Velocity of Money

The velocity of money is the rate at which money changes hands. The Federal Reserve Bank of St. Louis, which publishes the series, defines it as "the frequency at which one unit of currency is used to purchase domestically-produced goods and services within a given time period," adding: "In other words, it is the number of times one dollar is spent to buy goods and services per unit of time."

The point that matters about it is not what it means but where it comes from. Nobody counts transactions per dollar. The published series is a quotient: the Velocity of M2 Money Stock is "calculated as the ratio of quarterly nominal GDP to the quarterly average of M2 money stock," and the Velocity of M1 Money Stock is "calculated as the ratio of quarterly nominal GDP (GDP) to the quarterly average of M1 money stock (M1SL)." Velocity is therefore defined into existence by two other statistics, both of which are measured by other agencies for other purposes.

Follow the arithmetic and one habit of commentary collapses. If velocity is nominal output divided by the money stock, then a fall in velocity means the numerator grew more slowly than the denominator, and nothing more. So a sentence like "prices did not rise because the money supply grew but velocity fell" contains no independent information: the second clause is a restatement of the first observation about output, expressed as a ratio. The published series can describe what happened, and it cannot serve as evidence for why, because it has no source data of its own to bring: it is built from the very numbers whose movement it is being offered to explain. Whether the underlying behavior, how readily households and firms part with the money they hold, drives anything is a real economic question. The measured ratio cannot answer it, and an argument that cites a fall in velocity as the reason output grew more slowly than money has restated its observation rather than explained it.

There is a narrower use that is legitimate, and it is bookkeeping rather than explanation. Velocity is the term that connects the quantity of money to the value of transactions, so it is what makes "more money means higher prices" a conditional claim rather than an identity. Money can grow while measured velocity falls, in which case nominal output need not grow at all. That is a statement about the arithmetic relationship between three published series, not a verdict on how monetary policy works, and the pages on monetary policy and inflation are where that debate belongs.

The most useful practical warning concerns M1 velocity across May 2020. The M1 money stock was redefined that month when savings deposits were reclassified into M1, and the Federal Reserve put the resulting increase at approximately $11.2 trillion. Because M1 is the denominator of M1 velocity, an overnight increase in the denominator produces an overnight collapse in the ratio. The series notes for M1 velocity carry the redefinition in their own text: "Beginning May 2020, M1 consists of (1) currency outside the U.S. Treasury, Federal Reserve Banks, and the vaults of depository institutions; (2) demand deposits at commercial banks ...; and (3) other liquid deposits, consisting of OCDs and savings deposits (including money market deposit accounts)." A chart of M1 velocity spanning that date shows a cliff that is a bookkeeping artifact. M2 velocity is not affected, because M2 was unchanged by the reclassification.

Two smaller cautions follow from how the series is built. It is quarterly, because nominal GDP is quarterly, so velocity cannot be read monthly no matter how monthly the money data are. And it is a unitless ratio rather than a percentage or a dollar amount, so a "velocity of 1.2" is not 120 percent of anything; it is output divided by money for that quarter, on that definition of money.

The calculation is one division, and it can be checked by hand from published series. Take nominal GDP for a quarter and the average money stock for the same quarter, and divide the first by the second.

A hypothetical shows both the mechanics and the trap. The figures below are invented round numbers chosen so the arithmetic is easy to follow, not readings for any real period. Suppose in one quarter nominal GDP is $10.0 trillion and the average money stock is $8.0 trillion. Velocity is $10.0 ÷ $8.0 = 1.25. In the next quarter, suppose nominal GDP rises to $10.2 trillion, a gain of 2.0 percent, while the money stock rises to $8.5 trillion, a gain of 6.25 percent. Velocity is now $10.2 ÷ $8.5 = 1.20. Velocity fell by 4 percent even though output grew, because money grew faster.

Now suppose a commentator reports that "spending slowed because velocity fell." The numbers refute the framing: spending, measured as nominal output, rose 2.0 percent. What fell was a ratio, and it fell because the denominator outran the numerator. The same arithmetic can run the other way. If the money stock had instead been redefined upward by a reclassification, with no change to output at all, velocity would have fallen with nothing whatsoever having happened in the economy. That is precisely what an M1 velocity chart shows at May 2020.

What it is useful for

• It is a compact way to summarize the relationship between the size of the money stock and the value of measured output.
• It makes the link between money growth and nominal spending explicit rather than assumed, which is what turns "more money means higher prices" into a conditional statement.
• The published series is free, quarterly, and computed from named source series, so any reader can reproduce it.

Where it misleads

• It is derived, not measured, so it cannot serve as evidence about anything its own two inputs do not already show.
• Treating a change in velocity as a cause is circular. The change is the ratio of two other changes.
• The denominator's definition has changed, so a long chart is not necessarily one consistent series. M1 velocity has a break at May 2020.
• It is quarterly and unitless, which makes it easy to compare across periods and easy to misdescribe as a percentage.
• Different money measures give different velocities for the same economy, so "the velocity of money" is not a single number without saying which aggregate it uses.