## Sunday, February 1, 2015

### Taylor Rules, the Zero Lower Bound, Inflation, and Larry Summers

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.

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. "

If the obvious cure for the stagflation of the 70's was supply-side economics , in which we responded with the familiar policy suite of the Reaganomics Revolution , why is it not the obvious cure for stag-disinflation to reverse those policies ?

Economics seems to have many areas where symmetry is evident , but never when that symmetry would recommend a policy of raising taxes on the rich , or raising workers' pay.

It's certainly puzzling.

Or very convenient.

1. "...If the obvious cure for the stagflation of the 70's was supply-side economics , in which we responded with the familiar policy suite of the Reaganomics Revolution..."

Who said that? What happened in the 70s was that we agonized about central bank commitment to low inflation and how to get it, and then Volcker and his descendants delivered it.

2. " Who said that? "

Oh , c'mon. Are you really going to make the argument that the policy debate at that time was only about monetary policy ? Milton Friedman was just about monetary policy ?

Here's a couple of quotes on just two topics - progressive taxation and unions - that gives us some idea about how the economic consensus has changed relative to that of the pre-1970s era :

"There is no doubt that an increase in the progressivity of the tax system has a negative effect on aggregate economic welfare by way of incentives."

"....most economists have the opinion that unions perform no useful economic role in modern society."

Now , during the stagflation of the 1970's , I can sort of understand the rationale that would cause economists to come to these ( debatable ) conclusions. But today , given the extremes in inequality that have developed - which may be causative in the demand deficiency we see ( absent debt-driven demand ) - these statements would have to be called into question by any fair-minded economist. Our current situation is the mirror image of stagflation , requiring a reexamination of priors. My point is that these statements won't be re-examined , because that would only endanger the high returns being enjoyed at the top of the distribution.

Like I said , economics is convenient. For some.

( BTW , if you're wondering , the quotes above are yours : )

http://press.anu.edu.au//apps/bookworm/view/Agenda,+Volume+18,+Number+3,+2011/7641/Text/williamson.html

3. Seems you are a bit off topic.

2. If it turns out that central banks can and will push interest rates below zero, the Taylor rule may not be so bad. I still think that a 5-6% NGDPL growth rule would be better, which only requires more willingness to use QE.

1. Yes, the ECB and the Swiss National Bank pay negative interest on central bank balances. Actually, that doesn't solve the problem. If you set the lower bound below zero, you'll just have lower inflation when you stay at the lower bound for a long time. On QE: Apparently massive QE has not produced more inflation in Japan. How come?

2. Stephen Williamson, what do you mean QE has not produced more inflation Japan? http://www.tradingeconomics.com/japan/core-inflation-rate

3. It helps to look at the levels. It won't make much difference if you do core CPI or raw CPI. Raw CPI in April 2013, when QE started in Japan was 99.7. Raw CPI in December 2014 was 103.3. So, the increase from the beginning of QE to December 2014 was 3.6% in total. But note that the consumption tax rate increased from 5% to 8% in April 2014. Further, note that the CPI jumped from 101.0 in March 2014 to 103.3 in April 2014. So, if we adjusted for the effects of the consumption tax, that's not much inflation for such a large QE program, don't you think?

4. Further, the CPI is virtually unchanged from April 2014 to December 2014.

3. We will have to see if those central banks will lower rates enough to get inflation back up to target. That remains to be seen. Has even Japan committed to buying long term assets without limit until the hit their inflation target? Certainly the Fed did not and ECB has only now begun a limited program. The Fed gives every indication that it does not in fact have even a 2% inflation target but rather a 2% inflation ceiling target. No wonder QE did not have more effect than it did.

1. You seem to believe that low nominal interest rates, and QE will, sooner or later, and if we do enough QE, produce more inflation. How much evidence do you need that this won't happen?

4. Steve, I think you have to be a bit more precise in terms of how to achieve the higher interest rate. One way is by increasing the supply of Treasuries until their yields begin to rise (indicating a reduction in their scarcity). I think most people would agree with that. The other way is increasing the interest rate on reserves. I am not sure what is the mechanism by which this would work (e.g. by creating inflationary expectations?).

