# Money, Velocity, Levels, and Changes

Back in March 2021, I wrote about the explosive growth of M2. Several commenters noted that part of this increase was offset by the dramatic drop in velocity. I have since pointed out that relying on changes in velocity to offset bad monetary policy was not a good idea. This article discusses the reasons, explains why income velocity may not be the best measure of the rate at which money circulates through the economy, then presents an argument favoring the idea that velocity may have decreased permanently. Along the way I’ll discuss the difference between growth rates and levels of economic variables.  As always, my methods and data are transparent.  Click here to download the Excel workbook.

The income velocity of money is generally defined as nominal gross domestic product divided by the quantity of money in circulation.

In this equation, P is the average price level measured by the GDP deflator, Y is real GDP, and M is the quantity of money in circulation. PY is, by definition, nominal GDP. M is M2. This is a definition. Monetarist economists try to convert it into a behavioral equation by multiplying both sides by M and changing the identity sign into an equals sign (≡ to =).

Velocity is assumed to be a behavioral variable, determined by institutional factors in the banking system and decisions by people and businesses. Intuitively velocity measures the number of times the stock of money is spent during a time period. One major question is how to measure “spending.” That creates the distinction between three measures of velocity: income velocity, spending velocity, and transactions velocity. I’ll discuss each of these.

## Income Velocity

Since May, 2020, when the definitions of M1 and M2 changed, M2 has become the best measure of the money supply. Here’s what has happened to income velocity since 2010.

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During the early days of the COVID pandemic, velocity dropped sharply from in the fourth quarter of 2019 to in the second quarter of 2020. In response the Fed increased M2 sharply, with an annual growth rate of over 20% from the second quarter of 2020 through the first quarter 2021. Let’s put this drop in velocity in perspective to see why this explosive growth in M2 was a good idea (at least for the first two quarters).

In the fourth quarter of 2019, M2 was \$15.2 trillion. GDP was \$21.7 trillion, so velocity was . If M2 had not changed, nominal GDP in the second quarter of 2020 would have been \$15.2 trillion x = \$16.8 trillion, a drop of 22.5%. That’s in the range of the early years of the Great Depression. Not a very good idea. But thanks to the Fed, nominal GDP in the second quarter of 2020 was actually \$19.5 trillion, a drop of “only” 10.2%. Rah, Fed!!

Or maybe not. Let’s consider a simple fact. Between 2019:4 and 2020:2, M2 increased from \$15.2 trillion to \$17.6 trillion. In 2021:1 M2 was \$19.6 trillion. The money created by the 2020 explosive growth in M2 did not evaporate once the crisis has eased. Instead it is the basis for new money growth.

Another counterfactual will illustrate this. As noted earlier, In the fourth quarter of 2019, M2 was \$15.2 trillion, GDP was \$21.7 trillion, and velocity was . If velocity had returned to in the first quarter of 2021 (when M2 was \$19.6 trillion), GDP would have been \$27.9 trillion, fully \$5.9 trillion above its actual level. If you think inflation is bad now, be happy velocity has remained low. I promise that a good chunk of that additional \$5.9 trillion nominal GDP would have been caused by an increase in the price level (inflation).

## Spending Velocity

Regular readers of this blog will understand that this is a misuse of GDP. Gross domestic product measures production, not spending. (If you’d like an explanation, here’s a link to my earlier article on the subject.) The only justification for using nominal GDP in the numerator is the national income accounting identity that says national income equals national product. Spend a few minutes delving into the definition of national income and you’ll quickly learn that there are many items that bear little relationship to money transactions.

A better measure is spending velocity. Gross national spending is consumption plus investment (omitting inventory change) plus government spending. Here’s the spending velocity of money since 2010.

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Spending velocity has the same general shape as income velocity, but its values are about 0.1 greater. That’s because not all income is spent. Some is saved. Including saving in velocity seems wrong. But that’s what the income velocity does.

## Transactions Velocity

But there’s a third measure of velocity: transactions velocity. As far as I know, transactions velocity only exists in theory. That’s because it recognizes that there are many transactions not included in C + I + G. For starters, that’s only spending on final goods and services. We know money is used to pay for intermediate goods (parts that are components of a final good, for example). Then there are asset transactions whose volume dwarfs GDP. In other words, we’d like to measure all transactions in which money is used. (That includes transactions in illegal goods.) As I said earlier, as far as I know no one has tried to measure the total volume of transactions. Transactions velocity is

where T is the money value of all transactions in the economy.

## Growth Rates, Levels, and Common Misconceptions

Here’s the growth rate of M2 since 2010.

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From 2020:2 through 2021:1 M2 grew at rates exceeding 20% per year. By 2020:1 the level of M2 was \$19.6 trillion. From 2021:2 through 2022:1 growth gradually dropped from 15.1% to 10.8%. The important point is that the lower growth rate is still positive, meaning that the level of M2 continued to rise, reaching \$21.7 trillion in 2022:1. This is the important point: as long as the growth rate of anything is positive, the level of that thing will continue to grow. Shrinking M2 requires a negative growth rate.

This idea extends to a number of other areas of economics. For example, the inflation rate is the rate at which the average price level increases. If the inflation rate falls from 10% to 5%, the average price level is still rising. Economists call this disinflation. A decrease in the price level requires deflation, a negative growth rate. For any positive rate of inflation, the average price level is rising.

I’ll just note that even though velocity has not returned to its pre-pandemic levels, it has stopped falling. That means growth rates in M2 become growth rates in PY and C + I + G . Given supply constraints in the U.S. economy, real GDP seems unlikely to grow much. More inflation is on the way.

## Why Has Velocity Remained Low?

This is the remaining question. The answer is the long-term impact of the COVID pandemic and policy responses to it. Spending velocity fell to in 2020:2. It has risen slightly since then but remains well below the level of 2019:2. The reason is the major change in the payments system.

An early misconception about COVID was that it could be transmitted by physical contact and from surfaces. Retail businesses rushed to implement no-contact payment systems. Apple Pay and Google Pay became very popular since customers literally did not have to touch anything except their smartphone. These transactions are mainly financed with credit cards. Similarly, online shopping and home delivery boomed. Walmart and Target began delivering groceries ordered online to homes and businesses. Third-party delivery services such as Doordash and Instacart boomed.

The result of all this was to further erode the link between money and spending. Transactions shifted sharply to credit, with money only used to pay the credit card bill. Money is being spent at a lower rate. This is a decrease in velocity. Further, these changed spending habits are unlikely to change in the near future because they simplify spending. In effect, buying a pair of shoes with Apple Pay costs less than paying with cash or even a physical credit card.

## Conclusion

This stuff is important. Understanding the relationship between money and spending is critical to understanding how an economy works. Knowing how levels of a variable are affected by its growth rate is fundamental. An added bonus from all this is being able to figure out why velocity dropped so abruptly and has not bounced back.