The Neo-Fisherian Question

On the "Neo-Fisherian" idea that maybe raising interest rates raises inflation, Nick Rowe asks an important question. What about the impression, most recently in a host of countries that seemed to raise rates "too early" and then backed off, that raising interest rates lowers inflation? (And thanks to commenter Edward for the pointer.)

Partly in answer, and partly just in mulling it over, I think I can boil down the issue to this question:

If the central bank pegs the nominal rate at a fixed value, is the economy eventually stable, converging to the interest rate peg minus the real rate? Or is it unstable, careening off to hyperinflation or deflationary spiral?

Here are some possibilities to consider. At left is what we might call the pure neo-Fisherian view. Raise interest rates, and inflation will come.

I guess there is a super-pure view which would say that expected inflation rises right away. But that's not necessary. The plot in Monetary Policy with Interest on Reserves worked out a simple sticky price model. In that model, dynamics were pretty much as I have graphed to the left: real rates rise for the period of price stickiness, then inflation sets in.

Now,  here is a possibility that I think might satisfy  Neo-Fisherism, Nick, and a lot of people's intuition:

In response to the interest rate rise, indeed in the short run inflation declines. But if the central bank were to persist, and just leave the target alone, the economy really is stable, and eventually inflation would give up and return to the Fisher relation fold. (I was trying to get the model of "Interest on Reserves" to produce this result, but couldn't do it. Maybe fancier price stickiness, habits, adjustment costs...?)

This view would account for the Swedish and other experience.

We don't see the Fisher prediction because central banks never leave interest rates resolutely pegged. Instead, they pursue short-run pushing inflation around.


And there's nothing really wrong with that if they know what they're doing. If you have a system with this kind of short run dynamics, you can get inflation where you want it faster by pushing the short run dynamics around, rather than pegging interest rates and just waiting for the long run to arrive. Lower rates, which pushes inflation up in the short run, then follow inflation up, with a quick burst of high rates to stop inflation, then back to normal.

I think the revival of Neo-Fisherism occurs by watching our period of zero rates, in which central banks can't push rates down any more. If you held the last view,  raising rates and waiting for the long run seems like a possible strategy.

But these dynamics are not the standard view. The standard view is that the economy is inherently unstable. If the central bank were to raise rates and leave them there, the economy would spiral off to never ending deflation. Conversely, a too low interest rate peg would send the economy off to spiraling inflation.

Now, we don't see such spirals. But that is because central banks don't peg interest rates.

In the standard view, a central bank would soon see inflation spiraling down, would quickly lower interest rates to push it back up again. Upside down, this might be a stylized view of the 1970s and 1980s.

Alas, central banks pushing short-run dynamics around in my second neo-Fisherian view graph would lead to time series and impulse responses that look like this as well.

So in normal times it would be devilishly hard to tell long run stability from long run instability by looking at time series of inflation and interest rates. (Most impulse response functions do feature interest rates with interesting dynamics after a shock. So we can't really tell if the resulting inflation path is due to the initial shock or to the subsequent behavior of interest rates)

We can put the issue more generally as, if the central bank does nothing to interest rates, is the economy stable or unstable following a shock to inflation?

For the next set of graphs, I imagine a shock to inflation, illustrated as the little upward sloping arrow on the left. Usually, the Fed responds by raising interest rates. What if it doesn't?  A pure neo-Fisherian view would say inflation will come back on its own.

Again, we don't have to be that pure.

 The milder view allows there may be some short run dynamics; the lower real rates might lead to some persistence in inflation. But even if the Fed does nothing, eventually real interest rates have to settle down to their "natural" level, and inflation will come back. Mabye not as fast as it would if the Fed had aggressively tamed it, but eventually.

By contrast, the standard view says that inflation is unstable. If the Fed does not raise rates, inflation will eventually careen off following the shock.

We don't see that outcome in the data, because even if not right away (as the Taylor rule recommends), eventually central banks wise up, raise rates, and bring inflation back again.

Which brings us to the current moment.

The last 5 years have brought us a delicious opportunity for measurement. Once we hit the zero bound, interest rates can't move any more. So the whole problem of empirically verifying long run dynamics is a lot easier.

What happened when the Fed kept interest rates at zero for 5 years? Pretty much nothing! OK, you see inflation going up and down, but look at the left hand scale -- one percentage point. Given the colossal scale of other events in the economy, that's nothing. Japan has been at it even longer, with similar results.

We seem to have in front of us a pretty clear measurement that long run dynamics are stable.

"Nothing" is astounding. This dog that did not bark has demolished a lot of macroeconomic beliefs:

• MV = PY. Sorry, we loved you. But when reserves go from $50 billion to $3 trillion and nothing at all happens to inflation -- or at most we're arguing about percentage points -- it has to go out the window. 
• Keynesian deflationary spirals. Just as much as monetarists worried about hyperinflation, Keyensians' forecast of a deflationary spiral just didn't happen. 
• The Philips curve. Unemployment went to levels not seen since the great depression; the output gap went to 10 percent and ... inflation moved less than one percent. Adieu. (Actually, Phillips curve lovers turn this on its head, to proclaim that all we need is 1% more inflation to bring the economy roaring back, but you can see how tortured that one is.) 
• Fiscal stimulus... well, we'll take that up another day

So, I bring you the question, which is not so obvious as Nick makes it sound.

If the Fed completely and permanently pegs interest rates, is inflation in the long run stable or unstable?

In response to shocks (left arrows) and after a period of short-run dynamics (squiggly path), will inflation eventually return to the Fisher relation?

Or, will inflation eventually diverge -- until the Fed gives up on the target?

Think of holding a broom upside down. That's the standard view of interest rates (on the broom handle) and inflation (the broom). Anytime the Fed sees inflation moving, it needs to quickly move interest rates even more to keep inflation from toppling over -- the Taylor rule. To raise inflation, the Fed needs first to lower interest rates, get the broom to start toppling in the inflation direction, then swiftly raise rates, finally raising them even more to re-stabilize the broom.

The neo-Fisherian view says the Fed is  holding the broom right side up, though perhaps in a gale. To move the bottom to the left, move the top to the left, and wait.  But alas, the broom sweeper has thought it was unstable all these years, so has been moving the handle around a lot.

Theories: Both monetarist and old Keynesian theories are of the unstable sort.

For Keynesian models, I like very much John Taylor 1999 Journal of Monetary Economics This paper (or at least my reading of it starting p. 601 here) shows that old-Keynesian models with fixed interest rate targets are unstable, with explosive eigenvalues. Adopting a Taylor rule with inflation coefficient greater than one makes the economy stable -- the Taylor rule says, move the broom handle more than the top of the upside-down broom is moving, and you'll keep it balanced.

For monetarism, read (re-read!) Milton Friedman's "Role of monetary policy" starting on p. 5 regarding interest rate pegs.

Adaptive expectations are, I think, the key features that make these models unstable. By contrast, new-Keynesian models, with rational forward-looking expectations produce stability with interest rate pegs. They produce too much stability, and thus multiple equilibria. (Stephanie Schmitt-Grohe' and Martin Uribe's papers on this topic are a good place to look.)  Fiscal theory removes the indeterminacy, so seems to give a determinate Neo-Fisherian answer. And it empahsizes, that what will happen both in the short and long run depends on fiscal policy.

At the cost of repeating myself (this means you, Nick!) the issue is the long run stability of inflation under an interest rate peg (and appropriate fiscal policy!), not short-run dynamics. And it's not so easy to tease out of the data, though certainly worth the challenge. A clever VAR, noting periods of forced pegging due to the zero bound, might help.