Velocity

I first encountered the Quantity Theory of Money about 26 years ago. Over the course of those 26 years, I’ve gotten a PhD in economics (macroeconomics, specifically) from a reputable university and been employed professionally as an economist, but I have to confess, I’m still having trouble understanding the Quantity Theory of Money.

For the benefit of any readers who may be unfamiliar with it, I will note that the Quantity Theory is, formally speaking, one of the simplest economic theories one is ever likely to come across. There are 4 variables:

• M = money (the quantity of money)
• V = velocity (the velocity of money)
• P = price (the general price level)
• Y = national income or output

and the theory states that

MV = PY

(“Y” is sometimes replaced by “Q” for “quantity” – actually the way I learned it – or by “T” for “transactions” – the latter being apparently a slightly different version of the theory.) The nature of my confusion may be stated succinctly: What the hell is “velocity”?

Velocity is typically defined as something like “the number of times an average dollar changes hands.” To be more precise (for the “Y” or “Q” version, but not for the “T” version), it should probably be “the number of times an average dollar changes hands for purposes of purchasing newly produced goods and services (but not including any constituent part of those goods and services that is not newly produced).”

I can kind of understand this – at least in a stylized example. If all our money took the form of dollar bills, and if we placed a check mark on a dollar bill every time we used it to purchase value added, then the velocity of money would be the number of check marks added to the average dollar bill in a year. (The “value added” concept makes things a bit difficult, though: If a hot dog vendor buys a frankfurter and a bun for $1 each, he puts check marks on each dollar he uses; if I then buy a fully assembled hot dog for $3, I have to be careful to check one of the dollars but not the other two, since only one of those dollars is being used to purchase value added.)

OK, but I have two questions: First, how is this example analogous to anything in the real world? We don’t have just one denomination of currency; we have many. Most of our transactions are electronic, anyhow. And we don’t put check marks on the currency when we use it. And even if we did, the check marks wouldn’t make any difference to anyone except maybe the people who operate printing presses on behalf of the Fed. Which leads to my second question: Why should we care? Why, in particular, should we expect this number called “velocity” to have any interesting properties, to be constant or stable or in any way predictable? Nobody has ever been able to give me a satisfactory answer to this question.

But I’ve come up with another way of thinking about the Quantity Theory, a way that does make some sense to me. Is it really, perhaps, not a theory about the circulation of money but a theory about the demand for money? Is the theory simply saying that people (and businesses and governments) choose to hold money in proportion to their intention to purchase value added? (Or perhaps, that they choose to hold money in proportion to their income, which would be equivalent because of the national income identity. Though I don’t see any reason to hold money in proportion to ones income independently of how much one intends to spend.)

If I look at the Quantity Theory as a theory about the demand for money, the “V” makes sense. Rearranging the Quantity Theory to look like a money demand equation, we have:

M/P = Y/V

In this formulation, V is simply the fraction (expressed in reciprocal form, as a “Vth,” one might say) of intended annual value added purchases that people choose to hold in real money balances. I don’t see why that fraction should be called “velocity,” but I suppose it doesn’t matter; you can call it whatever you want.

The theory is still a bit ragged around the edges: You might think people would hold money in proportion to their total intended purchases; it’s a little harder to see why money holdings would depend on value added purchases but not on resale purchases. (For example, wouldn’t I hold money in proportion to my whole $3 hot dog purchase? And wouldn’t the hot dog vendor also hold money in proportion to his $2 bun and frankfurter purchases?) But this difficulty doesn’t bother me so much, because I can see why we might expect the ratio of total purchases to value added to be roughly constant, at least in the short run.

Then, if someone wants to get more sophisticated and say something like, “The velocity of money may rise in response to rising interest rates,” I can be comfortable interpreting that to mean, “If interest rates rise, people may choose to hold a smaller fraction of their intended purchases as money balances.” Or if someone says, “The velocity of money may rise due to the increasing availability of credit cards,” I can interpret that to mean, “Credit cards reduce the need to hold money balances.” I think I’m finally learning how to translate from Monetarist-ese into English.