Larry Summers Writes It Down

This Financial Times article by Larry Summers articulates ideas that he has been talking about recently.

First, I take it as a good sign that Summers understands that the Phillips curve is not all it's cracked up to be:

...the idea that below normal unemployment will necessarily lead to accelerating inflation as suggested by the so called Phillips curve is very uncertain. Contrary to such predictions, inflation did not decelerate by much even a few years ago when unemployment was in the range of 10 per cent. Nor was there much evidence of accelerating inflation in the 1990s when the unemployment rate fell below 4 per cent.

But Summers is trying to make the case that, for the Fed, continuing with ZIRP (zero interest rate policy) would be a good thing. He says:

...if inflation were to accelerate a bit this would be a good thing. It is now running and is expected to run below the Fed target. Prices are about 4 per cent below where they would have been if 2 per cent inflation had been maintained since 2007. So there is a case for some inflation above 2 per cent to catch up to the Fed’s price level target path. There may also be a case for inflation a little bit above 2 per cent for the next few years to allow real interest rates low enough to promote recovery when the next recession comes.

So, here he seems confused. If the Phillips curve doesn't explain what's going on, how do we get more inflation with continued ZIRP except through a Phillips curve mechanism? Further, Summers seems worried about the "next recession." Presumably if the Fed still has ZIRP at that point, it's powerless (except perhaps with unconventional tools) to do anything about it.

Next, we enter the realm of the bad analogy:

...a plane that accelerates too rapidly as it takes off may cause passengers discomfort while a plane that accelerates too slowly may crash at the end of the runway. Historical experience is that inflation accelerates only slowly so the costs of an overshoot on inflation are small and reversible with standard tightening policies. In contrast, aborting recovery and risking a further slowing of inflation is potentially catastrophic — as Japan’s experience demonstrates. So in a world where economic forecasts are highly uncertain, prudence in avoiding the largest risks counsels in favour of Fed restraint in raising rates.

His assumption, again, is that continued ZIRP will make the inflation rate go up. But "as Japan's experience demonstrates," 20 years of ZIRP just serves to produce low inflation.

Pining for the Fjords

This post by Simon Wren-Lewis brings the dead parrot sketch to mind (with Simon playing the Michael Palin role). I'm interested in the last couple of paragraphs of his post. Simon is analyzing the U.K. policy problem, and asserts:

For whatever reason (resistance to nominal wage cuts being the most obvious), inflation ceases to be a good indicator of underutilised resources when inflation starts off low and we have a major negative demand shock.

First, for inflation to "cease" to be a good indicator of underutilized resources, it must have once been a good one. I have run into economists who think that the unemployment rate is a good measure of underutilized resources. Then, if inflation is a good "indicator" of underutilizaiton, there must be a stable Phillips curve - a negative relationship between the unemployment rate and the rate of inflation.

Clearly, Simon thinks that there has been a "major demand shock" - presumably he means the financial crisis - which caused the Phillips curve to break down. So, suppose we look at the data on CPI inflation and the unemployment rate in the U.K. for 2000-2006. That's arbitrary of course, but if this Phillips curve is so stable, we should see it in the data for that period. Here's the time series (quarterly data):

The inflation rate rises steadily over that period; the unemployment rate goes down, and then up again. Here's the scatter plot, with the observations connected in chronological order:

You can see that's not much of a Phillips curve. Suppose I knew that the inflation rate was 1.8%, and I could not observe the unemployment rate. What would the observed inflation rate tell me about the unemployment rate, given the last chart? Not much. And, in fact, I can observe the unemployment rate. So what is the inflation rate telling me about underutilization?

So after the "major demand shock" - otherwise known as the financial crisis - occurred, what does the Phillips curve in the U.K. look like? We'll first plot the data for 2007-2014 (quarterly) using the headline CPI to measure the inflation rate. Here's the time series:

I think you can tell that this isn't going to produce a nice Phillips curve. Here's the scatter plot:

In particular, note that, from peak unemployment during the recession, the unemployment rate drops about 2 1/2 points, while the inflation rate drops about 3 points. You can see why Simon is worried about the inflation rate as an indicator of underutilizaiton. Presumably utilization has been rising in the U.K., but inflation is dropping like a rock.

