Bryan Caplan  

What Is Money Velocity?

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A key feature of the financial crisis was a massive fall in the velocity of money.  But what exactly is "money velocity"?  By definition, V=PY/M.  In English: Velocity=Nominal Income divided by the Money Supply.  When asked for some intuition, economists often respond that velocity is the "average turnover" of a dollar.  A velocity of 2, for example, means that the average dollar gets spent twice per year.  Except in a world without resale, however, this explanation is incorrect.  Suppose all new production ceased.  Money would still "turnover" as assets change hands, but nominal income would be zero - and velocity would be too.

I think I have a better way to explain velocity.  Forget turnover.  Velocity is the inverse of the percentage of income that people keep in the form of money.  If nominal income is $100B and the money supply is $10B, then velocity is 10 - which means that average money holdings equal 10% of annual income. 

Velocity is therefore essentially a measure of income-adjusted money demanded.  The higher velocity, the lower income-adjusted money demand.  When velocity plummets, as in 2008, this means that income-adjusted money demand has spiked.

What measure of money do I have in mind?  All of them.  For every monetary aggregate, there is a corresponding velocity.  Velocity of the monetary base might equal 100, indicating that people hold 1% of their annual income in (cash plus reserves).  Velocity of M3 might equal 2, indicating that people hold 50% of their annual income in (cash plus reserves plus checkings plus savings plus whatever).  Usually the various velocities move in tandem, but they don't have to.

Pedagogically, the best feature of my explanation is that you can calculate person-specific velocities.  If a student has annual income of $10,000, and on average holds $2000 in cash plus checking, then his corresponding velocity for M1 equals 5.  You can then ask the student questions like: What would happen to your velocity if interest rates fell?  If credit cards became more widely available?  If you suddenly got nervous about your financial security?

Once the student "gets" the microeconomics of his own velocity, it's a lot easier to grasp the macroeconomics of velocity.  There's just one crucial intellectual bridge to cross: An individual can reduce his personal velocity simply by increasing his money holdings; for people in general to reduce velocity, in contrast, there has to be a corresponding change in nominal income (unless, of course, the quantity of money changes).  So if the average person decides he'd rather hold 40% of his income in the form of cash rather than 20%, and everything else stays the same, the nominal income of the economy has to halve.

Economists occasionally dismiss MV=PY as a mere tautology.  Whenever I've taught macroeconomics, however, I've found that it's an immensely useful tautology - especially once students intuitively understand all four variables in the equation.


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COMMENTS (19 to date)
Doc Merlin writes:

I find some of the most powerful truths are tautological in nature.

E. Barandiaran writes:

You write
"I think I have a better way to explain velocity. Forget turnover. Velocity is the inverse of the percentage of income that people keep in the form of money. If nominal income is $100B and the money supply is $10B, then velocity is 10 - which means that average money holdings equal 10% of annual income."
That's exactly what I learned more than 40 years ago and what I used to teach in my courses in the 1970s. I learned it from work on hyperinflation by P. Cagan, Gordon Tullock (he wrote in the 1950s about hyperinflation in China), and others. The only problem was, and still is, the relevant definition of money (as Friedman and many others acknowledged you want to identify a stable demand for money but as shown later by Charles Goodhart and others there is no aggregate for which we can claim a stable demand).

Bill Woolsey writes:

Bryan,

It is an equilibrium condition following from
Ms = Md.

As you explain, Md = kY

Ms = Md

Ms = kY

k = 1/V (definition)

MsV = Y

Y = Py (definition)

M = Ms (convention to drop the "s")

MV = Py

Tautology Ms = Md because all existing money is held by someone.

Equilibrium condition Ms = Md because people will adjust their spending until desired balances equal actual balances.

These ideas are the fundamental ideas of monetary theory.

Bill Woolsey writes:

Bryan,

You might appreciate this.

Thinking about income adjusted money demand requires not only that the services from holding money is a normal good, but that it is exactly on the cusp between being a luxury and a necessity.

