# The Fishermen

Stephen Williamson and John Cochrane have raised a radical question: What if we have the sign wrong for monetary policy? What if low interest rates reduce inflation and high interest rates raise it, that is, rather than the other way around?

Their basic argument is this: If the real interest rate is fixed, then when the central bank raises the nominal interest rate, it also raises the inflation rate; when it lowers the nominal interest rate, it also lowers the inflation rate.

You can see that in the Fisher relation, which is:

*i = (1+r)(1+*

*π) ≈ r + π*

*i*is the nominal interest rate,

*r*is the real interest rate, and

*π*is the inflation rate. The time preferences of agents in the economy fix the real interest rate, and the central bank specifies policy in terms of the nominal rate.

I think there are basically two problems with the debate. The first is that the Fishermen wrap a dubious claim in an identity and a modeling assumption. The second, which follows from the first, is that if this debate is about anything, it's not really about the Fisher relation at all. It's about the wrapped-up claim.

Look back to the Fisher relation, and you'll see that it's true by the construction of the model that when the central bank raises the nominal interest rate, the inflation rate must rise. That's an identity, and we've said that the real interest rate is fixed.

But the problem with this argument, which looks airtight, is that it misconstrues what the Fisher relation is. What it really says is when the central bank raises the nominal interest rate, the inflation rate consistent with a steady-state equilibrium also rises.

Note that what I've done here is add in the words "consistent with a steady state equilibrium." This isn't mere semantics. It matters because the central bank's power in one sense is materially weaker: It no longer picks the current rate of inflation off a menu, but rather only the rate of inflation that can be sustained. Yet it also means that the central bank's power is, in another sense, materially stronger: It can distort the real interest rate in the short run.

Why does this matter? Because what I've shown is that wrapped inside Williamson's and Cochrane's point about the Fisher relation, which is just plain true, is an actual claim, and a dubious one: After the central bank raises the nominal interest rate, and thereby the steady-state rate of inflation, inflation will actually rise to that steady state. Cochrane embeds this assumption to the model if you look carefully; Williamson doesn't seem to discuss it.

So the first point is that the Fishermen aren't wrong. In fact, they can't be wrong. They're wrong about what their conclusion is. The second point is that the Fisher relation is in fact tangential to the whole debate. If Williamson and Cochrane are arguing anything at all, what they're arguing is the point about dynamics -- i.e. that inflation is well-behaved and goes to the new, higher steady state the central bank chooses when it picks the higher nominal interest rate.

Does the inflation rate explode when it starts out above the central bank's choice of equilibrium? Or does it converge nicely to the equilibrium? Do we fall into catastrophic deflation when inflation starts out above the central bank's choice of equilibrium? Or can we actually raise inflation by hiking rates? And, even if the dynamics aren't explosive, the interest-rate peg still means that the price level can float anywhere, depending on the sequence of shocks.

In case it's not totally obvious, I think we're in the second world. That's a view informed by a longstanding theoretical tradition in macroeconomics that the price level is indeterminate when the central bank pegs an interest rate.

It's also a view informed by data. Beckworth beat me to the punch when he looked at historical episodes of interest rate pegs and saw exactly what Sargent and Wallace predicted. I would also point out that we have really strong evidence, also from Sargent, that the way to stop hyperinflation is to hike interest rates hard. That would be literally the worst thing you could do if you cast your line with the Fishermen.

*More: Via Tony Yates, I am reading Cochrane (2011), which gets into many of these issues. Also, I just noticed this new working paper from Williamson, which, interestingly, also digs into the indeterminacy problem. If you look on page 12, his argument about the Fisher relation pops up. Update: I got rid of the illustration because Noah found it confusing.*