• In this article, I hope to provide readers with a new perspective on one of the great enigmas of economics: the velocity of money. Using some of the basic concepts discussed in previous articles, we will derive a simple model for the velocity of money and examine the implications of this model.

• This simple model for the velocity of money can be used to demonstrate that the velocity of base money is a dependent variable. More specifically, fluctuations in the velocity of base money merely reflect changes in the total market value of real output (V_G q) relative to the total market of the monetary base (V_M M).

• Moreover, the velocity of money is critically dependent upon the value of money. In the slide above, we isolate the “market value of money” V_M by measuring the market value of money in absolute terms using a “standard unit” for the measurement of market value. If the value of money V_M falls, then, all else remaining equal, the velocity of money of money must rise. If money is less valuable (in the absolute) and there is the same amount of base money outstanding, then the monetary base must turn over more times to cover the value of the transactions in the economy.

• At the end of this post, we will briefly discuss a more complex expectations-based model for the velocity of money that is derived from the Discounted Future Benefits Model for Money (a valuation model for money developed in The Velocity Enigma).

Introduction: A New Perspective on the Velocity of Money

The velocity of money is a key concept in economics, primarily because the velocity of money is one of four critical variables in the famous “equation of exchange”. Consequently, any quantity theory of money depends upon some assumption or theory regarding the behavior of the quantity theory of money.

Early proponents of the quantity theory of money argued that the velocity of money was relatively stable over the long term and, therefore, an increase in money supply that was in excess of a corresponding increase in real output over a certain period of time would lead to a rise in the price level.

While quantity theory remains a very useful concept over very long-term time horizons, it fails to be useful in any horizon less than 10-15 years because of the large variations that occur in the velocity of money. The velocity of money (or more specifically, the velocity of the monetary base) has experienced enormous swings over the past fifty years.

Despite much debate and discussion, economics has largely failed to produce useful models for forecasting major shifts in the velocity of money. The focus of this week’s post is to apply the basic principles of The Enigma Series to derive a simple equation for the velocity of money. Hopefully, this simple model for the velocity of money will provide readers with a better understanding of the key drivers of the velocity of money.

While we will discuss this model in more detail later, there are two key points that I want to highlight.

First, the velocity of base money is merely a ratio, a ratio that reflects the total absolute market value of real output transacted in a given period relative to the total absolute market value of the monetary base. If the absolute market value of the monetary base falls, say due to a fall in the absolute market value of money V_M , then the monetary base must turn over more times in order to achieve the same absolute market value of transactions (V_G q). The key to understanding this point is noting that the market value of goods and money can be measured in absolute terms (in terms of a standard unit for the measure of market value), a concept that we shall discuss shortly.

Second, the velocity of money is a dependent variable. In other words, rising velocity of money does not cause inflation; rather, it is simply a dependent variable that responds to changes in other causal variables (it is the changes in these other variables that cause inflation). This view echoes the thoughts of Henry Hazlitt who wrote an article titled “The Velocity of Circulation” (1968) in which he concludes by noting that the “velocity of circulation is a result, not a cause.” Hazlitt further notes that the velocity of money is “a passive resultant of changes in people’s relative valuations of money and goods”, a notion that is clearly supported by the equation above.

In order to understand the simple model for the velocity of money, one must understand how the property of market value can be measured in both the absolute and the relative. So, let’s briefly discuss the measurement of market value and then use this to derive the simple model for the velocity of money.

Deriving a Simple Model for the Velocity of Money

The process of deriving our model for the velocity of money is very simple, however, the conceptual logic behind the model is not. At issue, is the concept of “market value”, or, more specifically, the various ways in which the property of market value can be measured.

The view expressed in The Inflation Enigma, the second paper of The Enigma Series, is that every price is a relative expression of market value. A “price” is merely one method of measuring the market value of a particular economic good. More specifically, it is a way of measuring the market value of one good in terms of the market value of another good.

The problem with measuring the market value of one good (the “primary good”) in terms of the market value of another good (the “measurement good”) is that the market of the measurement good is not constant. The price of the primary good, in terms of the measurement good, can rise either because (i) the market value of the primary good rises, or (ii) the market value of the measurement good falls.

The Inflation Enigma posits that there is an alternative way to measure the property of market value and that is in terms of a theoretical and invariable measure of market value called “units of economic value”. A unit of economic value is merely an invariable measuring stick of market value, just as an “inch” is an invariable measuring stick of length.

By measuring the market value of goods in terms of this invariable measure of market value, we have a way to measure what one might call the “absolute market value” of each good.

The price of the primary good, in terms of the measurement good, can now be expressed in mathematical terms as illustrated in the slide opposite

In our modern money-based economy, the measurement good mostly commonly used to measure the market value of other goods is money. Every “money price” is nothing more than a relative expression of the market value of a good relative to the market value of money. In other words, the price of a good depends upon both the market value of the good itself and the market value of money. As the market value of money falls, then, all else remaining equal, the price of the good, in money terms, will rise.

