Several people have written recently telling me that price inflation is under control only because the velocity of money (the alleged rate at which money circulates) is falling.

Reader Mark pinged me with this statement “Falling velocity is deflationary. It indicates people are saving their cash.” Others have expressed similar opinions, typically in reference to this chart by the Fed.


Discussion of Ratios

That chart looks ominous. Is it?

First, please note the chart says velocity is a “ratio”. A ratio of what?

Velocity = Value of Transactions/Supply of Money.
The value of transactions = Price * Transactions.
In other words
V = (P)(T/M) where V stands for velocity, P stands for average prices, T stands for volume of transactions, and M stands for the money supply.

Multiplying both sides by M  yields the frequently cited equation: M(V) = P(T).

Economists use real GDP as a measure of P(T).
Thus M(V) = GDP. And of course V = GDP/M

The ratio in the above chart is Real GDP/M2.  Clearly velocity is falling.

Velocity Theory

The widely presented theory is “prices will rapidly rise if velocity increases.” One problem with making such assumptions is in regards to measurement.

What is Money? Is it M1, M2, M3 (discontinued), MZM, TMS1, or TMS2? Each one will give you a different measure of velocity. The Fed provides Three Measures of Velocity.

And what about GDP? Recall that government spending, no matter how useless, adds to GDP. If the government paid people to spit at the moon it would add to GDP by definition. And as stupid as that sounds, it would have been less destructive than bombing Iraq to smithereens, making enemies in the process, and reducing the supply of oil at the same time.

If GDP is debatable and money is debatable, and prices cannot be precisely measured in the first place, can velocity mean much?

Three Important Statements Regarding Velocity

  1. Velocity is falling because money supply is rising faster than GDP. 

  3. If the Fed stops printing (more precisely if money supply is constant) and GDP goes up, velocity will go up automatically. Prices could actually drop with rising velocity if the volume of transactions goes up enough to make up for it!

  5. As an implied result of statements one and two, we can correctly deduce that rising or falling velocity will not cause anything in particular to happen to prices.

Is Velocity Like Magic?

Also consider some similar observations made by Frank Shostak in the Mises Daily article Is Velocity Like Magic?

Velocity Has Nothing To Do With the Purchasing Power of Money

Does velocity have anything to do with prices of goods? Prices are the outcome of individuals’ purposeful actions. Thus John the baker believes that he will raise his living standard by exchanging his ten loaves of bread for $10, which will enable him to purchase 5kg of potatoes from Bob the potato farmer. Likewise, Bob has concluded that by means of $10 he will be able to secure the purchase of 10kg of sugar, which he believes will raise his living standard.

By entering an exchange, both John and Bob are able to realize their goals and thus promote their respective well-being. In other words, John had agreed that it is a good deal to exchange ten loaves of bread for $10, for it will enable him to procure 5kg of potatoes. Likewise, Bob had concluded that $10 for his 5kg of potatoes is a good price for it will enable him to secure 10kg of sugar. Observe that price is the outcome of different ends, hence the different importance that both parties to a trade assign to means.

In short, it is individuals’ purposeful actions that determine the prices of goods and not some mythical notion of velocity.

Consequently, the fact that so-called velocity is “3” or any other number has nothing to do with average prices and the average purchasing power of money as such. Moreover, the average purchasing power of money cannot even be established. For instance, in a transaction, the price of $1 was established as one loaf of bread. In another transaction, the price of $1 was established as 0.5kg of potatoes, while in the third transaction the price is 1kg of sugar. Observe that, since bread, potatoes, and sugar are not commensurable, no average price of money can be established.

Now, if the average price of money can’t be established, it means that the average price of goods can’t be established either. Consequently, the entire equation of exchange falls apart. In short, conceptually, the whole thing is not a tenable proposition, and covering a fallacy in mathematical clothing cannot make it less fallacious.

Velocity Does Not Have an Independent Existence

Contrary to mainstream economics, velocity does not have a “life of its own.” It is not an independent entity–it is always value of transactions P(T) divided into money M, i.e., P(T/M). On this Rothbard wrote: “But it is absurd to dignify any quantity with a place in an equation unless it can be defined independently of the other terms in the equation.” (Man, Economy, and State, p. 735)

Since V is P(T/M), it follows that the equation of exchange is reduced to M(PxT)/M = P(T), which is reduced to P(T) = P(T), and this is not a very interesting truism. It is like stating that $10=$10, and this tautology conveys no new knowledge of economic facts.


Most of the discussion to date regarding the velocity of money has been ridiculous.

  • Velocity can rise when prices are going up
  • Velocity can fall when prices are going up
  • Velocity can rise when prices are falling
  • Velocity can fall when prices are falling

Given GDP = P(T), you can repeat the above four statements substituting GDP for prices. Doing so, please note that rising prices with falling GDP would be the dreaded stagflation scenario, something Keynesian theory once suggested was “impossible”.

In short, it may very well be that prices rise with rising velocity, but they may also rise with falling velocity. Thus …

Velocity is an essentially meaningless result in an essentially meaningless equation. Rising or falling velocity will not cause anything to happen.

Yet, the debate over the importance of velocity rages on.

Mike “Mish” Shedlock