How (un)stable is velocity?

Traditional monetarists used to consider money-velocity as rather stable and predictable. In the simple textbook version of monetarism V in MV=PY is often assumed to be constant. This of course is a caricature. Traditional monetarists like Milton Friedman, Karl Brunner or Allan Meltzer never claimed that velocity was constant, but rather that the money demand function is relatively stable and predictable.

Market Monetarists on the other hand would argue that velocity is less stable than traditional monetarists argued.  However, the difference between the two views is much smaller than it might look on the surface. The key to understanding this is the importance of expectations and money policy rules.

In my view we can not think of money demand – and hence V – without understanding monetary policy rules and expectations (Robert Lucas of course told us that long ago…). Therefore, the discussion of the stability of velocity is in some way similar to the discussion about whether monetary policy whether monetary policy works with long and variable leads or lags.

Therefore, V can said to be a function of the expectations of future growth in M and these expectations are determined by what monetary policy regime is in place. During the Great Moderation there was a clear inverse relationship between M and V. So when M increased above trend V would tend to drop and vice versa. The graph below shows this very clearly. I use the St. Louis Fed’s so-called MZM measure of the money supply.

This is not really surprising if you take into account that the Federal Reserve during this period de facto was targeting a growth path for nominal GDP (PY). Hence, a “overshoot” on money supply growth year one year would be counteracted the following year(s). That also mean that we should expect money demand to move in the direct opposite direction and this indeed what we saw during the Great Moderation. If the NGDP target is 100% credible the correlation between growth in M and growth in V to be exactly -1. (For more on the inverse relationship between M and V see here.)

The graph below shows the 3-year rolling correlation growth in M (MZM) and V in the US since 1960.

The graph very clearly illustrates changes in the credibility of US monetary policy and the monetary policy regimes of different periods. During the 1960 the correlation between M or V was highly unstable. This is during the Bretton Woods period, where the US effectively had a (quasi) fixed exchange rate. Hence, basically the growth of M and V was determined by the exchange rate policy.

However, in 1971 Nixon gave up the direct convertibility of gold to dollars and effectively killed the Bretton Woods system. The dollar was so to speak floated. This is very visible in the graph above. Around 1971 the (absolute) correlation between M and V becomes slightly more stable and significant higher. Hence, while the correlation between M and V was highly volatile during the 1960s and swung between +0 and -0.8 the correlation during the 1970s was more stable around -0.6, but still quite unstable compared to what followed during the Great Moderation.

The next regime change in US monetary policy happened in 1979 when Paul Volcker became Fed chairman. This is also highly visible in the graph. From 1979 we see a rather sharp increase in the (absolute) correlation between money supply growth and velocity growth.  Hence, from 1979 to 1983 the 3-year rolling correlation between MZM growth and velocity growth increased from around -0.6 to around -0.9. From 1983 and all through the rest of the Volcker-Greenspan period the correlation stayed around -0.8 to -0.9 indicating a very credible NGDP growth targeting regime. This is rather remarkable given the fact that the Fed never announced such a policy – nonetheless it seems pretty clear that money demand effectively behaved as if such a regime was in place.

It is also notable that there is a “pullback” in the correlation between M and V during the three recessions of the Great Moderation – 1990-91, 2001-2 and finally in 2008-9. This is rather clear indication of the monetary nature of these recessions.

The discussion above illustrates that the relationship between M and V to a very large degree is regime dependent. So while it might have been perfectly reasonable to assume that there was little correlation between M and V during the 1950s and 1960s that changed especially after Volcker defeated inflation and introduced a rule based monetary policy.

MV=PY is still the best tool for monetary analysis

So while V is far from as stable as traditional monetarists assumed the correlation between M and V is highly stable if monetary policy is credible and there is a clearly defined nominal target. Therefore MV=PY still provides the best tool for understanding monetary policy – and macroeconomics for that matter – as long as we never forget about the importance of monetary policy rules and expectations.

