Yesterday, I asked:

Why did Milton Friedman say inflation was always a monetary phenomenon when his own equation says it is a combination of 3 variables?

— John Aziz (@azizonomics) March 8, 2013

It is true that the equation I am referring to — MV=PQ, where M is the money supply, V is velocity, P is the price level and Q is output — is not exactly Friedman’s equation. It was initially theorised by John Stuart Mill, and formulated algebraically by Irving Fisher, but adopted by Friedman and his monetarist followers to the extent that Milton Friedman had it as his car number plate:

MV=PQ itself is a tautology that ties together three disparate variables — the money supply (M), the price level (P) and the output (Q) — by creating a quantity — velocity (V) — that is not observed directly, but is instead computed retrospectively from the three other variables. But, nonetheless, so long as we can overlook the fact that V is not directly observed (which ultimately we should not, but that is another story) it is true that MV=PQ accurately describes monetary reality.

Friedman’s famous quote seems to contradict his beloved equation:

Inflation is always and everywhere a monetary phenomenon, in the sense that it cannot occur without a more rapid increase in the quantity of money than in output.

Within the parameters of the equation, an increase in P can come from any of the other three variables in the equation — all else being equal a decrease in Q, or an increase in M, or an increase in V.

The only way that Friedman’s statement could be true is if V and Q were stable. Friedman did actually claim that V was largely stable, but empirical data rules this out. Here’s velocity:

And here’s output:

Neither of these are constant, or even particularly stable, meaning that it is impossible within the parameters of Friedman’s own equation for inflation (changes in P) to solely be a monetary phenomenon. Inflation by Friedman’s own mathematical definition is a result of a combination of factors. And in the real world, it is far, far, far more complicated — a price index generalises a staggering array of human actions, each one the outcome of an equally vast array of psychological, social and economic influences.