## What I Hope Is the Last Word on Stephen Williamson...

A question from the floor:

As I understand Kocherlakota and Williamson, theyre saying that in the long run, fundamentals determine the real return, r (ie monetary neutrality).  The Fed then can choose i or pi and the other is then pegged.  So low interest rates lead to deflation.... I thought the Fisher equation is a (long-run) no-arbitrage condition.  In that sense, theres no reason to talk about causality.  We choose i or pi and the other one is set by fundamentals (ie, r) and no-arbitrage...

Yes, you are confused.

The Federal Reserve chooses pi by choosing the rate of growth of the money stock. If i is then below pi + r, you can make profits by borrowing in nominal dollars and investing in physical capital that yields the real return r. You do so. The supply of bonds goes way way up as bond issuers make money hand over first, and that enormous flood of the supply of bonds pushes the interest rate i up until it is equal to r + pi.

Now suppose the Federal Reserve sets i, and once again i is below pi plus r--i minus r is less than pi. You can still make money by issuing bonds. But when you issue bonds that has no effect on i--remember, the Fed is pegging it. So you issue more bonds. And then you take the bonds and use them to buy up factors of production in order to make more physical capital. And the increased demand for factors of production increases wages and prices, so pi rises as well. And the gap between i and r + pi is now bigger. And so you issue even more bonds.

When the Federal Reserve pegs the money stock growth rate, the arbitrage trade drives i to r + pi. When the Federal Reserve pegs the interest rate, the arbitrage trade drives pi away from i - r. In one case, arbitrage gets you to the rational expectations equilibrium. In the other case, arbitrage pushes you away from it--thus it is hard to see how you would ever get to the rational expectations equilibrium at all.

All of this is, I think, said better in Howitt (1992)...

And we have Andy Harless and Rajiv Sethi in comments:

Stephen Williamson Makes His Play for the Second Stupidest Man AliveTM Crown: Andy Harless writes:

Basically, it all depends on how pi^e (expected inflation) responds to changes in i. It's reasonable to think that, if the Fed raises i, pi^e will rise too, because the increase in i probably reflects higher inflation expectations on the part of the Fed, and private agents will take that into account in making their own forecasts. In order for Kocherlakota's argument to be valid (i.e., in order to get a system that converges to the rational expectations equilibrium at a constant value of i) the change in pi^e has to be at least one-for-one (in the same direction) with the change in i. That seems highly improbable to me. If I'm expecting 0% inflation, and the fed raises the funds rate by 50 basis points, I will not start to expect 0.5% inflation.

Rajiv Sethi said in reply to Andy Harless...

Andy, the thing is, in an RE model the extent to which expectations respond to changes in interest rates is not a behavioral parameter - it's determined endogenously in equilibrium. And one can set up very standard, currently mainstream models with or without sticky prices that give you an equilibrium response that is strong enough for Narayana's claim to be valid (Jesus Fernandez-Villaverde has convinced me of this in email correspondence over the past couple of days). The question, then, is whether the models themselves are robust to departures from RE, for instance with respect to learning. This is what Howitt's paper addresses so nicely.

And I say, crossing with Rajiv's comment:

I would add to the requirements. I would say it has to be (a) a robust equilibrium that (b) people can find via some normal learning process.

Now, as Robert Waldmann points out, we have run the natural experiment: the Reichsbank pegged its discount rate at 3.5% nominal after World War I. The outcome was not price stability or slow deflation, but rather hyperinflation.