However, the discussion above also shows that we should be less worried about maintaining a stable rate of growth in M than traditional monetarists would argue. In fact the market mechanism will ensure a stable development in MV is the central bank has a credible target for PY. If we have a credible NGDP targeting regime then the correlation between M and V will be pretty close to -1.


PS This discussion of course is highly relevant for what happened to US monetary policy in 2008, but the purpose of this post is to discuss the general mechanism rather than what happened in 2008. I would however notice that the correlation between growth in M and V dropped in 2008, but still remains fairly high. One should of course note here that this is the correlation between the growth of M and V rather than the level of M and V.

PPS In my discussion and graph above I have used MZM data rather than for example M2 data. The results are similar with M2, but slightly less clear. That to me indicates that MZM is a much better monetary indicator than M2. I am sure William Barnett would agree and maybe I would try to do the same exercise with his Divisia Money series.

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  1. Bill Woolsey

     /  March 18, 2012

    A constant growth rate rule for M2 only makes sense if M2 velocity doesn’t change much. Presumably, if it doesn’t change much it is rather predictable in a sense, though I suppose part that isn’t constant might not be very predictable.

    If velocity of one sort or another changes a good bit, it makes a constant growth rate rule for some measure of the money supply unattractive. I think that market monetarists have generally come to the conclusion that velocity changes too much for a constant growth rate rule to be desirable. Instead, some monetary regime where quantities of money have a negative correlation on one with velocity are the least best approach.

    However, as a matter of theory, if velocity is literally unpredictable, then the notion is that it is unimportant. It is just the ratio of nominal GDP to the quantity of money and depends on nothing in particular. Or more exactly, the quantity of money has nothing to do with spending on output.

    I identify velocity with the demand to hold money–assumed proportional to real income and inverted. It is a rather awkward way to looking at monetary equilibrium/disequilibrium. As long as the demand for money depends on real income, and people choose to hold real balances, then velocity is determined. On the other hand, if the real demand for money is just a residual–for example people decide to spend and just passively adjust money holdings according to what is left. Or people decide to lend and just passively adjust their money holdings to what is left, then monetary equilibrium/disequilibrium analysis is pointless.

    It is this theoretical notion that “predictability” relates to. Money doesn’t matter. However, for mainstream macroeconomists, the point of this exercise (and everything really) is whether or not a central bank can be helped to manipulate the economy. And so, the notion of “predictability” of velocity gets tied up to determining whether we can estimate current velocity and then adjust some quantity of money so that a target for nominal GDP can be hit. (Or, they could instead be using inflation, or inflation and an output gap.) To me, when we say “predictability” rather than say, “determined,” this suggests such a narrow purpose for the analysis.

    However, I agree with your analysis that the monetary equilibrium and disequilibrium depend very much on expectations and the monetary regime. Thought experiments about how the market system would blindly adjust to exogenous changes in the growth rate of the quantity of money don’t apply very well to monetary regimes where the growth rate of the money supply isn’t given. And really, thought experiments where rational expectations are assumed and the growth rate of the money supply changes aren’t much help.

  2. Brito

     /  March 18, 2012

    I think you can use MV = PY short run dynamics to distinguish between schools of thought. Old fashioned right wingers basically think that the quantity theory of money holds even in the short run, thus V and Y is invariant of M. New Keyensians have Y and V invariant of M in the long run but in the short run hold P constant due to price rigidity and allow Y to vary with M. Market Monetarists focus on what I like to call the quantity theory of nominal income (QTI?), i.e. holding V constant but NOT Y, thus an increase in M must increase PY (ngdp), but whether it is a rise in P or a rise in Y or both causing the rise in NGDP is unimportant, as long as it PY is stable over the business cycle everything will be fine.

    Does this sound accurate, Lars?

  3. Bill, thanks for your comments.

    My point is the velocity is not just jumping around without any relationship to the monetary policy regime. I do agree V is not constant – is changed by a lot of factors – for example financial sector regulation. Furthermore, I would stress that I do not advocate a Friedman style constant growth rule for M.