By the way, how do you interpret that many European government bonds now have negative nominal yields? Does this mean that they are more liquid than reserves?

1. "...how to achieve the higher interest rate"

In the U.S. currently, roughly that means increasing the interest rate on reserves - a little more complicated than that, for various reasons.

"I am not sure what is the mechanism by which this would work."

Well, you start with the intertemporal Euler equation that prices nominal bonds. That always has to hold. There can be endogeneity in the real rate, but suppose you have a model in which the long run real rate is a constant, which makes it easier. So, in the long run, the Fisher relation has to hold - nominal rate equals real rate (a constant in the long run) plus inflation rate. So in the long run, an increase in the nominal rate increases the inflation rate one-for-one. But obviously that long-run equilibrium has to be supported by a lot of other things that have to happen. For example, all nominal asset quantities that matter have to be increasing at a higher rate. The money stock for example. So, this has to be accommodated by open market operations. In the current regime in place, that's not an issue, except after the balance sheet of the central bank normalizes. Further, the fiscal authority has to be accommodating this - nominal government debt has to be growing at a sufficient rate. And yes, expectations are rational, so they're accommodating this too. But it's not a multiple equilibrium story. You should read the paper and see how it works. In any of these things you have to be up front about what fiscal policy is doing, and the relationship between monetary and fiscal policy. People don't always do that, except perhaps implicitly.

2. OK, will read the paper, thanks. Unfortunately I don't think fiscal authorities can/will commit on a policy that works in tandem with monetary policy, and for practical purposes monetary authorities should take this as given, though I will be happy to be proven wrong.

Finally, I know it is a bit off topic, but I am still interested in your thoughts on the negative European bond yields if you have any.

3. The fiscal policy is tricky. While we have a lot of experience thinking about monetary policy rules, fiscal policy rules are another thing. The typical assumption in monetary models was to just assume that fiscal policy is completely passive - e.g. money is injected by lump-sum transfers, so monetary policy effectively is fiscal policy. If you're more serious about it, you have to recognize that the central bank can only expand outside money by purchasing assets, and so fiscal policy could constrain monetary policy, as the fiscal authority issues the government debt that the central bank purchases. You can make some reasonable assumptions, and get somewhere on this, though.

On the bond yields, I haven't looked at this closely. Why would the yields on 2 and 5-year German bunds be negative? First, the interest rate on ECB deposits is now -0.20%, and I think it's expected to stay there for a long time, if not go lower. So short rates are expected to be negative for a long time. Second, maybe the markets are expecting a prolonged deflation, so there's a negative inflation premium. But how can these rates go below zero? It's hard to arbitrage with the zero nominal interest rate on currency. Large quantities of currency are inconvenient to hold - the stuff takes up space and can be stolen. I have to look at this more closely though.

5. "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."

Sersiously, you are still believing in that accounting identity nonsense? Monetary policy does not just influence nominal but also real rates so your theory is false.

1. "Monetary policy does not just influence nominal but also real rates so your theory is false."

Most of what I'm saying holds in any standard macro model. Under some conditions, and in some of the models I write down, monetary policy has effects on real rates in the short run, and in the long run. These ideas are quite robust, and hold across a wide array of models with different bells and whistles. Maybe you think all mainstream macro is "false"?

6. Your nonsense is the very opposite of mainstream macro. You derive at this ridiculous result, that lower nominal rates would lead to lower inflation, via taking an accounting identity I=N-R and wrongly assuming that monetary policy only influences the nominal rate N while taking R as exogenous and fixed.
Typical problem of guys coming to econ from macro (Kocherlakota also had this problem until he wisened up in 2012). Sorry dude, but econ is a social science and good economists don't just state at equations but consider the actual mechanisms. In this instance the mechanism is that of lowering nominal rates via injecting liquidity into the monetary market. This always leads to higher inflation. Now if we are in a liquidity trap / if the velocity of money is low the effects of expansionary monetary policy upon inflation are smaller or even nonexistent. But they are always weakly positive and never negative.

