Velocity of Money

 There are periodic outbreaks of commentators trying to resuscitate the money supply data as a tool for explaining inflation. One superficial way I pass judgement on such work is to search for the word 'velocity.' Dr. Cowen's piece is an example that does. (See Section 1.2 of the textbook for background.)

Underlying such explanations of inflation is the Quantity Theory of Money MV=PY, but to say something about the connection between M and P requires assumptions about V and Y, about which some are more forthcoming than others. Those that are explicit say something like real GDP fluctuates around a natural rate and velocity is stable.

Even before evaluating those issues, there's a more basic question about money:  What is it? By that, I mean identifying the quantity should we look at.

Here are some the prime candidates expressed as growth rates along with inflation:

M1 and M2 are the usual suspects. MZM stands for Money Zero Maturity and is essentially M2 with money market funds. M1 is causing trouble since its growth rate exceed 150% in early 2021, so it disappears off the graph around then.

The connection between the money growth numbers an inflation is immediately suspect, since inflation is so much smoother. The correlation between inflation and M2 growth of 0.18 is the best among the money growth rates. In fact, the correlations between the other money growth rates and inflation are negative. 

Is velocity stable? Again, growth rates g are relevant. Log differencing the quantity equation where inflation is π_t gives

g_m,t + g_v,t = p_t + g_y,t

Again, the troublemaker is M1, whose velocity growth rate is almost 150% in late 2020, compensating for the high money supply growth rates in the first graph. The first point is that velocity is anything but stable. The most stable is velocity growth for M2, and that series frequently exceeds 5%. There may be a connection between the money supply and inflation, but the velocity growth numbers mean it pretty flimsy.

Dr. Cowen and Dr. Hendrickson have pointed to the elevated money supply growth rates as helping to explain inflation recent inflation, which is correct, but there were a number of spikes in the money supply during the recovery from the Great Recession, when inflation remained stubbornly below target. 

Best case conclusion:  Pay attention to the Quantity Theory when M2 growth rates exceed 20%.

In the Quantity Theory, all aspects of aggregate demand besides money are rolled into velocity. Most macro theories give a more detailed account of demand (C, I & G for example) for good reason.

 It’s good to know the Quantity Theory, but money supply data is not particularly helpful with the exception of extreme events like a financial crisis or a pandemic. In that case, examining flows of funds for many asset classes is important.