First, we have to understand what the equation of exchange is: without additional assumptions, it’s a tautology. Velocity, “V”, is defined as the number such that MV = PY will hold. Unless V happens to be relatively stable, or obey some kind of predictable pattern in response to other variables (e.g. the nominal interest rate), the equation tells us nothing.
As James Hamilton observes (and as economists since the 1980s have understood), “V” isn’t stable: instead, it moves around almost exactly opposite to “M”, as nominal GDP (“PY”) does its own thing. Of course, this isn’t entirely fair. Financial innovation has made “V” meaningless today, but decades ago, the old-school monetarists had reason to think that it was stable.
But even then, I contend that the equation of exchange was near-useless as a practical way of thinking about monetary policy. Why? Well, we have to think about why it could conceivably be a valid approximation in the first place. This involves constructing some model where money is closely related to consumption, perhaps through a cash-in-advance constraint or through complementarity in the utility function. And in such a model, the assumption that “V” is stable translates into an assumption that there is some kind of tight constraint connecting economic activity to real money balances.
But in such a model, the nominal interest rate is a sufficient statistic for the extent to which this constraint binds—after all, it’s the cost of holding money. If a lack of money is hurting output in the direct way implied by MV=PY, the nominal interest rate has to be high enough that holding money is costly, and agents in the economy cut back on activities complementary to money. Maybe an 8% nominal interest rate is just enough to make certain activities uneconomical: operating a cash-intensive business, or spending regularly at a market. Regardless of the specific effect, a truly meaningful shortage in quantities should be reflected by a spike in prices. And that price is the nominal interest rate.
Scott Sumner is fond of citing the following remark from Milton Friedman:
“Low interest rates are generally a sign that money has been tight, as in Japan; high interest rates, that money has been easy.”
This is very true, and very wise. But this is precisely the kind of observation that MV=PY cannot rationalize: given the economic model implicit in the equation of exchange, nominal interest rates are sufficient to summarize the stance of monetary policy. And that’s why the basic monetarist model is such a poor tool for analyzing the effect of money.
Don’t take it from me. Take it from Milton Friedman.
(Disclaimer: Since I don’t want to perpetuate any popular misconceptions, I should mention that no credible monetary economist is a “monetarist” anymore, at least in the old sense of the term. The profession moved on long, long ago. But since I still see MV=PY popping up quite frequently on the internet, I think it’s important to emphasize what a poor model it really is.)