Steve Bain

The Income Velocity of Money

As an introduction to the concept of ‘velocity of money’ I should start by clarifying that in this article I am referring to the income velocity of money rather than the transactions velocity. There are some technical differences, but there is no difference in conceptual meaning or policy implications.

For anyone who needs to dig into the weeds, the PDF link at the bottom of the page includes details on the technical differences between the two. As a heads up, the difference refers to the two slightly different quantity theory of money equations that you may have come across: MV=PY and MV=PT.

Serious difficulties arise even with the seemingly simple task of measuring income velocity in the first place, because it cannot be measured directly and has to be inferred from measuring other variables. Putting these difficulties aside, lets delve into the much more interesting philosophical debate between competing economic schools of thought.

Debate has raged for decades about the velocity of money and its relevance to macroeconomic policy formulation. The key issue relates to whether or not velocity can be relied on to be stable in the short-term, because this has key implications for the influence of monetary policy in the fight to control inflation.

United States M2 Velocity of MoneyUnited States M2 Velocity of Money since 1960.

As explained in my article about the Quantity Theory of Money, MV=PY is actually an accounting identity. It simply means that the stock of money in the economy, multiplied by the number of times that it is spent in a year, is equal to the total amounts of goods produced in that economy over that year, multiplied by the average price of goods.

It is not controversial to hold Y (economic output i.e. goods produced) constant in the short-term when the economy is in equilibrium and with unemployment at its natural rate. As mentioned, the controversy is all about whether or not V, the velocity at which the money stock circulates through the economy, can also be expected to be stable under this equilibrium.

There’s no doubt that velocity can change significantly when equilibrium is disturbed, and no doubt either that it can change over the longer term even when in equilibrium, but the monetarist school of economics contends that velocity is stable in the short-term under equilibrium.  

Interest Rates, Money Demand and Velocity

As explained in my article about the LM Curve, the demand for money is negatively related to the interest rate. This is because the interest rate is basically the price of holding money or spending it on consumption today i.e. if I save it for a year I can earn interest on it and increase its purchasing power. The higher the interest rate, the higher the cost of current consumption, and therefore the lower that the demand for money will be.

The diagram below is taken from my page about the LM curve and for a refresher on how the model works please refer to that page. If you are comfortable with the model then consider how velocity is affected by an increase in the money supply when income/output (Y) is constant and the price level (P) is constant.

The demand for money with fixed income/output

The real money supply increases from M1/P to M2/P, causing a fall in the interest rate from R1 to R2. At the lower interest rate money supply equals money demand, as shown by the downward sloping money demand curve L.

Since M has increased whilst P and Y are held constant, it must be that V has decreased. This is self-evident from the accounting identity MV=PY.

So, under these assumptions we can deduce that the demand for money is inversely related to the income velocity of money. A higher demand for money caused by a lower interest rate and increased money supply, will cause a lower velocity of money for any given level of output (Y) and prices (P).

It follows from this analysis that velocity is positively related to the interest rate. From this, economists began to model velocity as a function of interest rates and output, and went on to argue that in a state of equilibrium, with a stable level of Y and a stable interest rate, it must be that velocity is also stable.

With a stable velocity and output level under equilibrium, it means that any increase in the much more unstable money supply (which is largely influenced by banking sector credit creation) must result in an increasing price level. Thus the monetarists argued for strict control of the money supply as a means of controlling inflation.

Long-term data trends supported the idea that velocity was a function of interest rates and output until the early 1980s, after which time the relationship broke down. This breakdown has been the main counter to the whole monetarist theory of inflation.

Monetarist Velocity of Money Theory

Milton Friedman has outlined his theory on the demand for money, and by association the velocity of money, as depending on many more variables than output and interest rates alone. His point is that these other variables are relatively slow to act, and play only a minor role in the short term.

The most important of these factors is:

Wealth – the idea here is that spending reacts less to changes in income if they are seen as temporary, and more to people’s idea of what their long-term income is likely to be. This is the permanent income hypothesis, and whilst it is difficult to estimate directly what level of income people will perceive themselves to have in future years, their wealth might serve as a proxy.

The data that has been collected here has not been overwhelmingly convincing, and you can read more about this via the PDF link below. Nevertheless, the theory does have a logic that is difficult to dismiss, and the data on wealth that has been collected is fraught with problems, so perhaps we shouldn’t place too much stock in the disappointing results here.

Regardless of the ability of the permanent income hypothesis in establishing a new basis for believing that velocity is stable, it does appear that the income velocity of money is capable of significant movement over the short-term, and for reasons that cannot be modeled.

It seems that there is a significant problem with building inflation forecasts based on empirical evidence alone, and just because the quantity theory of money has been successfully applied retrospectively to show that inflation spikes in the past have always been the result of excessive growth in the money supply, that doesn’t necessarily prove that inflation will always result from money supply growth.

This does not mean that I am siding with the Keynesians, it just means that the monetarist theory looks incomplete. The best approach to forming rational economic forecasts seems to be to adopt the Austrian approach, and try to think in a logical fashion given all available information about any specific problem.

Other variables that may affect velocity

At the current time, following the global pandemic, the west has experienced rapid growth in its money supply as governments have printed huge sums of money to fund fiscal stimulus packages. 

Monetary policy has more or less been operating on a peddle-to-the-metal basis too, but ever since the 2008 financial crisis the US and UK have been in a liquidity trap – meaning that expansion of base money by the central banks has not led to a significant increase in lending via the high street banks. This in turn means that there is a serious lack of any money multiplier effect from the banking system, and therefore monetary policy boosts have been of limited effect.

Clearly, in a liquidity trap, money supply growth alone is unlikely to cause significant inflation, but it remains to be seen how long the trap will remain. If the trap exists because interest rates are so low that the banking sector is reluctant to make risky loans for little return, then what happens if the central banks start to raise interest rates - will we see a surge of new lending given the very large growth in base money already created by the central banks? If so then recent falls in velocity might be reversed, with huge pressure on prices to rise as predicted by quantity theory.

Velocity of money does seem to be affected by market sentiment, business confidence and consumer confidence. All of these factors have taken a hit because of the pandemic, not so much from younger people but certainly from older people and those most vulnerable.

The lockdown itself has obviously caused a direct reduction in velocity, because with people locked in their homes they are unable to get to shops, restaurants, bars, gyms and sporting facilities, none of which have been open for business anyway. Online spending has picked up, partly mitigating the lockdown, but overall velocity is down very sharply.

Then there is the long-term deflationary background that has been driving a gradual decline in velocity since the 1990s. Demographic changes such as an aging population and low birth rate have reduced the velocity of money.

There are of course many more factors to consider before forecasting higher inflation based on money supply growth. There have been serious supply chain issues that have affected prices, some of these issues will be resolved, others will remain. Then there is growing debt levels and the burden that they bring. There’s also the seemingly endless trade deficit, and budget deficit. Let’s not forget that the strength of our western currencies is also under the spotlight, with a strong possibility of depreciation that will impact prices.

The list goes on, and whilst the velocity of money and the quantity theory of money will continue to have relevance in normal times, should normal times ever return, we need to recognize that current times are far from normal, and old economic models built on historical evidence, whilst useful, are far from complete.


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