In case you're wondering what happens if we use core inflation instead of headline inflation, here's what that yields:

So, that's even worse - the Phillips curve has the wrong slope.

Simon goes on:

...it seems quite possible that GDP continues to be quite a few percentage points below where it could be without inflation exceeding its target...

So, in spite of the fact that Phillips curve logic is inconsistent with the data - and the problem seems more severe post-recession, Simon continues to use that logic. He imagines that it is underutilization that is holding back the inflation rate, as he states:

...so we continue to waste resources on a huge scale. This is money down the drain that we will never get back. It is like taxing households thousands of pounds or dollars or euros a year and burning that money.

Thus, the possibility of an output gap becomes a certainty - it's now a waste of resources on a huge scale.

Simon finishes the post with:

...if, at low inflation rates, inflation becomes a noisy, weak and asymmetric indicator of the output gap, then focusing on inflation is going to perform badly. In these circumstances it could be many years before it becomes clear that we have been continually running the economy under capacity, and needlessly wasting resources. Unfortunately even when that point of realisation arrives, for obvious reasons monetary policymakers are going to be reluctant to acknowledge the mistake.

Simon's chief worry is the latent output gap - the inefficiency he suspects is there, but seems at a loss to measure. It's unclear why we can't see it now, but might realize sometime in the future that it was there all the time - massive, and highly persistent. That certainly doesn't seem like a Keynesian inefficiency - or, to be more accurate, a New Keynesian inefficiency - as that's a temporary phenomenon. If Simon is so certain this beast exists, he should be able to tell us what it is.

I think it might help Simon, as a start, if he declares the parrot dead. The Phillips curve is not resting, sleeping, or pining for the fjords. It is dead, deceased, passed away. It has bought the farm. Rest in peace.

The Bank of England has been close to the zero lower bound for a long time. The Bank Rate has been set at 0.5% since March 2009. Here's the latest inflation projection from the Bank:

And here's the latest inflation data, up to December 2014:

So, like Simon, the Bank seems not to have learned that the parrot is dead. In spite of a long period in which inflation is falling while the economy is recovering, they're projecting that inflation will come back to the 2% target. But 20 years of zero-lower-bound experience in Japan and recent experience around the world tell us that sticking at the zero lower bound does not eventually produce more inflation - it just produces low inflation.

Neo-Fisherianism Spreads

The Turkish President is in a fight with his central bank governor over monetary policy. Possibly President Erdogan came up with this idea on his own, or maybe he's been reading blog posts. In any case, he certainly sounds like a neo-Fisherite.

“They’re simply going to drive one mad. They say they will cut interest rates if inflation falls, this is not a proper understanding; this is the wrong logic because the causality is not one of inflation as reason and rates as outcome. Rates are the reason, inflation is the outcome,” Mr. Erdogan said, reiterating his thesis that is contrary to economic orthodoxy.

Phillips Curves and Deflationary Panic

Paul Krugman has an interesting post on Phillips curves and monetary policy. There are two pieces of "theory" at the heart of his argument: (i) the Phillips curve; (ii) the "deflationary trap." He shows us annual observations on the unemployment rate and core inflation for 2007-2014, estimates a linear Phillips curve, then argues, assuming anticipated inflation is 2% for the whole period, for an estimate of 4.9% for the natural rate of unemployment. Then, he draws a policy conclusion, which is:

Raise rates “too late”, and inflation briefly overshoots the target. How bad is that? (And why does the Fed sound increasingly as if 2 percent is not a target but a ceiling? Hasn’t everything we’ve seen since 2007 suggested that this is a very bad place to go?) Raise rates too soon, on the other hand, and you risk falling into a deflationary trap that could take years, even decades, to exit.

