About that velocity thing again

Yesterday, I wrote an extensive post on why I think the quantity theory of money is obsolete and should not be used to forecast inflation. Yet, unlike the cases when I criticise CAPM or PPP and other empirically unreliable theories, I get way more reader comments and criticism when I dunk on monetarist theories. It seems there is much more passionate believe in these theories than in others.

So, for today only, I want to entertain the many readers who still read my missives even though they disagree with my views and employ the concept of velocity of money to try to understand where inflation may be heading in the next couple of years. I think these readers deserve a lot of applause because reading other people’s opinions and trying to understand their arguments can only improve your thinking. So, as a special bonus for these readers I will break my empiricist habits and discuss a theory’s predictions for real life outcome. I promise, I am fine and not in need of medical help. Normal service will resume tomorrow.

Yesterday, I showed the chart below that shows the velocity of money and how it has declined for the last 30+ years. So, let’s think about where this chart might trend…

Velocity of money

Source: Bloomberg. Note: Velocity of money based on M2

In order to think about the velocity of money, I prefer to think along a modified model described in this paper.  It’s a simple model that only requires first year economics knowledge to understand, so feel free to read the whole thing if you are so inclined.

The model realises that in the original formulation of the quantity theory of money by Fisher (and yes, I know that the theory can be traced back to Ricardo, Hume and others, but Fisher was the first one to write down the equation in the way we use it today) the model assumes that there is no debt. In real life, however, money is created in two ways. First, banks create money by getting base money from the central bank and multiplying this into broader forms of money through the miracle that is fractional reserve banking. But banks also lend money to businesses and households. Thus, they create ‘money’ through lending. Essentially all forms of money whether broad money or debt are just two sides of the same thing. But the velocity of money is different for money and debt. Because loans are typically fixed in terms of maturity with penalties associated with early repayment, the velocity of debt is generally lower than the velocity of money (in which I mean broad money like bank deposits, short-term deposits, as well as cash). So, Fisher’s formula P * Y = M * V can be rewritten as:

P * Y = M * Vm + D * Vd

Where P is the price level, Y the output of the economy, M is the monetary base, Vm is the velocity of money for the components of this monetary base, D is the debt level in the economy and Vd is the velocity of debt (i.e. how fast debt is rolled over into new debt).

Now, we can start to think about the change in the two velocities over the coming years. One key driver is inflation and the changes in interest rates triggered by it. With inflation rising, holding cash and other non-interest paying forms of money becomes more costly. So the velocity of money Vm should start to increase. This is the normal process we see during every business cycle. In a recession, people hold on to their cash and falling interest rates and inflation make holding cash less costly than in normal times. As inflation rises and interest rates increase in an economic recovery, the cost of holding cash and other forms of money rises and the velocity of money increases again. I would suspect that this was a major driving force behind the increase in the velocity of money in the 1990s visible in the chart above.

But if you look at the second term in our equation, the velocity of debt, this will decline when interest rates rise. As interest rates rise, it will become less and less attractive for households and businesses to refinance their debt early and replace longer maturity debt with shorter maturity debt. On the other hand, when interest rates drop, refinancing a home mortgage can be beneficial even if there are penalties involved for early repayment of the loan. So, you see that as interest rates rise, the velocity of money Vm rises, while the velocity of debt Vd drops.

Whether the overall velocity of money increases or decreases depends on the relative change in Vm and Vd as well as the relative size of the stock of money and the stock of debt. I do not know by how much the velocity of debt will decline and how that compares to the increase in velocity of money. But I do know that over the last 20 years the ratio of debt to money has increased significantly. That means that relative to the 1990s the velocity of debt has increased in influence and the velocity of money has decreased in importance. If this view is correct, it could explain why since 2000 after every recession (2001, 2009, 2020) the recovery in the overall velocity of money became weaker and weaker. We have piled up more and more debt in our economy and that becomes a drag on the overall velocity of money. And of course since the change in price level (i.e. inflation) is to a large part driven by the change in overall velocity of money, the theory predicts that with more and more debt in the economy, inflation should be lower and lower over time.