock exchange speculation of 1928-29,
and to some extent the commodity speculation of 1973
to early 1974.
b. When such speculation is rampant, a large amount
of purchasing media (usually checking accounts or
demand deposits) that otherwise would be circulating in
the usual manner for the purchase of things offered in all
markets is retained in the market where speculation is
focused. There such purchasing media rapidly change
hands from one speculator to another rather than flowing
out into the channels of trade. Unless the total of
purchasing media available is otherwise increased, such
retention of large amounts in the principal speculative
arena reduces the amount available for more usual
purposes and tends to reduce the level of prices exclusive
of those things that are the principal medium for
speculation.
c. Frequently, however, the total amount of purchasing media available is increased by excessive lending
for speculative purposes by the commercial banks. Some
of the additional purchasing media is not retained in the
principal speculative arena but is used by the more
successful speculators for increased purchases of everything from fur coats and diamonds for blondes to new
houses, automobiles, yachts, etc. As this portion of the
additional purchasing media moves out into the channels
of business, the usual symptoms of boom prosperity are
experienced.
Second Conjecture:
a. At times purchasing media may be hoarded or
held idle, that is, not used in the channels of trade at all.
This occurred for both currency and demand deposits on
a very large scale during World War II. One result was
that only the portion of wartime inflationary purchasing
media that was used in the channels of trade (i.e., was
not hoarded or held idle) affected prices. The rise in
prices generally therefore was nowhere nearly comparable
with the increase in total purchasing media available for
use, simply because much of the inflationary or excess
purchasing media was not used but was hoarded or held
idle.
b. Gradually after the end of World War II the
purchasing media held idle during the war were used as
new automobiles and new houses became available and as
new plants and equipment could be purchased. The
velocity of money as usually measured increased almost
continuously as also did prices generally in proportion to
the purchasing media in use rather than in proportion to
total purchasing media (including the decreasing amount
held idle until 1963). During each recession, the
continued availability and use of purchasing media
previously hoarded or idle tended to cut short recessions
and stimulate further business expansion.
Third Conjecture:
a. Many economists believe that increases in saving
reduce the velocity of money. However, the opposite is
true. When transfers are made from current income to
savings, the saver or initial recipient of the income does
not spend the portion saved. However, the person or
business that borrows the saved protion does spend it
promptly. By passing the savings through an intermediary
such as a savings bank, at least one additional turnover of
the amount in a demand deposit results, unless one
assumes that savings intermediaries usually hold idle
additional demand deposits when the savings coming in to
them are increasing. The comprehensive data available
prove that this is not the situation. Therefore, saving
ordinarily results in at least one additional turnover of a
demand deposit than would be the situation if the funds
were not saved. Apparently, savings intermediaries such as
savings banks, the time deposit and savings departments
of commercial banks, savings and loan associations, and
life insurance companies so plan their activities that cash
flows out as rapidly as it comes in, or with negligible
divergences.
b. Clearly, there is no reason why the increases in
velocity attributable to a higher rate of saving should
affect the general level of prices.
c. The remarkable increases in velocity of money
during recent years, with turnover of demand deposits in
New York City reaching unprecedented levels, probably
reflect at least two significant developments:
(1) Short-term interest rates reached extremely
high levels. This made profitable close attention by
comptrollers and other money managers to using any
temporarily unneeded balances for buying short-term
commercial paper or Treasury bills.
(2) A few years ago, most commercial banks
began permitting transfers of temporarily idle checking
accounts to savings deposits on which interest would be
paid provided the deposits were not drawn upon more
than once a month. Naturally, most businesses have taken
advantage of this privilege in order to increase earnings.
CONJECTURES VS. HYPOTHESES
The conjectures described above would by many
inquirers be called hypotheses. We prefer the name
"conjecture" rather than "hypothesis" because it seems to
assist readers in understanding that our use of conjectures
in the course of inquiry differs from what many
theoreticians have been accustomed to doing with
hypotheses.
Hypotheses have been widely used as intermediate steps
to logical or at least purportedly logical reasoning.
Frequently, a logical chain of successive hypotheses is
developed. All too often, inquirers in the past have been
so impressed with the logical chain developed, sometimes
in mathematical form and perhaps even aided by modern
computers, that they have overlooked the tentative nature
of conjectures or hypotheses and their other possible use
in inquiry. The chances of reaching useful conclusions by
the commonly used procedures may be small indeed.*
The procedures of inquiry that we attempt to apply
use each conjecture as a signpost pointing at additional
facts to be investigated before proceeding to the next step
in achieving an adequate description of what happens
under specified circumstances. Sometimes the additional
facts are only different aspects of facts already observed;
sometimes what had been accepted as a pertinent fact is
found not to be pertinent; and sometimes unexpected
facts are found as a result of following the signposts. If
* For example, if an elaborate series of mathematical
equations or shorthand logic is developed for, say, 10
successive conjectures or hypotheses and their logical connections, and if each conjecture were one of 10 possible
conjectures, the chances that the conclusion would be useful
would be .1 x .1 x .1 x .1 x .1 x .1 x .1 x .1 x .1 x .1,
or one chance in 10 billion. Even a much shorter chain of
successive conjectures does not offer favorable odds that the
conclusions wül be useful.
one conjecture does not point to new or different facts,
another conjecture is tried, etc.†
To illustrate what we have done in this connection:
1. With reference to the First Conjecture, above, the
concentration of land speculation in Florida during the
mid-1920's resulted in a high velocity of checking
accounts in that area, and the 1928-29 speculation in
stocks accounted for a high velocity of demand deposits
in New York. These facts have been investigated and
confirm Part a of the conjecture. Part b was supported by
the trend of commodity prices. Part c was supported by
the record of brokers' borrowings.