Bill Woolsey writes:

A measure of the quantity of money with a "stable" demand is only the holy grail if you think it is possible and desirable to control that measure of the quantity of money. Keep M2 on a stable growth path, and then macroeconomic stability is achieved. Oh.. M2 doesn't work. Let's find the holy grail...

If one gives up on a money supply rule, then the "stable" money demand function remains important if you want to manipulate "the" quantity of money to stabilize something. You observe changes in things that impact money demand in a predictable way, then you make adjustments in the quantity of money to offset them and, again, you have achieved macroeconomic stability.

However, if your only purpose is to explain what is going on, why it is that nominal expenditures are subject to fluctuations, and there is no preconception that the point of all of this is to manipulate the sum of some aggregation of assets, then there is no need to find a "stable" money demand function.

Supply and demand analysis of skirts provides insight, even if we cannot predict fashion. I suppose if the purpose of supply and demand analysis was to help skirt manufacturers predict skirt prices or choose skirt production levels, then an inability to find a stable demand function for skirt would make the exercise useless.

But supply and demand analysis isn't about helping manuracturers. It is about understanding the market economic system.

And that is the proper standard for monetary theory.

And just as we "know" that a effective price ceiling for skirts will lead to shortages (which exceptions,) we may be able determine, for example, that people borrowing too much doesn't lead to recessions--unless it somehoe impacts either the quantity of money or the demand to hold money.

Bob Layson writes:

If velocity is 'a measure of income-adjusted money demanded' and presumedly held (for what is actually demanded at some price is actually obtained) then it would be better termed immobility.

fundamentalist writes:

Velocity is nothing but the basket that holds everything not in the equation that affects demand for money. It's highly correlated with P, too.

Ryan Vann writes:

As a student, either definition would have implied pretty much the same things: namely that income and expectations will affect Md, thus affecting V, thus affecting Py.

fundamentalist writes:

Mises: “But if once public opinion is convinced that the increase in the quantity of money will continue and never come to an end, and that consequently the prices of all commodities and services will not cease to rise, everybody becomes eager to buy as much as possible and to restrict his cash holding to a minimum size. For under these circumstances the regular costs incurred by holding cash are increased by the losses caused by the progressive fall in purchasing power. The advantages of holding cash must be paid for by sacrifices which are deemed unreasonably burdensome.”

“This phenomenon was, in the great European inflations of the '20s, called flight into real goods (Flucht in die Sachwerte) or crack-up boom (Katastrophenhausse). The mathematical economists are at a loss to comprehend the causal relation between the increase in the quantity of money and what they call "velocity of circulation."
http://mises.org/daily/3844

Lee Kelly writes:

Although "MV = PY" is a tautology, all that means is that the [i]equative relation[/i] between "MV" and "PY" must be true. What that doesn't tell you is whether there is anything in the world that actually corresponds to "MV" and "PY." In other words, "MV = PY," as a description of quantities and relations, may be false, i.e. may not describe anything that exists.

If "MV = PY" is describing real quantities, then calling the [i]equative relation[/i] between "MV" and "PY" isn't a reason to dismiss it. By those standards, all logical deductions should also be immediately dismissed, since they too are all tautologies much the same reason.

Mike Sproul writes:

MV=Py is just as true of IBM stock as it is of money. Just let M=the number of shares in existence, V= the number of times per year each share is spent, P=the number of shares it takes to buy a unit of y, and y=the things bought with shares of IBM.

We all know better than to use MV=Py when valuing stocks, because we know it is a tautology. But when it comes to money, we wave our hands and say "It is a useful tautology."

When it comes to economists' understanding of money, the profession is about where astronomers were before Copernicus came along.

Doc Merlin writes:

@Mike
It would be a lot better if they treated money like the commodity that it is and stopped treating it as somehow magical.

fundamentalist writes:

Ludwig von Mises on velocity: "But if once public opinion is convinced that the increase in the quantity of money will continue and never come to an end, and that consequently the prices of all commodities and services will not cease to rise, everybody becomes eager to buy as much as possible and to restrict his cash holding to a minimum size. For under these circumstances the regular costs incurred by holding cash are increased by the losses caused by the progressive fall in purchasing power. The advantages of holding cash must be paid for by sacrifices which are deemed unreasonably burdensome.

