## Things I Forgot to Post Months Ago: Does Stephen Williamson Understand the Monetary Economics He Teaches Edition?

Sorry. This should have gone up… months ago...

I see Stephen Williamson is [was] ranting about how he teaches people monetary theory while I teach them John Stuart Mill, Wicksell, Fisher, Friedman, and Hicks…

From my perspective, the problem is that Stephen Williamson does not understand the monetary theory he purports to teach--and does not understand it because he does not know Mill, Wicksell, Fisher, Friedman, and Hicks. Consider Stephen Williamson's

Suppose a cash-in-advance model with a representative consumer, period utility u(c), discount factor b, constant aggregate endowment y. c is consumption. The consumer needs cash to buy c each period. Suppose y is a fixed quantity of output received by a firm, which is sold for cash within the period, and then the cash is paid as a dividend to the consumer at the end of the period. Have the money stock grow at a constant rate m. The real interest rate is constant at 1/b - 1. The nominal interest rate is (1+m)/b - 1, and the inflation rate is m. Constant m implies a constant nominal interest rate and a constant inflation rate. If m < 0, there is deflation, and the nominal interest rate is sufficiently low to support the deflation. I can think of the instrument the central bank sets as either the money growth rate or the nominal interest rate - that part is irrelevant.... What's the problem?"

This is simply wrong, wrong, wrong, wrong, wrong.

Setting a credible forward path for the nominal interest rate is not at all the same thing as setting a credible forward path for the money stock growth rate. The strategy spaces are different. And that makes a difference.

The problem, of course, is that Williamson does not have a model--a set of behavioral relationships and equilibrium conditions. Rather, all he has is a set of equilibrium conditions. But in order to figure out whether an economy is or can be expected to be evolving along a steady-state equilibrium path, you need not just the equilibrium conditions but the behavioral relationships. You need a model. And Williamson ain't got one.

The standard, conventional monetary theoretic model for the case when the Fed chooses a nominal interest rate target can be drawn on a graph with the nominal interest rate i on the vertical axis and the inflation rate π on the horizontal axis. This model has a "Wicksellian balance" condition--Williamson's r* = i - π --that does not hold at all times but, rather, is a steady-state equilibrium condition: if the economy is to the left of and above the Wicksellian balance line so that the real interest rate will be high, inflation is falling; if the economy is to the right of and below the Wicksellian balance line so that the real interest rate is low, inflation will be rising. And the Federal Reserve will not achieve its target interest rate all the time either: if the interest rate i above the red policy rule line, the nominal interest rate will be falling as the Federal Reserve pumps out the money; if the economy is below the interest rate will be falling as the Fed sells bonds for cash:

In this model the point where the blue and the red curves cross--the point where Williamson says inflation and nominal interest rates are constant--ain't a point where inflation and nominal interest rates are constant: we do not expect the economy to be there. What we expect to happen is that if the economy starts to the left of the green line it heads off toward deflationary Valhalla at point C, and if it starts to the right of the green line it heads off to inflationary Valhalla.

Of course, nobody believes that when inflation reaches 120% per year the Fed will still maintain its policy of pegging the nominal interest rate at 2% and so pumping out the money at 120% per year. Instead, we all believe that at some point--when inflation is too high--the Fed will abandon its nominal interest peg and cut back on money growth, and so its policy rule line will have a kink in it, like so:

We expect that if the economy starts to the right of the green line it will ultimately head for point A--and that if it starts to the left it will still head for deflationary Valhalla at point C. In this model, lowering the leftmost constant-nominal-interest rate peg arm of the policy rule is not a way to reduce inflation. Instead, it is a way of moving the green line to the left and increasing the set of initial conditions for which the economy converges to point A.

By contrast, the model in which the central bank sets a money-stock growth rule has very different dynamics--no explosion to either deflationary or inflationary Valhalla...

You cannot "think of the instrument the central bank sets as either the money growth rate or the nominal interest rate - that part is irrelevant". That part is not irrelevant. The two different instruments imply very different dynamics for the economy.