If there is one concept that illustrates the difference between a top-down macro-economic approach and the reality of everyday life it is the velocity of circulation of money. Compare the following statements:

"The collapse in velocity is testament to the substantial misallocation of capital brought about by the easy money regimes of the past 20 years." Broker's research note issued September 2014; and

"The mathematical economists refuse to start from the various individuals' demand for and supply of money. They introduce instead the spurious notion of velocity of circulation according to the pattern of mechanics." Ludwig von Mises, Human Action.

This article's objective is not to disagree with the broker's conclusion; rather it is to examine the basis upon which it is made.

The idea of velocity of circulation referred to arose from the quantity theory of money, which links changes in the quantity of money to changes in the general level of prices. This is set out in the equation of exchange. The basic elements are money, velocity and total spending, or GDP. The following is the simplest of a number of ways it has been expressed:

Amount of Money x Velocity of Circulation = Total Spending (or GDP)

Assuming we can quantify both money and total spending, we end up with velocity. But this does not tell us why velocity might vary: all we know is that it must vary in order to balance the equation. You could equally state that two completely unrelated quantities can be put into a mathematical equation, so long as a variable is included whose only function is to always make the equation balance. In other words the equation of exchange actually tells us nothing per se.

This gives analysts a problem, not resolved by the modern reliance on statistics and computer models. The dubious gift to us from statisticians is their so-called progress made in quantifying the economy, so much so that at the London School of Economics a machine called MONIAC (monetary national income analogue computer) used fluid mechanics to model the UK's economy. This and other more recent computer models give unwarranted credence to the idea that the economy can be modelled, derivations such as velocity explained, and valid conclusions drawn.

Von Mises's criticism is based on the philosopher's logic that economics is a social and not a physical science. Therefore, mathematical relationships must be strictly confined to accounting and not be confused with economics, or as he put it human action. Unfortunately we now have the concept of velocity so ingrained in our thinking that this vital point usually escapes us. Indeed, the same is true of GDP, or the right hand side of the equation of exchange.

GDP is only an accounting identity: no more than that. It ranks gin with golf-balls by reducing them both to a monetary value. Statisticians select what's included so it is biased in favour of consumer goods and against capital investment. Crucially it does not tell us about an ever-changing economy comprised of successes, failures, and hard-to-predict human needs and wants, which taken all together is economic progress. And because it is biased in its composition and says nothing about progress the value of this statistic is grossly exaggerated.

The only apparent certainty in the equation of exchange is the quantity of money, assuming it is all recorded. No one seems to allow for unrecorded money such as shadow banking, but we shall let that pass. If the money is sound, as it was when the quantity theory of money was devised, one could assume that an increase in its quantity would tend to raise prices. This was experienced following Spain's importation of gold and silver from the new world in the sixteenth century, and following the gold mining booms in California and South Africa. But relating an increase in the quantity of gold to prices in general is at best a summary of a number of various factors that drive the price relationship between money and goods.

Today we no longer have sound money, whose purchasing power was regulated by human preferences across national boundaries. Instead we have fiat currencies whose purchasing power is formalised in foreign exchanges. When the Icelandic krona on 8th October 2008 halved in value, it had nothing to do with changes in the quantity of money or Iceland's GDP. Yet if we try to interpret velocity in this case, we will find ourselves pleading a special case to explain its substantial increase as domestic prices absorbed the shock imparted through the foreign exchanges.

Iceland's currency collapse is not an isolated event. The purchasing power of a fiat currency varies constantly, even to the point of losing it altogether. The truth of the matter is the utility of a fiat currency is entirely dependent on the subjective opinions of individuals expressed through markets, and has nothing to do with a mechanical quantity relationship. In this respect, merely the potential for unlimited currency issuance or a change in perceptions of the issuer's financial stability, as Iceland discovered, can be enough to destabilise it.

According to the equation of exchange, this is not how things should work. The order of events is first you have an increase in the quantity of money and then prices rise, because monetarist logic states that prices rise as a result of the extra money being spent, not as a result of money yet to be spent. With a mechanical theory there can be no room for subjectivity.

It is therefore nonsense to conclude that velocity is a vital signal of some sort. Monetarism is at the very least still work-in-progress until monetarists finally discover velocity is no more than a factor to make their equation balance. The broker's analyst quoted above would have been better to confine his statement to the easy money regimes of the past 20 years being responsible for the substantial misallocation of capital, and leaving out the bit about velocity entirely.

A small slip perhaps on the way to a sensible conclusion; but it is indicative of the false mechanisation of human behaviour by modern macro-economists. However it should also be noted that is impossible to square the concept of velocity of circulation with one simple fact of everyday life: we earn our salaries once and we dispose of it. That's a constant velocity of roughly one.