    However, I do argue that one of the reasons that V was rather volatile doing the Great Moderation was that not only the Federal Reserve, but central banks around the world implemented more or less credible nominal targets. With credible nominal targets MV becomes endogenous.

    In term of the Cambridge k versus V I clearly prefer V. One reason is exactly the V (or k) is NOT constant.

  4. Brito,

    It is important to stress that MV=PY always hold – both in the short run and in the long run. The question is only one of causality.

    I basically think the Market Monetarist positions can be described within the framework of MV=PY. I will try to outline that in a post later by let me just raise a few points.

    1) MV determines PY
    2) In the short-run there is a high degree positive correlation between MV and Y, but a small correlation between MV and P. Prices are rigid.
    3) In the long run there is a near one-to-one correlation between MV and P and no correlation between MV and Y. The Phillips curve is vertical and money is neutral in the long run.
    4) The monetary transmission mechanism is complicated, but expectations for further M and V is important. The transmission mechanism work via long and variable leads to quote Scott Sumner.
    5) With a clear target for P or PY the central banks can guide and/or change expectations. This will impact V. If the central bank for example credibility announced an increase in PY of 15% and said it would increase M as much as necessary to achieve this then V would like jump and little increase in M would be necessary.
    6) There might or might not be a correlation be V and interest rates, but that is mostly irrelevant for monetary policy. Interest rates play a small role in the monetary transmission mechanism.

  5. W. Peden

     /  March 18, 2012

    In the case of US M2 and the instability of its velocity during the 1990s, I recall reading that this was largely due to changes in the opportunity cost of holding M2 balances.

    I do recall noticing that if one combined the rate of change in UK M0 and M4 and divided it by two, one had a rough-and-ready guide to changes in NGDP from 1979-2005 i.e. the regulatory, technological and interest-rate effects on one aggregate tended to offset each other. So, for instance, M4 velocity fell in 1979 and the early 1980s due to a sharp increase in the demand for time deposits, but M0 velocity rose even more sharply and so the Thatcherite disinflation was indicated. Equally, M0 velocity rose in the late 1980s as the demand for cash fell, but M4 velocity fell as well.

    Just looking at M4 and M4x (M0 was discontinued in 2006, though it has recently been revived by the BoE) when one looks at non-financial sector holdings of M4 and M4x, there is a rule-of-thumb that the UK demand for broad money increases in booms and into recessions, and falls after recessions and in early expansionary phases. Timetric isn’t working right now, but here’s M4x recently-

    In general though, I prefer to regard the M and PY relationship as most true at the international level. OECD broad money and OECD PY are closely correlated with very little noise-

    Broad money and NGDP, while always closely related in the long run, would be even more closely related in a totally closed economy, to the point where a k percent rule might even be a good idea (though still inferior to an NGDP target).

  6. Diego Espinosa

     /  March 18, 2012

    MM’s seem to reject the dominant causal role that financial intermediation plays in velocity. The question is whether the intensity of financial intermediation is exogenous or dependent on NGDP growth expectations themselves. If exogenous, causality runs from the health of the financial system to NGDP, rather than visa versa.

    Is every banking crisis the result of a monetary policy error? This would seem to be the implication of MM thinking. If, instead, banking crises occur independently of monetary policy, then the implication is that “V” is difficult to manage (and so is NGDP) along a stable path.

    There are many reasons to think that banking crises occur exogenously, and that they have to do more with agency issues, lemons problems, the procyclical behavior of bank capitalization, and the feedback loops between asset prices and credit risk premia, etc. There is exhaustive literature on the subject from the likes of Gorton, Brunnemeier, Adrian, and others. As I’ve written before, Market Monetarism would be more robust if it accepted the work of financial economists rather than holding to the notion that V is completely a function of central bank-determined expectations.

