Unconscious Norms
Santa and Forgiveness

MV = PQ ?

By Jonathan B. Wight

Okay, this will date me.  I learned macro the old fashioned way. Yes, the Keynesian (or Hicksian) IS/LM stuff that went out of fashion by the late 1970s.

Turns out, the old IS-LM model has done pretty well in helping explain life in a zero lower bound interest world with a liquidity trap. 

But I also studied monetarism, the idea that money matters, and that a set growth in the money supply should produce a set change in nominal GDP.  In short:

M*V = P*Q is true as an identity. 

The money supply times its rate of spending or velocity always must equal prices times outputs (nominal GDP).  We know this has to be true because we calculate velocity as PQ/M, hence the equation must be true after the fact.

The Model. Monetarists turn this into a model for predicting the future by making claims about the behavior of money demand, which in turn affects velocity. 

If economic transactions become more efficient over time (think of ATM machines), then it will take less money to conduct the same value of transactions as before.  This means that each dollar works harder, and velocity rises.

Suppose that financial innovation (growth in V) proceeds at about 4% per year.  Suppose also that real output potential (Q) grows by about 2% per year.  This implies that if money grows by 3% per year, the resulting inflation will be:

3 % + 4 % = % P + 2 %

Money growth + velocity growth = Nom. GDP growth = inflation + real output growth.

In this example, nominal GDP will be increasing by 7% and the inflation rate will be 5%. 

This approach sounds reasonable, and monetarism held high sway for a few years in the early 1980s when velocity behaved somewhat predictably.  In fact, some pundits suggested doing away with the Fed entirely and simply replacing it with a monetary rule (increase money by 3% each year, come hell or high water).

[This is a nice fantasy, that we don’t need anyone minding the store of money.  Or alternatively, we should simply do away with government fiat money and return to private bank money (ask Adam Smith about the Scottish banking panics….).]

Downfall of the Model. But by the mid-1980s the whole thing was a mess: no one could accurately predict money demand, and hence no one could predict the impact of money on nominal GDP. 

Come the Great Crash of 2008, the demand for money as a safe store of assets soared, hence the infamous liquidity trap: people and businesses wanted to hold money as an asset on their balance sheets because all the alternatives were too risky.  The Fed cooperated by increasing bank reserves. The result, as shown below, is a massive build-up of money and virtually no inflation.  People are holding money as a hedge against financial market risk.  Since they aren’t spending it, it won’t cause inflation.

The Ethics of the Fed:  Hence, the ethics of the Fed's actions during this crisis can be seen in a new light once we understand that the monetarist vision, while certainly and absolutely true in times of hyperinflation, do not apply to economies in a liquidity trap.  Of course, if sufficient confidence returns, people may decide to spend and the Fed would have to back-pedal.


Given the narrowing of the macro models now taught in graduate school, I had to help a new colleague recently who had never worked with IS/LM and didn’t know where it came from.  Age and maturity has a few perks!

If you’re curious, read Sir John Hicks "Mr. Keynes and the Classics – A Suggested Interpretation", 'Econometrica v. 5 (April 1937): 147–159.


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