The Money Velocity Myth

Popular Imagery of Money on the Move

For most financial commentators an important factor that either reinforces or weakens the effect of changes in the money supply on economic activity and prices is the “velocity of money”.

An image from an article on the intertubes that “explains” the velocity of money (one of the articles we came across started out as follows: “The economy runs smoothly only when there is enough money in circulation. How much is enough?”  The effect reading this has on us is not unlike that produced by the sound of fingernails scraping a chalkboard). We have found that many people find it extremely difficult to wrap their mind around the fact that the velocity concept actually doesn’t make sense, and that the matter has to be viewed from a different perspective. As an aside, we have noticed in discussions that even those who do eventually accept that a different conceptual approach is required, often insist on continuing to use the term because it “doesn’t matter what we call it”, or “to keep things simple” and similar excuses. It makes one feel like a priest trying to exorcise a particularly stubborn demon.

It is alleged that when the velocity of money rises, all other thing being equal, the buying power of money declines (i.e., the prices of goods and services rise). The opposite occurs when velocity declines.

If, for example, it was found that the quantity of money had increased by 10% in a given year, — while the price level as measured by the consumer price index has remained unchanged — it would mean that the velocity of circulation must have slowed by about 10%.

The Mainstream View of Money Velocity

According to popular thinking the idea of velocity is straightforward. It is held that over any interval of time, such as a year, a given amount of money can be used again and again to finance people’s purchases of goods and services. The money one person spends for goods and services at any given moment can be used later by the recipient of that money to purchase yet other goods and services.

For example, during a year a particular ten-dollar bill might have been used as follows: a baker by the name of John pays the ten dollars to a tomato farmer, George. The tomato farmer uses the ten dollar bill to buy potatoes from Bob, who uses the ten dollar bill to buy sugar from Tom. The ten dollars in this example served in three transactions. This means that the ten-dollar bill was used 3 times during the year, its velocity is therefore 3.

The chart above depicts the quantity equation fudge factor… err, the velocity of the narrow money stock M1. As an aside, although the “V” charts of the official monetary aggregates essentially look very similar, in the broader aggregates (which include savings accounts, as well as a number of credit instruments), “V” began to decline much earlier already – namely around the time the first major global monetary policy-induced crisis of the post 1970s era started, i.e., the Asian crisis (note that previous post 1970s crises of this sort were not global in scope, such as e.g. Mexico’s peso crisis). The scale of the V graph of M2 is very different (because M2 is much larger), so we haven’t included it here, as it would be hard to compare visually. It wouldn’t contribute anything w.r.t. the principles under discussion anyway, as the theoretical points to be made about money velocity apply to all depictions of it. As we point out further below, these charts may be interesting from an economic history perspective though.

Velocity of M1 Money Stock, 1960 - 2017

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The importance of money as an economic indicator however diminishes once velocity becomes less stable and hence less predictable. It is held an unstable velocity implies an unstable demand for money, which makes it so much harder for the central bank to navigate the economy along the path of economic stability.

Now consider this chart, which depicts the broad US true money supply TMS-2 (black line), nominal GDP (red line) – both indexed – and the “velocity” of M1 (the formula is simply [nominal GDP/money stock]).  What does this really tell us? Consider in particular the time period within the blue rectangle (which coincides with the sharp decline in “V”), and compare it to the preceding era. The trends within the rectangle essentially tell us “the Fed printed a lot of money, which did not translate into equivalent GDP growth”. Well… duh (if it had, we would actually not have experienced a lot of growth, but a runaway surge in consumer prices – remember that nominal GDP is employed in the calculation). Moreover, prior to the GFC, when the creation of additional money was largely accomplished by fractionally reserved banks expanding credit, GDP growth merely tracked the pace of monetary inflation (this fact is actually worth a separate article). What can not be concluded from this chart is that “velocity” has any meaning besides being a fudge factor in the tautological “equation of exchange”. In short, the empirical data appear to be in line with what economic logic already tells us. Obviously,  the demand for money (i.e., the demand for holding cash balances) will be a major driver affecting the purchasing power of money, ceteris paribus. Since society as a whole  cannot lower its cash balances (someone always has to hold the existing money stock), a decline in the demand for money will simply result in a decline of its purchasing power. When people lose confidence in government-issued money –  which usually happens after its supply has increased at an uncommon pace for a considerable time period and a sufficiently large number of people abandons the belief that the expansion will ever stop –  this may well show up in “velocity” charts, particularly in the final stage of an inflationary process, when the monetary system begins to break down (currently observable in Venezuela). This will mainly indicate that a “flight into real values” has commenced and that the collapse in purchasing power is beginning to exceed the speed at which new money is printed. This is a typical feature of such end games  – concurrently with deep contractions in real economic output. The main point is that the associated surge in “velocity” would be a symptom, not a cause.

TMS - 2, Nominal US GDP and Velocity of M1, 1988 - 2017

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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 one dollar was established as one loaf of bread. In another transaction the price of one dollar was established as 0.5kg of potatoes, while in the third transaction the price is one kg 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. Conceptually the whole thing is not a tenable proposition and covering a fallacy in mathematical clothing cannot make it less fallacious.

The only knowledge we can have of the determinants of price is the knowledge deduced logically from the axioms of praxeology. Mathematics can at best only translate our previous knowledge into relatively unintelligible form.

Even if we were to accept that the essential service of money is its speed of circulation, there is no way that this characteristic of money could explain the purchasing power of money. On this Mises explains in Human Action:

Even if this were true, it would still be faulty to explain the purchasing power — the price — of the monetary unit on the basis of its services. The services rendered by water, whiskey, and coffee do not explain the prices paid for these things. What they explain is only why people, as far as they recognize these services, under certain further conditions demand definite quantities of these things.

TMS - 2 and Nominal GDP, 1986 - 2017

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