2. With reference to the Second Conjecture, above,
research revealed that currency was being hoarded and
that some demand deposits were being held idle rather
than used. The measures of these facts found to be
observable were accurate as to orders of magnitude and
supported this conjecture. Part b is supported by the
further continued research that investigated the facts
pointed to by a and b.
3. With reference to the Third Conjecture, above,
the actual cash holdings of financial intermediaries during
the periods when savings were increasing rapidly were
ascertained. The findings supported Part a of this
conjecture. Part b is supported or at least not refuted by
the records of additions to savings and trends of
commodity prices. Part c is supported by some instances
investigated but comprehensive observation of the pertinent facts has not as yet been achieved.
CONCLUSIONS
A leading financial journal has argued that: "If there is
a sharp rise in velocity, even a modest increase in the
money supply can result in a strong upward pressure on
prices.**
The statement continued, "A sharp drop in velocity, on
the other hand, can lead to deflation even if the money
stock, defined as currency and bank checking accounts,
keeps on growing." This is a seriously inadequate
description of what happens under specified circumstances.
The author reports, "Some economists, however,
contend that unexpected changes in velocity can offset
conscientious efforts to stabilize the economy by
promoting a steady and moderate growth in the money
stock." This also refers to an inadequate description of
what happens under specified circumstances. Apparently,
marked changes in velocity reflect extraordinary developments of one kind or another. In some instances, these
have been restrictions on production during wartime and
the resulting lack of new automobiles, new houses, and of
new plant and equipment for peacetime uses. In other
instances, the extraordinary developments have been
extreme speculation in the markets for commodities on
one occasion in this century and for common stocks on
another. In every instance that we now know about, large
changes in velocity (as ordinarily computed) have
† Conjectures are notions or ideas that occur to the inquirer
attempting to solve a problem situation, that is, to describe what
happens under specified circumstances. When unable to make
progress with a useful description for any reason, imagination
provides possible additions to the knowledge available up to that
point. These ideas, notions, or conjectures, when used as guides to
further observation rather than as supposed or seemingly
reasonable solutions to the immediate block in inquiry, are some
of the means by which useful or scientific inquiry is advanced.
** Lindley H. Clark, Jr., "Speedy Money," The Wall Street
Journal, August 26, 1974.
reflected seriously unsound banking procedures when
great inflationary increases in the money supply have
occurred. When an adequate description of what has
happened under specified circumstances is achieved, little
basis is found for believing that changes in velocity have
initiated or are likely to initiate serious money-credit
maladjustments.
One further aspect of the matter should be mentioned.
FIFO and LIFO have become familiar to all cconcerned
with business as abbreviations for "first in, first out" and
"last in, first out" as applied to inventory pricing for
profit and loss and for balance-sheet statements. Less
familiar, as yet, is NIFO, the abbreviation for "next in,
first out." When Germany experienced hyperinflation in
1922-23, merchants finally refused to do business on a
LIFO basis. (Those who had not abandoned FIFO earlier
had become bankrupt.) The time came when a merchant
had to price his items for sale not on a LIFO basis but on
the basis4of what he expected to have to pay for the next
replacements for inventory. Thus was NIFO born of
necessity. Only the merchant who adopted NIFO could
long remain in business.
One result was a frantic scramble to buy in all markets, a
rapid escalation of velocity of money as ordinarily calculated, and an uprush in prices the rate of which far exceeded
the rate of increase in the money supply. Some economists
attributed the phenomenon of prices increasing more rapidly than the money supply to an increase in velocity as the
initiating influence. Surely a more reasonable description of
what happened would be to the effect that increasingly
great increases in the money supply made possible such
increasingly rapid increases in prices that alert merchants
were forced to change from LIFO to NIFO, which in turn
accounted for the increases in prices at a more rapid rate
than the money supply increased.
Finally, the aspects of the money-credit problem
discussed above suggest that monetary order cannot be
restored as long as inflating continues. As long as a
money-credit system is permitted to depart more and
more from sound commerical banking strictly controlled
by the most effective monetary governor, gold, rather
than by political considerations; as long as this situation
continues, the only "progress" will be toward irretrievable
economic disaster.
PUBLICATIONS OF AMERICAN INSTITUTE FOR ECONOMIC RESEARCH
HOW TO AVOID FINANCIAL TANGLES
Section A: Elementary Property Problems and Important Financial Relationships
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Section C: Harvest Years Financial Plan by E. C. Harwood
LIFE INSURANCE FROM THE BUYER'S POINT OF VIEW
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ANNUITIES FROM THE BUYER'S POINT OF VIEW by the Editorial Staff, edited by William B. Kirby
WHAT WOULD MORE INFLATING MEAN TO YOU? by the Editorial Staff
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INVESTMENT TRUSTS AND FUNDS FROM THE INVESTOR'S POINT OF VIEW
by C Russell Doane and Charles W. Hurll, Jr.
THE RUBBER BUDGET ACCOUNT BOOK
THE LOST ART OF COMMERCIAL BANKING by E. C Harwood
USEFUL ECONOMICS by E. C. Harwood
CAN OUR REPUBLIC SURVIVE? Twentieth Century Common Sense and the American Crisis
by the Editorial Staff, compiled and edited by James T. Gibbs
WHY GOLD? by the Editorial Staff, edited by James T. Gibbs
RECONSTRUCTION OF ECONOMICS by E. C. Harwood
CAUSE AND CONTROL OF THE BUSINESS CYCLE by E. C. Harwood
UNDERSTANDING THE "MONEY MUDDLE" And How It May Affect your Family's Future
by the Editorial Staff, under the direction of C. Russell Doane
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