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John Sloan


The concept 'velocity' of money is one of the standard measures' described in economics literature today. I believe the idea that during the course of a year the individual bits of 'money' are used to finance asset exchanges more than once, but no one is collecting actual data on this. I do not think it is even possible to assemble such information. Therefore the theory that relies on knowledge of 'velocity' is just a theory. And the real world results from relying on this theory may be flawed. I give some links to several standard descriptions of 'velocity' and 'quantity theory' and then my comments.

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Frederick Mishkin - Money, Banking & Financial Markets - especially Chapter 19 - The Demand for Money - pgs., 500 -516 - The entire book shows the manner in which current economists rely on mathematical models.

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Lawrence H. White - The Clash of Economic Ideas - especially pgs., 313 - 331 - but the entire book is greatly enlightening by showing we are dealing with multiple 'theories' espoused by competing individuals

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Federal Reserve Blog - Velocity of Money - the official FED definition and its results

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Investopedia - Velocity of Money - another definition with explanatory example

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Wikipedia - Quantity Theory of Money - the general theory that includes ( requires) the theory about the velocity of money


The Quantity Theory of Money -
Mishkin writes: "Developed by the classical economists in the nineteenth and early twentieth centuries, the quantity theory of money is a theory of how the nominal value of aggregate income is determined. Because it also tells us how much money is held for a given amount of aggregate income, it is a theory of the demand for money."
After defining 'velocity' he continues: "Because the Quantity theory of money tells us how much money is held for a given amount of aggregate income, it is, in fact, a theory of the demand for money." We can see this by dividing both sides of the equation of exchange by V, thus rewriting it as

M=1/V times PY where nominal income P x Y is written as PY. He continues for more pages to elaborate theory.
But STOP - another illegal algebraic substitution.

I believe Mishkin knows this also. He proceeds, however, to describe theories espoused by Keynes and Tobin and then Friedman. These theories are critical because on their basis the FED and governments take actions in the real economy involving setting interest rates and attempting to manipulate the 'demand for 'money.'
Lawrence White in his The Clash of Economic Ideas discusses the 'quantity theory of money on pages 314 -331. He presents essentially the same story as Mishkin including biographies of Fisher and Friedman. Interestingly, he looks back for prior efforts related to quantity theory and cites John Locke. But he does not mention Locke's fatal mistake. Locke was the preeminent English philosopher at the time the new Bank of England (coming with the Dutch) was issuing 'perpetuals' - negociable bonds with a fixed annual interest but not to be redeemed. He was asked if these were 'money' and replied that NO - only gold and silver coin was money. But the British Crown financed a century of war on the basis of these 'credit' instruments. They gave the British economy a form of money that did not require the Exchequer to mint coin from scarce silver.


The definition of the 'velocity' of money
Mishkin writes: "The clearest expression of the classical quantity theory approach is found in the work of the American economist Irving Fisher ....- 1911. Fisher wanted to examine the link between the total quantity of money M (the money supply) and the total amount of spending on final goods and services produced in the economy P x Y, where P is the price level and Y is aggregate output (income). Total spending P x Y is also thought of as aggregate nominal income for the economy or as nominal GDP. The concept that provides the link between M and P x Y is called the VELOCITY OF MONEY - the average number of times per year (turnover) that a dollar is spent in buying the total amount of goods and services produced in the economy.
Velocity V is defined more precisely as total spending P x Y divided by the quantity of money M. "

V equals P x Y divided by M
If, for example, nominal GDP (P x Y) in a year is $5 trillion and the quantity of money is $1 trillion, velocity is 5, meaning that the average dollar bill is spent five times in purchasing final goods and services in the economy"
"By multiplying both sides of this definition by M, we obtain the equation of exchange, which relates nominal income to the quantity of money and velocity: M x V=P x Y."
STOP illegal algebra - not allowed to substitute a dependent variable defined in terms of the same variable in an equation.

And Mishkin knows this as he continues with " As it stands, Equation 2 is nothing more than an identity - a relationship that is true by definition. Mishkin proceeds to write several paragraphs describing Fisher's assumptions and theories within theories to justify the conclusion that this can derive a valid 'quantity theory of money'.


The standard formulae that describe the quantity theory are: FISHER'S EQUATION OF EXCHANGE - M x Vt=sum (pi - qi)=pt times q - M is total amount of 'money' in circulation Vt is transaction velocity of 'money' - that is average frequency across all transactions with which a unit of 'money' is spent pi and q- are price and quantity of the i-th transaction.
or M x Vt=Pt times T - in this M is amount of 'money' and Vt is velocity and Pt is price level and T is an index of real value of transactions.
And the Cambridge approach - Md=k times P times Y but lets skip this one
and Milton Freidman's Quantity theory PQ=f(M) and P=g(M) - this merely means that PQ is a function of M and so is P. (what 'function' not mentioned.
"So lets use M times V=P times T


The formula for 'velocity' of money is V=PT (or PQ - or GDP) divided by M - this is the stated way V is calculated according to the Federal Reserve Bank of St. Louis - thus V=PT/M by definition.


By standard algebra we have:
(1) M times V equal PT
(2) V equal PT/M
substituting PT/M from (2) for V in (1) we have
M times PT/M=PT
cancel the two M results in PT=PT
This is no doubt true - but what does it mean?