1. Same troll, different day. Ignoramus Rex, half of your nonsense makes reference to New Keynesian theory and half to the quantity theory. You are in conflict even with yourself! Homework: Were nominal interest rates high or low in the 1970s, when monetary policy was expansionary?

2. My favorite one is the Volcker disinflation. If you look at the time series, Volcker succeeded in reducing the inflation rate by reducing the nominal interest rate.

3. Nope. Volcker succeeded in reducing inflation because during the first two years in office he actually raised the FFR from around 10% to around 20%.

I gotta admit though that it is entertaining to read Mirror Universe economists.

4. John, a large amount of nonsense does not wrap around the torus and become sense. Give it up and go away.

5. Yup. As I said, look at the whole time series, and get the timing right relative to what's announced.

7. But doesn't it seem like the ECB's rate hikes in 2011 led to lower inflation?

And don't all central banks subscribe to the belief that rate hikes lead to lower inflation?

1. It's not certain whether they did or not. In general, we think there are short-run liquidity effects, so yes, in the short run this could have led to lower inflation. That's the whole issue. The choices are to sit at the zero lower bound, and continue to bear low inflation, or raise the nominal rate, and possibly bear even lower inflation in the short run, so you can have higher inflation in the long run.

8. "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 ECB..."

I think this is factually incorrect. IIRC the BoJ did raise rates in 2006. (I can't recall if they also did so in 1999.) And the ECB did in 2011. And we can observe that the inflation rate in the US, where the Fed has not yet raised rates after hitting the ZLB, is higher than in Japan or the Eurozone.

1. See my next post:

http://newmonetarism.blogspot.com/2015/02/phillips-curves-and-deflationary-panic.html

After the Bank of Japan lowers rates in mid-1995, the overnight rate never goes above 50 basis points for roughly 20 years. What do you want, zero forever? And I think we can correctly characterize these other central banks as being resolutely zero-lower-bound. Some of them have even relaxed the lower bound to something below zero. Conclusion: You are nit-picking.

2. "And we can observe that the inflation rate in the US, where the Fed has not yet raised rates after hitting the ZLB, is higher than in Japan or the Eurozone."

What significance do you think that has?

3. Well, it's only one data point, so obviously it doesn't prove anything, but it is suggestive that the conventional view is correct: that staying at the zero bound is a more inflation-inducing policy than leaving it. Granted, 50 basis points isn't a big deal in itself, but I think it's important as a signal of the bank's general policy tendencies. Show that you are willing to tolerate a little more inflation, and markets will keep on trying to test higher inflation rates; show that you won't tolerate even a little bit of above-target inflation, and markets will give up and keep inflation too low.

Which brings me to the question of what do I want, zero forever? I'd say I want zero until you convince markets that you're going to stay at zero a little too long, at which point they will push the inflation rate higher, and you'll end up leaving zero (a little too late, which will turn out to be earlier than "a little too soon" would otherwise have been).

It's all about coordinating expectations IMO. You can argue that higher interest rates would coordinate expectations of higher inflation, but I don't find that argument convincing. I think demonstrating a reaction function is what coordinates expectations.

You can also argue that fiscal policy expectations will tie down the price level in the long run, but I suspect that fiscal policy commitment is even harder than monetary policy commitment. Then the open question of where the long run price level is really tied down (given that future fiscal policy is unknown) becomes a bigger issue in determining today's inflation rate than the interest rate policy that determines the transition.

4. So you want to convince markets to believe something they know you're not going to do? Good luck with that.

9. Why not just break the Taylor rule and set 0 < a < 1? This seems to eliminate the extra equilibrium at R = 0 and achieve inflation targeting. I could not easily Google a definition of "local determinacy" or its relevance. Is the issue, as we scientists would say, stability?

1. Yes, if the central bank was told that it had to follow a Taylor rule, then we could make a case that 0 < a < 1 is a good idea.