"This phenomenon was, in the great European inflations of the '20s, called flight into real goods (Flucht in die Sachwerte) or crack-up boom (Katastrophenhausse). The mathematical economists are at a loss to comprehend the causal relation between the increase in the quantity of money and what they call "velocity of circulation."

from Human Action. The full article is at mises.org

ionides writes:

I agree with this. In fact, I posted the following as a comment to a previous entry:

I have always thought that velocity is the wrong way to picture this. I prefer the other equation:
M/P = kY, the demand for real balances is a fraction k of national income.

Algebraically, it is the same equation as
MV = Py, allowing k to be Y/V.

But the picture is more realistic. Velocity doesn't really change. You don't have people running to spend money at different speeds. What changes is the amount of money that is circulating vs the amount in idle balances. If there is an increased demand for money, k rises. If k rises, and real money supply M/P is constant, then Y must fall. If k rises as M rises, then the outcome depends on relative magnitudes.

The behavioral picture associated with k is something like this: people get paid at the beginning of the period and their money holdings are at the maximum. As they spend, balances decline. If they want their end-of-period balances to be higher than before, they spend less. I think this is a more realistic picture than velocity.

Simon K writes:

I like this way of thinking about velocity, but isn't it important to consider what happens at the higher aggregates: the velocity is more and more strongly determines by financial institutions, not by individuals or companies. In a financial crisis like the one in 2008, the initial crash in velocity wasn't individuals increasing their holdings at M3, but financial institutions reducing their leverage ratios. Only later, once the scale of the problem because evident, did individuals start to move funds into more liquid holdings, exacerbating the problem for the banks.

Scott Sumner writes:

I agree, and so did the Cambridge (England) economists of the early 20th century. They used the M=kPY equation Bill discussed above. And also discussed the value of k for individuals.

I always tell my students that V isn't really the velocity of circulation, but k really is the ratio of money to gross income.

V shouldn't even be called "velocity" is should be called "the multiplier", but the term is already taken for something closely related.

MikeDC writes:

Doc Merlin,
But money is magical. It's not just a fiat commodity created (and grown) as a medium of exchange by the government, we know that new money is *created* daily by banks when they lend out most of our deposits for use by others.

In this respect, money has a unique function. It binds together three things; the real world of our current wealth, the fiat world of amounts of dollars on paper we use for accounting, and our prospective or expectation based world in which we get loans for things we can't pay for yet (like houses, cars, and - crucially - businesses).

Ryan Vann writes:

I'm still not seeing the issue with calling velocity velocity. From a physics perspective, velocity is just a vector ratio of distance over time. In Economics, it is the ratio of income to money.

"V isn't really the velocity of circulation,"

Wouldn't it make more sense to say V is circulation?

Let's ignore P for a moment, and just deal with the simple equation M=Y. All income/wealth is assumed to have been gained by an exchange of money. It isn't necessary that all money was exchanged, or that one unit was only exchanged once.

Thus, we assume money circulates to make up the disparity between M and Y. We add the variable V (representing circulation) to get MV=Y. Of course, we normally can measure what M and Y are, and solve for V and get V=Y/M.

So basically, using the word velocity gives the student an intuitive idea of what is being described, while the mathematical identity of V as a ratio has macro implications. Maybe I'm missing something.

Philo writes:

You write: "Velocity is the inverse of the percentage of income that people keep in the form of money." But income is a flow, while money-held is a stock. You need to specify a time-period for the income, obtaining a stock. You might, for instance, specify one year; replace "income" in your definition with "annual income." But this would be arbitrary--any other time-period would do as well. Instead you might define '[time-period]-velocity' instead of 'velocity' simpliciter. If I steadily earn $10,000 over the course of a year, and at any moment I hold, on average, $2,000 in money (of some sort), then my annual-velocity (for this sort of money) is 5, while my monthly-velocity is 5/12 and my daily-velocity is 5/365, etc. (My momentary-velocity is infinitesimal.)

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