  7. David Eagle

     /  March 19, 2012

    I have four comments to make here:

    1. Lars claims that the Federal Reserve acted as if it were targeting the growth rate of Nominal GDP (NGDP). My empirical study (see Eagle, 2012, below) supports Lars’ claim, although it also supports the hypothesis that the Federal Reserve targeted inflation. Both inflation targeting and NGDP-growth-rate targeting result in NGDP base drift, something my empirical work documents did occur in the Early 1990s Recession and the Early 2000s Recession. That NGDP base drift also has occurred in the latest recession but to a much greater degree (and with much worse devastation than the earlier two recessions).

    2. Lars’ plot of money growth vs. the percent change in velocity is something I have not seen before. Lars, is this something that you have seen before or are you the first to document it. If the latter, publish a paper on it as I find it very interesting and with hindsight very obvious (I wish I had found it!). Whether the Federal Reserve targeted NGDP growth or inflation, my empirical observation is that except for the recessions, the growth rate in NGDP has been fairly stable. MV=N=PY implies that m+v=n where m, v, and n are the (instantaneous) percent changes in M, V, and N (N is of course nominal GDP). Hence if n is stable (constant), then m=-v+n implies a correlation of -1, which is close to Lar’s -0.8 to -0.9 correlation.

    3. I do not agree with Lars that the high negative correlation between m and v is because the central bank acts with a delay to changes in velocity. While I looked at Lars’ graph, I do not see a lag; it looks more simultaneous. Given that the Federal Reserve and most central banks peg the interest rate, not set the money supply, the high negative correlation between m and v will occur naturally with no lag as long as the central bank’s policy leads to a stable growth rate in NGDP, which it has except around the recessions. To further understand how this all works, please look the theoretical graphs on p. 11 of my paper, Eagle (2005). When you read that paper, you will find that whether or not pegging the interest rate leads to stability in NGDP growth or not depends on which is more stable, an N-Fisher money demand function or velocity (See my point #4 below).

    4. In 1975, I discovered an error in macroeconomics after I took “Intermediate Macroeconomics” during my junior year in college. That error is what motivated me to go to graduate school. Alas, I still have not been able to get that error published. The error is the supposed equivalence between the money-demand function and velocity as best depicted in the Cambridge equation and the Cambridge k. Macroeconomics and monetary economists have believed that the money-demand function is the reverse of the velocity function. I disagree and I can show that point with an example (I do have papers written on this from many years ago, but I have yet to put these on the internet). When I discussed this issue with Tom Sargent in 1980, he correctly steered me in the direction of the identification problem in econometrics, although in this case it is a theoretical identification problem, not an empirical one. Basically, my position is that the structural velocity function differs from the structural money demand function. Over time, I have been able to convince many other economists that I am right, but I have not been convinced any journal to published my logic. Jonas Salk, discoverer of the polio vaccine, said, “There are three stages of truth:” In the first state, they say it “’can’t be true.’” In the second stage, they say, “’if it’s true, it’s not very important.’” In the third stage, they say “’Well, we’ve known it all along.’” In my attempts to publish this error, I have encountered all three stages. I am hoping the internet can provide more control of economists slipping from one stage to another. So for now, I hope that some economists will speak up and take positions that what I said cannot be true, so that when I do provide proof that structural velocity and the structural money demand functions are different, then they cannot weasel out of their previous statements.

    The two papers I referred to in this note are:

    Eagle, David (2005). “The Inflation Dynamics of Pegging Interest Rates,” Macroeconomics 0502029, EconWPA, available at

    Eagle, David (2012). “Nominal GDP Targeting for a Speedier Economic Recovery,” working paper available at: (Revised as of March 8, 2012).

  8. W. Peden

     /  March 20, 2012

    David Eagle,

    When you talk about the non-equivalence of the money demand function and the velocity function (which, if I understand you correctly, is the equivalent of saying that money demand does not equal the inverse of velocity) do you mean the income velocity of money or the transactions velocity of money?

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