# 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.
2012-03-18