This is another one for my students of EC102.

Possibly the simplest model of aggregate demand in an economy is this equation:

MV = PY

The right-hand side is the nominal value of demand, being the price level multiplied by the real level of demand. The left-hand side has the stock of money multiplied by the *velocity of money*, which is the number of times the average dollar (or pound, or euro) goes around the economy in a given time span. The equation isn’t anything profound. It’s an accounting identity that is always true, because V is constructed in order to *make* it hold.

The Quantity Theory of Money (QTM) builds on that equation. The QTM *assumes* that V and Y are constant (or at least don’t respond to changes in M) and observes that, therefore, any change in M must only cause a corresponding change in P. That is, an increase in the money supply will only result in inflation.

A corresponding idea is that of Money Neutrality. If money is neutral, then changes in the money supply do not have any effect on *real* variables. In this case, that means that a change in M does not cause a change in Y. In other words, the neutrality of money is a necessary, but not sufficient condition for the QTM to hold; you also need the velocity of money to not vary with the money supply.

After years of research and arguing, economists generally agree today that money neutrality does *not* hold in the short run (i.e. in the short run, increasing the money supply does increase aggregate demand), but that it probably does hold in the long run (i.e. any such change in aggregate demand will only be temporary).

The velocity of money is an interesting concept, but it’s fiendishly difficult to tie down.

- In the long-run, it has a secular upward trend (which is why the QTM doesn’t hold in the long run, even if money neutrality does).
- It is extremely volatile in the short-run.
- Since it is constructed rather than measured, it is a residual in the same way that Total Factor Productivity is a residual. It is therefore a holding place for any measurement error in the other three variables. This will be part, if not a large part, of the reason why it is so volatile in the short-run.
- Nevertheless, the long run increases are pretty clearly real (i.e. not a statistical anomaly). We assume that this a result of improvements in technology.
- Conceptually, a large value for V is representative of an efficient financial sector. More accurately, a large V is contingent on an efficient turn-around of money by the financial sector – if a new deposit doesn’t go out to a new loan very quickly, the velocity of money is low. The technology improvements I mentioned in the previous point are thus technologies specific to improving the efficiency of the finance industry.
- As you might imagine, the velocity of money is also critically dependent on confidence both
*within*and*regarding*banks. - Finally, the velocity of money is also related to the concept of fractional reserve banking, since we’re talking about how much money gets passed on via the banks for any given deposit. In essence, the velocity of money must be positively related to the money multiplier.

Those last few points then feed us into the credit crisis and the recession we’re all now suffering through.

It’s fairly common for some people to blame the crisis on a global savings glut, especially after Ben Bernanke himself mentioned it back in 2005. But, as Brad Setser says, “the debtor and the creditor tend to share responsibility for most financial crises. One borrows too much, the other lends too much.”

So while large savings in East-Asian and oil-producing countries may have been a push, we can use the idea of the velocity of money to think about the pull:

- There was some genuine innovation in the financial sector, which would have increased V even without any change in attitudes.
- Partially in response to that innovation, partially because of a belief that thanks to enlightened monetary policy aggregate uncertainty was reduced and, I believe, partially buoyed by the broader sense of victory of capitalism over communism following the fall of the Soviet Union, confidence both within and regarding the financial industry also rose.
- Both of those served to increase the velocity of money and, with it, real aggregate demand even in the absence of any especially loose monetary policy.
- Unfortunately, that increase in confidence was excessive, meaning that the increases in demand were excessive.
- Now, confidence both within and, in particular, regarding the banking sector has collapsed. The result is a fall in the velocity of money (for any given deposit received, a bank is less likely to make a loan) and consequently, aggregate demand suffers.

Here are a couple of posts I left on the TBT Yahoo board. Any comment would be appreciated.

A question. The unit labels for price level in dollars is presumably $/(unit of good) and quantity is (units of good) so the right hand part of the equation unit label reduces to $. The left hand side is then $ x a scalar to make the units match. The term velocity is then a descriptive term with no units such as in physics but rather just a multiplier. Is this correct?

(next post)

Then I see a problem. If one wanted to learn the relationship of the change in price with the change in velocity for instance one would differentiate the equation with respect to time and manipulate to obtain the differential dV/dt. But the differential of a scalar times a variable yields only that scalar times the differential of the other variable (here money supply)giving V times dM/dt -i.e. no information about dV/dt. One might say “but the scalar (a constant) varies” but the sentence thus contains its own absurdity (a variable constant) and when that happens one must confront the definitional problem of the variable at least in the context of the posed equation.

Lets try to wriggle out another way. Since velocity is sometimes explained in terms of the turn over of money supply in a period of time lets define it as a frequency thus making it a variable having units of reciprocal time (time^-1). To make the units agree on the other side of the equation lets add an unknown variable X with the same units time^-1. To try to discover the meaning of V one may divide both sides of the equation by X to yield the ratio V/X such that the right hand side is again P times Q. So what is the meaning of V/X? The ratio leads one no closer to an understanding of the concept of V (velocity) as X is undefined.

In looking around last night I found that there is a “school” of economics called the Austrian school that doesn’t admit the validity of the velocity concept. Nothing so elemental as the paragraphs above however was given. One needs a defining equation for velocity to take the concept seriously.