# Does Y Determine MV Or Is It MV That Determines P?

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by: Lars Christensen

Scott Sumner a couple of days ago wrote a post on what he believes is a Great Stagnation story for the US. I don't agree with Scott about his pessimism about long-term US growth and I don't think he does a particularly good job arguing his case.

I hope to be able to write something on that in the coming days, but today I will instead focus on another matter Scott (indirectly) brought up in his Great Stagnation post - the question of causality between nominal and real shocks.

This is Scott:

I've been arguing that 1.2% RGDP and 3.0% NGDP growth is the new normal. The RGDP growth is of course an arbitrary figure, reflecting the whims of statisticians at the BEA. But the NGDP slowdown is real (pardon the pun).

The point Scott really is making here (other than the productivity story) is that it is real GDP that determines nominal GDP ("NGDP slowdown is real"). That doesn't sound very (market) monetarist does it?

Is this because because Scott - the founding father of market monetarism - suddenly has become a Keynesian that basically just thinks of nominal GDP as a "residual"?

No, Scott has certainly not become a Keynesian, but rather Scott knows full well that the causality between nominal and real shocks - whether RGDP determines NGDP or it is the other way around - is critically dependent on the monetary policy regime - a fact that most economists tend to forget or even fail to understand.

Let me explain - I have argued earlier that we should think of the monetary policy rule as the "missing equation" in our model of the world. The equation which "closes" the model.

It is all very easy to understand by looking at the equation of exchange:

M*V=P*Y

The equation of exchange says that the money supply/base (M) times the velocity of money (V) equals the price level (P) times real GDP (Y).

The central bank controls M and sets M to hit a given nominal target. Market Monetarists of course have argued that central banks should set M to hit an nominal GDP target. This essentially means that the central bank should set M to hit a given target for P*Y.

We know that in the long run real GDP is determined by supply side factors rather than by monetary factors. So if we have a NGDP target then the central bank basically pegs M*V, which means that if the growth rate in Y drops (the Great Stagnation story) then the growth rate of P (inflation) will increase.

So we see that under an NGDP targeting regime the causality runs from M*V (and Y) to P. Inflation is so to speak the residual in the economy.

But this is not what Scott indicates in the quote above.

This is because he assumes that the Fed is targeting around 2% (in fact 1.8%) inflation. Therefore, IF the Fed in fact targets inflation - rather than NGDP - then in the equation of exchange the Fed "pegs" P (or rather the growth rate of P).

Therefore, under inflation targeting the Fed will have to reduce the growth rate of M (for a given V) by exactly as much as the slowdown in (long-term) growth rate of Y to keep inflation (growth P) on track.

This means that under inflation targeting shocks to Y (supply shocks) determines both M and P*Y, which of course also means that "NGDP slowdown is real" (as Scott argues) if we combine a slowdown in long-term Y growth and an inflation targeting regime.

Scott won - so he is wrong about causality

Scott, since 2009, forcefully has argued that the Federal Reserve should target nominal GDP rather than inflation. I on the other hand believe that Scott has been even more successful than he believes and that the Federal Reserve already de facto has switched to an NGDP targeting regime (targeting 4% NGDP growth). Furthermore, I believe that the financial markets more or less realise this, which means that money demand (and therefore money-velocity) tend to move to reflect this regime.

This also means that if Scott won the argument over NGDP targeting (in the US) then he is wrong in assuming that the real shocks will become nominal (that Y determines M*V).

The problem of course is that we are not entirely sure what the Fed really is targeting - and neither are most officials. As a consequence we should not think that the monetary-real causality in any way is stable. This by the way is exactly why we can both have long and variable leads and lags in monetary policy.