Arnold Kling recently had a post entitled, “Monetarism Debated” in which he links to a post by Matt Rognlie entitled, “Is MV = PY Useful?”

Hopefully neither Arnold nor Matt think that this is what monetarism really was, but based upon the context, it seems that they do. As a result, I would like to discuss the use of MV = PY as well as monetarism to clear the air about what the equation of exchange really means and what monetarism was really all about.

First, let’s begin with the equation of exchange. Rognlie suggests that the equation of exchange isn’t useful:

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.

There are essentially two claims here: (1) the equation of exchange is just an identity, and (2) the only way the equation is useful is if velocity is a stable function of other variables. On point (1), I would mention that the New Keynesian Phillips curve and IS equation face the same identification problems as each of these is simply an equilibrium relation and tells us nothing about the direction of causality.

Now on to point (2). In Allan Meltzer’s paper entitled, “Learning About Policy From Federal Reserve History“, he plots (Chart 1 here) the velocity of the monetary base and the nominal interest rate (as measured by the AAA corporate bond rate) from 1919 to 1997. If you follow the link, you will find that this looks like a pretty stable relationship.

Rognlie continues:

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.

Has financial innovation made V meaningless? Not really. What has been observed by a number of individuals is that there appears to be “shifts” in velocity in the early 1980s for most monetary aggregates. This has typically been attributed to financial innovation. However, the problem with this type of analysis is that it ignores the way in which monetary aggregates are calculated. Monetary aggregates are typically just simple sums of the collection of assets included in the particular aggregate. This is not a correct form of aggregation. Why does this matter? It matters because in the early 1980s there were a number of assets that got added to the monetary aggregates. Since these aggregates are simple sums, this meant that there were temporary spikes in the growth rates of money that had nothing to do with the money supply itself, but rather how money is calculated. As such, when M significantly rises for reasons that have nothing to do with actual changes in the money supply and therefore be definition does not affect PY, it must be true that V falls significantly. If you are relying on simple sum measures of money to calculate velocity, you will be led to believe that it has become unstable when, in fact, this is a flaw of simple sum aggregation.

Rognlie makes the claim that the nominal interest rate is the only thing we need to know about monetary policy:

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.

The Friedman quote is great, except that it is not uniformly correct. The point that Friedman was making was a response to the same type of criticism he had received since the publication with Anna Schwartz of *A Monetary History of the United States*. A number of critics of their interpretation of the Great Contraction as well as critics of Friedman’s views on Japan would often cite low interest rates as evidence that monetary policy could not have been tight. Friedman would then point out that while nominal interest rates were low, real interest rates were higher. Of course, this statement is not uniformly true. Interest rates were high when monetary policy was tight during the Volcker disinflation. Interest rates were low when monetary policy was loose during the early part of the 2000s. Thus, it appears that nominal interest rates are not sufficient for understanding the stance of monetary policy.

Finally, Rognlie writes:

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.

What does this mean “no credible monetary economist is a ‘monetarist’ anymore”? Does it mean that nobody buys the quantity theory of money? Does it mean that nobody thinks that money matters? Does it believe that nobody believes in MV=PY? Rognlie isn’t clear. As a result, it is important to talk about what the quantity theory and monetarism are really about while also pointing out that *every* credible monetary economist today is a monetarist in the sense that they recognize that money growth causes inflation.

Let’s begin to answer these questions with a discussion of the quantity theory of money. Consider a simple static representation of the economy. Since we are concerned with the determination of the price level, we can limit our attention to the asset market. There are three assets, capital, bonds, and money. In equilibrium, the real stock of each asset is equal to the demand. These equilibrium relations are shown respectively:

K = K(Y, r, i)

B/ip = D(Y, r, i)

M/p = L(Y, r, i)

where M is money, K is capital, B is the supply of bonds, i is the interest rate, r is the yield on capital goods, and Y is income. Now suppose (as is the case in the New Keynesian model) that the capital stock is fixed. Consider the effects of an increase in the money supply. To do this we can ignore the capital equation and assume that r is constant. As such, we can differentiate the bond market equation and the money market equation to determine the effect of an increase in the money supply. In doing so we get the following result:

dp/dM = 1/∆p (D_{i} + B/i^{2}p) > 0

where

∆ = (D_{i} + B/i^{2}p)(M/p^{2}) – L_{i}(B/ip^{2}) > 0

In other words, an increase in the money supply leads to an increase in the price level. However, the increase in the money supply does not necessarily lead to an equiproportionate increase in the price level. In fact, it must be true that the bond supply is equal to zero for the money supply to have such an effect (if you don’t believe me, set B = 0 in the equations above). As such, we should expect velocity to change in response to changes in the money supply so long as the bond supply is positive.

So does this mean that the quantity theory is not valid? Of course not. Jurg Niehans explains in *The Theory of Money* (p. 219):

It may be worth repeating that the quantity theory does not maintain that all changes in the price level are caused by changes in the money supply. In terms of the present model, any number of shifts in the underlying functions may result in price changes. The historical observation, therefore, that movement in the price level do not always parallel the movements in the money supply does not invalidate the quantity theory for at least two reasons, namely, (1) because other exogenous assets like bonds would also have to be considered, and (2) because the quantity of financial assets is only one of the forces determining the price level. The quantity theory dos not ask us to adopt a monetarist view of economic history. It does claim, however, that the historical course of prices would have been different if the suplies of financial assets by the government had been different, all in roughly the same proportion. In this sense, which seems to be the correct one, it is neither false nor trivial, but one of the important, if elementary, insights of economic science.

Even if one disputes the admittedly simple example given above, the same insight is true even of the New Keynesian model. For all the talk about the interest rate being all that is necessary for the conduct of monetary policy, Ed Nelson has shown that even in the New Keynesian model money growth determines the steady state rate of inflation. (Bear in mind that the NK model implies that B = 0 because it assumes the government is following a Ricardian policy. Thus, money growth does affect inflation equi-proportionately.)

In other words, the quantity theory is relevant even in the context of the New Keynesian model in which money is perceived to be unimportant.

(Empirically, it might be hard to disentangle all of these different effects to determine to what extent money growth causes inflation. One method would be to look at Granger causality tests to determine whether money is useful in predicting inflation — or, for that matter, nominal income. It turns out that money is, in fact, useful in this respect. I can provide empirical evidence if anyone is both still reading this post and interested.)

This would then bring us to the point at which we question what monetarism was really about. The perspective that we seem to get from the Rognlie is that MV = PY is all that matters or that the quantity theory is valid. (Of course, the vast majority of monetary economist accept these propositions either explicitly or implicitly in the steady state of their models.) However, monetarism was about much more than the quantity theory. Monetarism was indeed about understanding the importance of money in economic fluctuations and inflation, but it was also about understanding the monetary transmission mechanism, the interaction between monetary and fiscal policy, and the behavior of money demand. Brunner and Meltzer’s work, in particular, on the monetary transmission mechanism was particularly important as it stressed the fact that “the” nominal interest rate was an imperfect measure of the transmission of monetary policy.

This post is already pushing 2000 words and few have likely made it this far, but if anyone is interested in what monetarism was really about I would urge you to read the work of Karl Brunner and Allan Meltzer and David Laidler in addition to the usual Friedman stuff. Anyone who reads Brunner and Meltzer cannot claim that monetarism was simply about MV = PY and still be taken seriously.

UPDATE: See also, Nick Rowe, David Beckworth, and Scott Sumner.