21 September 2015

The Trouble With The Zero Lower Bound

Most of the time, it seems that the monetarist view of inflation is pretty much correct. Inflation roughly tracks the monetary base and velocity is pretty stable and almost directly follows short term interest rates. Unfortunately, there is this thing called the zero lower bound that seems to throw monetarism off.

The US has been at the zero lower bound twice in the last 150 years, and both times monetary expansion has seemed to have an irrelevant - even a negative - impact on inflation.

Here's 1934-1945:

And here's 2009-2015:
Most monetarists seem to have trouble coping with the irrelevance of the monetary base at the zero lower bound, even though it does seem to be part of a lot of basic monetary models. Take the most simple of money demand functions - cash-in-advance. It is easy to figure out that as long as there is a cost to the household incurred by holding money, the cash-in-advance constraint will bind, but whenever there isn't a cost, the constraint ceases to bind. This effectively means that, rather than being stuck at unity, the velocity of money is indeterminate; increases in the money supply will no longer have any effect on the price level.

Money-in-the-utility-function models have similar properties in the sense that velocity also becomes indeterminate. MIUF models are slightly strange though because money demand itself actually goes to infinity when the zero lower bound binds. But, MIUF is a pretty bad assumption anyway, so it's fine to ignore this.

An easy modification to CIA models that, when calibrated properly, might be able to make them match the data pretty well is the addition of a non-cash good to the economy. The income-velocity of money will now fluctuate with the nominal interest rate while the effects above will still be present.

I digress, the key idea of this kind of rambling post is that the zero lower bound seems to do strange things to monetary policy which precludes central banks from being omnipotent as some would suggest...

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