I'm going to use quarterly data, and link the points in the scatter plot so that we can see what's going on. Here, I'll use the pce deflator (excluding food and energy) and stick to 2007-2014, as Krugman does. This produces:

The Phillips curve is an elusive thing. Sometimes you see it in the data, and sometimes you don't. In this particular data set, the observation in the top left-hand corner is 2007Q1, and the line traces observations to 2014Q4. From 2007Q1 until unemployment reaches a peak in the recession, there is a decline in inflation that coincides with the increase in unemployment, which of course is consistent with a Phillips curve story. But, as many people have noted, the implied Phillips curve is quite flat. Over that period, there's a drop of about 0.8 percentage points in the inflation rate, coupled with an increase of more than 5 percentage points in the unemployment rate. Then, from the peak in unemployment (the observation furthest to the right) to 2014Q4, there's a drop of more than 4 percentage points in the unemployment rate, and the inflation rate does not change at all. You can see that, over this later period, the economy is hardly tracing out a Phillips curve. This makes me wonder why anyone would be confident in using the Phillips curve as a basis for forecasting inflation, or thinking about policy. I have some ideas, none of which has anything to do with sound scientific practice.

Just for good measure, we could look at a similar plot, but using the raw pce deflator without stripping out food and energy. That's the measure the Fed focuses on, of course. Here's what we get:

So, that shows a larger decline in the inflation rate during the period when the unemployment rate was increasing rapidly (in part due to the steep decline in commodity prices of course), but essentially the same story from the peak in unemployment - unemployment declines by more than 4 percentage points with essentially no change in the inflation rate.

So, look again at the first sentence in the quote from Krugman's post, above. Clearly, Krugman thinks that, if the zero interest rate policy (ZIRP) continues, and barring unforeseen negative aggregate shocks, the unemployment rate will continue to decline, and the inflation rate will rise - at worst we go above 2% for a short time. But what makes the experience of the last five years make Krugman think that inflation will start to rise? We've had five years of declining unemployment and ZIRP, but no net change in the inflation rate. Further, we might look at Japan, where the Bank of Japan is an old hand at ZIRP. Here's the overnight interest rate in Japan from mid-1995:

As you can see, the overnight rate has been below 0.5% for most of this period of almost 20 years, and below 0.1% for the last five years. Here's the Japanese CPI for the same period:

As you can see, on average the inflation rate has been about zero over the whole period (there's also a story about the last large increase in the CPI in April 2014 - that goes away if you take out the effects of the consumption tax). So, if I looked at the last two time series, that would not give me much confidence that a long period of ZIRP will produce more inflation.

Krugman's chief concern is the risk of deflation - a "deflationary trap." He's been worried about that before, and we know how that turned out. I've discussed deflation terror in an earlier post. The deflation trap is another myth, like the Phillips curve, that we would be better off without. This is in part what formal economics is for. We're forced to write down our theories in the form of internally consistent mathematical language, and subject these models to the scrutiny of our peers, and the public at large. That weeds out a lot of nonsense. The "deflationary trap," while it may sound like convincing economics, particularly when it comes out of the mouths of Larry Summers, or Paul Krugman, has no formal economics behind it. I have seen plenty of models (and have written down some myself) in which there are liquidity traps, and deflation, but I've never seen a model of what Krugman is describing - a vortex that sucks you in and won't spit you out for a very long time. On the empirical side, there's nothing to suggest that we have ever seen such a phenomenon. The Japanese experience of the last 20 years doesn't indicate that deflation is some self-sustaining trap - even given ZIRP, average inflation was zero over that period, as I already noted. Also, this paper by Charlie Plosser has some examples of how deflation need not be associated with horrible stuff.

If there is a deflation trap, or a low-inflation trap, I think it's a policy trap, as I argued in my last post. As such, Paul Krugman and Larry Summers are part of the trap phenomenon. We could start calling this the Krugman/Summers advice trap, I think.

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.