My point is that V relates to two distinct monetary circulations:
V1 - money circulating in the financial economy or FIRE sector as Hudson has it;
V2 - money circulating in the 'real' economy.
It is the fiscal interface between these two monetary flows which is crucial. "Any economic unit can emit money. The serious problem is to get it accepted" Hyman Minsky
V_GPD is not, of course, either V2 or V1 ...
Switching to w for the wealth management FIRE sector and o for the output of real goods and services sector, because M1 and M2 for money stock allocated to the service of each sector is too confusing with the M1 and M2 monetary aggregates ...
In MV=PQ, which is due to, V:=$GDP/M, and Q:=($GDP/P)
... if M=Mw+Mo, Vo:=($GDP/Mo), so that the correction from the synthetic V_GDP to Vo is:
Vo = ($GDP/Mo) = [$GDP/(Mw+Mo)][(Mw+Mo)/Mo], so Vo = V_GDP[1+Mw/Mo] = V_GDP + V_GDP[Mw/Mo]
If V_GDP was to be rising while Mw/Mo is falling, it would be quite possible for Vo to be either stable or declining.
To the extent that the rate of change in Vo and Vw are both constrained by institutional rules (the real world equivalent of Friedman's arbitrary assumption that velocity is stable), it may well make sense to track them independently, since they would to a substantial extent be constrained by <i>distinctive</i> institutional rules. I've been accused of being a Marxist, yet while Harpo's my favourite, it's Groucho I'm always quoting. Odd, that.
