I was a bit confused by

this post by Tony Yates on the Taylor rule. I think this issue is important, and worth sorting out.

John Taylor first wrote about the rule in a

Carnegie-Rochester conference paper in 1993. The basic Taylor rule specifies a central bank reaction function

(1)

*R = ai + (1-a)i* + b(y*-y) + r,*
Where

*R* is the fed funds rate,

*i* is the inflation rate,

*i** is the target inflation rate,

*y* is actual output,

*y** is some measure of potential output (so

*y - y** is the "output gap"), and

*r* is an adjustment that is made for the long-run real interest rate. As well,

*a* and

*b* are coefficients, with

*a > 0* and

*b < 0*. The Taylor rule is not some universal optimal policy rule that can be derived from theory, though it is possible to coax it out of some New Keynesian (NK) models. The basic appeal seems to be that: (i) the rule is simple; (ii) it seems to empirically fit how the Fed actually behaves; (iii) Woodford (see

his book) argues that the rule is useful for achieving local determinacy in linearized NK models. For local determinacy, we typically require that

*a > 1*, i.e. the central bank needs to respond sufficiently aggressively to inflation - this is sometimes called the "Taylor principle."

A minimum requirement we might like the Taylor rule to satisfy is that it will lead to a long run steady state in which the central bank achieves its inflation target. From equation (1), it's easy to see why this Taylor rule satisfies that property. The long run Fisher relation

*R = r + i* must hold in a steady state, and if we plug that into (1), then when

*y = y**, then

*i = i**. But, when Taylor wrote down his rule, he wasn't concerned about the zero lower bound. To take this into account, write the Taylor rule as

(2)

*R = max[0,ai + (1-a)i* + b(y*-y) + r],*.

But, with the rule (2), there can be another steady state, which is

*R = 0*, a zero-lower-bound or liquidity trap steady state. If

*R = 0* and the Fisher relation holds, then

*i = -r*. Then, if the output gap is zero, this is a steady state equilibrium, from (2), if and only if

(3)

*(1-a)(r + i*) <= 0.*
or a >= 1. Thus, the liquidity trap steady states exists when the Taylor principle holds, i.e. the condition that gives local determinacy of the desired steady state (in which the central banker achieves his or her inflation target) in NK models also implies a liquidity trap steady state in which the central banker undershoots the inflation target.

We might not be concerned about the existence of the liquidity trap steady state if we could find some theoretical reason for ignoring it. But theory tells us we should not. As

Yates point out,

Benhabib et al. show, in a standard monetary model, and one with sticky prices, that there are in fact many dynamic equilibria that converge to the liquidity trap steady state. An accessible treatment of the idea is

Jim Bullard's paper.
But Yates doesn't want to take this seriously:

I don’t really think this can be the reason. The theory offers a knife-edge result, a trap that would be avoided by a Fed with even a slight tendency for discretion. And those who are briefing FOMC and even on it don’t use rules like this. Though many of them produced the papers exploring the usefulness of these rules, their instinct is to respond as they sit to events as they arise.

This is funny on a least a couple of dimensions. First, for our typical central bank, responding "as they sit to events as they arise" has consisted of sticking at the zero lower bound in the face of low inflation. That's what the Bank of Japan has done for 20 years, it's what the Swedish Riksbank is doing, the Swiss National Bank, the ECB, the Bank of England, etc. Second, if "...don't use rules like this..." means they never talk about it, he hasn't spoken to my colleagues in the Federal Reserve System.

There is plenty of pressure on central banks to act in ways that lead to convergence to a liquidity trap steady state. Representative of this is what Larry Summers has been saying lately. For example, see

this Telegraph article titled "Larry Summers warns of epochal deflationary crisis if Fed tightens too soon." You can hear much more in

this Charlie Rose interview. Summers subscribes to the "deflationary spiral theory" which, as far as I can tell, is not a theory. Further, if it were a theory it would be inconsistent with the evidence (see

this paper by Charlie Plosser, and

this post of mine). For Summers, terror of deflation makes him want to ignore the output gap at low rates of inflation, and respond aggressively to low rates of inflation with a zero nominal interest rate, in hopes that inflation will go up.

Much can go wrong with the Taylor rule. In a recent

working paper, David Andolfatto and I think about low-real-interest-rate economies in which there is a scarcity of safe assets. Basically you get something Larry Summers might think is secular stagnation - the return on safe assets is low, output is low, and consumption is low, indefinitely. This creates further complications for Taylor rules. For example,

*r* in equation (1) is not a constant in the long run, but some function of exogenous variables, to assure that there is a least one steady state in which the central banker hits the inflation target

*i**. But, even if the central banker gets the specification of

*r* correct, there can be more complicated multiplicity problems induced by the Taylor rule. When there is no scarcity of safe assets,

*a < 1* tends to eliminate the liquidity trap steady state, but if safe assets are scarce, then there can be multiplicity (and a liquidity trap steady state) even if

*a < 1*.

It was once thought that the key concern about central bankers was their proclivity to produce too much inflation. If anyone had told us in 1978 that the problem we would face 37 years later would be one of too little inflation, we would have had a good laugh. The key thing I think we need to understand about low inflation is that it's not a trap in the sense that, say, Larry Summers or Paul Krugman thinks it is - a potential deflationary trap. It's a policy trap. Monetary policy creates persistently low inflation, and it's monetary policy that can get us out. Tony Yates comes close to a solution:

In so far as monetary policy was at fault, the problem was that it was directed at a rate of inflation that with hindsight was just too low. Hence why I and others, PK and Blanchard included, have argued for a higher inflation target in the future. In the long run, higher inflation means higher central bank rates, one for one. And this means fewer and less severe episodes at the zero bound.

Maybe he knows the answer, but he's afraid to say it. He certainly understands Irving Fisher. That's what "in the long run, higher inflation means higher central bank rates, one for one" is all about. So take that a step further. Once at the zero lower bound for a long time, as in Japan for example, there is only one way to have higher inflation in the long run. The short-term nominal interest rate has to go up.