This microeconomic theory of price determination can be easily extended to a macroeconomic theory of price level determination called the “Ratio Theory of the Price Level”. In essence, Ratio Theory states that if the market value of money is the denominator of every “money price” in the economy, then the market value of money must be the denominator of the price level.

If the market value of money V_M falls, then the price level rises. Conversely, if the overall absolute market value of goods V_G falls (for example, due to global competition in goods markets), the price level falls.

Once “Ratio Theory” is established, deriving the simple model for the velocity of money is very straightforward. First, we take the equation of exchange. Then, we substitute for the price level p in the equation of exchange with the ratio of two absolute market values described by Ratio Theory. Finally, we rearrange this new equation to solve for the velocity of money.

What Determines the Velocity of Money?

We can use this simple model for the velocity of money to think in broad terms about what causes changes in the velocity of base money.

The model presented above suggests that the velocity of the monetary base depends on four key variables. Let’s think about how a change in each of these variables, all else remaining equal, might impact the velocity of base money.

1. Real output (“q”): all else remaining equal, if real output increases, then the velocity of money must increase. This should be a common sense result: if there is more activity in the economy, then each unit of base money needs to circulate more times.
2. Monetary base (“M”): all else remaining equal (most notably, the market value of money), if the monetary base increases, then the velocity of the monetary base will fall. We have seen a good example of this phenomenon in recent times: as the Fed increased the monetary base, the velocity of money fell.
3. The market value of money (“V_M”): all else remaining equal, a fall in the value of money will lead to a rise in the velocity of money. The logic is simple: if there is a certain value of transactions to be done in the economy (V_G q) and a fixed amount of base money (M), then a fall in the market value of money (V_M) will necessitate a rise in the number of times each unit of base money must change hands in order for all the transactions in the economy to be completed.
4. The market value of the basket of goods (“V_G”) or the “general value level”: all else remaining equal, if the absolute market value of the basket of goods V_G falls, then each unit of money needs to change hands fewer times in order to complete the total absolute market value of transactions in the economy.

The simplified examples above each assume “all else remaining equal”. But what happens if a change in one of the four variables also causes a change in another of the four variables. For example, what happens to the velocity of money if an increase in the size of the monetary base triggers a fall in the value of money?

In this scenario, it will depend on the relative moves. If the value of money falls by less (in percentage terms) than the increase in the monetary base, then the velocity of money will fall. However, this fall in the velocity of money will still be accompanied by an increase in inflation. Why? Assuming the absolute market value of goods is constant, inflation will rise because the value of money has fallen (see Ratio Theory slide).

As discussed earlier, this simple model for the velocity of money accords with Hazlitt’s general idea that the velocity of money is a dependent, not a causal, variable. Moreover, the velocity of money merely reflects the relative valuation of goods and money. In general terms, as the total value of economic activity rises, the velocity of money rises. Conversely, as the total value of the monetary base falls (as measured in absolute terms), the velocity of base money must rise in order to cover the same total value of economic activity.

An Expectations-Based Solution for the Velocity of Money

While this simple model for the velocity of money is interesting, it doesn’t say much about the role of expectations in the determination of the velocity of money. Importantly, it doesn’t have much to say about what determines the market value of money.

The view of The Enigma Series is that the market value of money is determined by a complex set of long-term expectations. This idea has been discussed in two recent posts: “Money as the Equity of Society” and “A Model for Foreign Exchange Rate Determination”.

As discussed in both of these posts, the view of The Money Enigma is that base money represents a long-duration, proportional claim on the future output of society. Using this theory, The Velocity Enigma (the third paper in The Enigma Series) derives a valuation model for money called the “Discounted Future Benefits Model for the Market Value of Money”.

We can use this valuation model for money to create an expectations-based solution for the velocity of money

The view explored in The Velocity Enigma is that the value of money depends primarily on the expected future path of the “real output/base money” ratio. Since the velocity of money is negatively correlated with the value of money (remember the simple model above), we can say that the velocity of money is correlated with the expected future path of the “base money/real output” ratio.

Let’s apply that idea to our present circumstances. The monetary base has increased and this has been accompanied by a fall in the velocity of money. Why? The velocity of money has fallen largely because the value of money has remained stable while the monetary base has risen.

However, what happens if the market begins to revise up its expectations for long-term base money growth and revise down expectations for long-term real output growth? The value of money will fall, the price level will rise and the velocity of money will rise.

This is the very real risk that policy makers face today. So far, the price level has remained contained while an increase in the monetary base has been absorbed by a fall in the velocity of money. But should expectations suddenly shift, for example, should the market suddenly become more pessimistic on the outlook for the US economy, the value of money could decline sharply, leading to a sharp rise in the velocity of money and an outbreak of severe inflation.