The above is the inevitable result of V being calculated as a function of M rather than being determined (measured) by a separate collection of data. That is by defining one variable in terms of another variable in the same equation. At this point we can mention also that the quantity of M is measured - but with several different definitions of WHAT is measured - that is what kinds of 'money' are included. 'Money' itself being an abstract concept it can be considered as a real world measure only by including in its definition specific kinds of financial instruments as desired - thus 'cash' - checks - deposits - resulting in a variety of M, M1, M2. M3 (discarded because it is too revealing). But NOT the largest category of all, namely Credit.


The result of this confluence of theories is the misunderstanding of the impact of changes in the quantity of 'credit' as the major component of this 'money'. I stress, the result of all this theoretical games man ship is to enable the FED to ignore the very real economic impact of 'credit' when 'credit' is included as the dominant part of the money supply and then the interest rates established for time value of 'credit' and manipulated. Also, there are many other institutions (companies and such) who have been creating 'credit' in the economy. Considering that since the earliest societies control of the real money supply has been something governments have demanded to do (unsuccessfully much of the time), today private entities creating as 'credit' a major component of the money supply might be considered countefitting.

The references provide several examples using notational transactions. So we do the same here.


Consider a society - and its economy - consisting of 10 producers - consumers - each producing One asset with market value of $1, dollar. And each member desires to exchange (sell and buy) assets with different others. That is, for instance, Mr. A can 'sell' his asset with Mr. J but wants to 'buy' the asset produced by Mr. B. And no one has 'money'.
So Mr. A goes to a 'bank' and borrows a $1 dollar - that is he exchanges with the bank his promissory note stating that he owes the bank $1. and the bank in return gives Mr. A a $1 dollar - (either a lovely piece of silver with a face on it) OR a nice engraved paper stating that the bearer on demand can receive 1 dollar from the bank.
Mr. A then exchanges this dollar with Mr. B so that A has the asset he wants and B has this a negotiable 'dollar'. He then can exchange this with Mr. C for the asset he wants. This continues with exchanges until Mr. J returns the 'dollar' to Mr. A in exchange for the asset Mr. A wants to 'sell', who then retrieves his promissory note from the bank in exchange for return of the 'dollar'.


Now, a Nobel prize wining economist looks at this and sees - (1) ten transactions of produced goods -so GDP is 10 - and (2) this was accomplished with ONE 'dollar' - so obviously the 'velocity' of exchange was 10=M times 10=10


Now, consider a different scenario that accomplishes the same result. Same 10 producer- consumers - same bank. But this time ALL 10 individuals approach the bank and each receives in exchange for an IOU ONE 'dollar' in the form of a piece of silver or a negociable bearer on demand note equal to a 'dollar.. They then perform the asset exchanges as desired, resulting in each individual now having a Different 'dollar' than they had before, whereupon they exchange it back to the bank to retrieve their IOU's.


Now the Nobel prize wining economist looks at this situation and he sees - (`1) there were 10 transactions of produced goods so GDP is 10 and (2) these were accomplished by exchange of 10 'dollars' once each - So M is 10 - thus - 10 times V=10 - ergo V=1.


Of course in the real world the exchanges of assets are conducted by an indeterminate mixture of the two processes. But we do know that 'credit' is a major component of 'money' and that 'credit' has been increasing greatly overall since 1973 with several significant periods of decrease due to FED actions. But note, the transactions also involve a mixture of use of nice silver coins and nice paper bearer notes. But, wait, now increasingly neither form of 'money' is being used - rather the transactions are accomplished by simple book keeping in accounts held by an intermediate. Actually that was the way assets were exchanged in ancient civilizations such as Mesopotamia before the much maligned 'coin' was invented. (Read Aristotle). Governments then sought to keep control of this supply of 'money' by coercion declaring that private minting of such 'coin' was counterfeiting. Likewise the printing of unsanctioned green paper. But during the European Middle Ages the lack of silver (plus danger in carrying it around) resulted in again much commercial transaction being financed by exchange of credit accounts, or 'true bills' between private institutions.
But with the shift to electronic 'money' we find that again all sorts of private institutions are creating 'money'. Even airlines with their 'frequent flyer' accounts. The government does not like this, and has commissioned the so-called Consumer Protection outfit to stop 'pay day lenders' and automobile salesmen, and others as they can from creating 'credit'. The FED hopes to regain total control over the money supply. Coming soon (if they can) the government wants to abolish 'cash' completely.


Another result of the published theories about 'money' , 'velocity', 'credit' and related (especially gold) is the inappropriate mixture of independent and dependent variables on graphs that purport to show something valid about some aspect of how the economy works. See several of these at the above links to the FED and Wikipedia.


We leave for another essay a discussion of 'value', 'money', currency, credit, but recommend readers study Setta von Reden's fine book - Money in Classical Antiquity. She demonstrates ,by using primary sources from ancient Egypt, Greece and Rome, that economies in those societies made full use of credit, had banks, and functioned in ways not generally considered by modern economists or historians.


We also leave a discussion of Mark Skousen's very different theory published in his The Structure of Production. And the whole 'Austrian School' approach to economics. Skousen's basic point is that the establishment economic theory described here leaves out all the intermediate steps in the process of production, which also involve exchanges of assets with use of 'money'.


We can leave for another day a discussion about the desire of various entities (and individuals) to create an international 'money' SDR and substitute it for the 'dollar'. And the related recent recommendations that the US simply abolish cash. And also the powerful effort of the misnamed - Consumer Protection Agency to reduce (prohibit) the ability of private sources to create 'credit' - Pay day loans, auto dealers' credit instruments - mortgage creation.


Return to Xenophon.