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*

where

*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.
Noah Smith has a useful summary of the debate; he counts himself among the supporters of the "Neo-Fisherites." I think the term "Fishermen" is catchier. David Beckworth, who prodded me to write up some thoughts on this, argues that economists have conclusive historical evidence against the Fishermen. After World Wars I and II, governments pegged the interest rates on their debt very low; what they got was explosive inflation. Ryan Avent also points out that expectations are key here -- and should be in the Fisher relation I wrote above.

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. That's exactly what the second picture shows: If you don't start out at 2, then the dynamics get completely out of control.

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.

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. That's exactly what the second picture shows: If you don't start out at 2, then the dynamics get completely out of control.

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.*
Sigh. Are academic economists living in an alternate reality? Volcker came in in the early eighties and raised short term rates to 20% to tame inflation. It worked. This was followed by Greenspan who engineered a disinflation until about 1998 when forward inflation expectations finally tamed. He did that by raising rates.

ReplyDeleteThis kind of silliness is why corporate economists mostly ignore academic ones, they are busy debating silly things that have nothing to do with the real world.

Right on. I could have written a post with a simple data analysis of "rate surprises" showing which way inflation breakevens moved. That would have been more convincing to me. Curious if that would have been better for you, too.

DeleteIsn't it possible that changes in central bank policy that result in a rise in i (nominal interest rate) could affect the economy in ways that affect r (real interest rate)? The idea that r is exogenous, independent of central bank policy, seems kind of ridiculous. Clearly, if some central bank policy that increases i also causes r to rise, then inflation can fall in response to a nominal interest rate hike.

ReplyDeleteAnd why would that happen? If the fed drives up nominal rates, and money market participants don't expect inflation, then lenders will demand a higher real rate of return because they have higher yielding risk-free options thanks to the central bank action, and borrowers will have to either pay up or stop borrowing, slowing economic

activity and fulfilling the prediction of low inflation.