Did inflation targeting destroy its own signal?

The Calvo Phillips Curve has a very special property: the subset of firms that change their prices in any period is a perfectly representative sample of all firms.

That property makes the Calvo Phillips Curve very easy to use, which is why macro modellers like to use it.

But that property stacks the modeller's deck in favour of inflation targeting and against NGDP targeting. Because it makes deviations of inflation from target a perfect signal of monetary disequilibrium.

The Calvo fairy flies around at random, touching firms with her wand, giving them permission to change price. Any firm she touches has a zero cost of changing its price; and any firm she does not touch has an infinite cost of changing its price. And there is a large number of firms. So the subset of firms that do change price is identical to the subset of firms that do not change price.

If all prices were perfectly flexible, monetary policy wouldn't matter much. Aggregate Demand shocks cause booms and recessions because some prices are sticky, so real output adjusts because some prices cannot easily adjust. The job of monetary policy is to try to ensure that those prices that cannot adjust do not need to adjust, so we avoid output adjustments due to monetary disequilibrium.

And that explains why inflation targeting has such desirable welfare properties in a macro model with a Calvo Phillips Curve. The firms that can change prices do exactly what the firms that cannot change prices would like to do if they could change prices. Deviations of inflation from target act as a perfect signal of monetary disequilibrium.

Real world central banks know that the Calvo Phillips Curve is flawed. They know that some prices are stickier than others. In the short run, they pay more attention to core inflation than to "noisy" headline inflation. Macroeconomists know this too; "target the stickiest price" is the slogan that captures this idea. But there is a problem with this policy advice: stuck prices don't change at all, and give the central bank no signal at all.

Take an extreme case, just to illustrate my point. Take a model where all prices are perfectly stuck. The Calvo fairy has gone on strike. "Target inflation" would be useless policy advice, because inflation will be 0% regardless of what the central bank does. The only sensible policy would be for the central bank to target real output or employment. Fluctuations in output and employment might be a noisy signal of monetary disequilibrium, because there are real shocks so some output fluctuations would be desirable, but they are a lot better signal than nothing at all. The Old Keynesians, who advocated targeting output or employment, were not totally stupid.

Now take another case. Suppose Calvo's fairy goes back to work, but decides to charge for her services. The more you pay her, the greater the probability she will touch your firm with her wand and give you permission to change price. Suppose half the firms produce apples, and half produce bananas. Real shocks cause the equilibrium relative price of apples/bananas to fluctuate. The economy is perfectly symmetrical between the two sectors. If the central bank targets the price of apples, the apple producers will be willing to pay little or nothing to Calvo's fairy for permission to change price. Because the central bank will ensure they won't want to change price. So apple prices become very sticky. But banana producers will be willing to pay the Calvo fairy a lot for frequent service, because they will be responsible for changing their nominal prices in response to real shocks to equilibrium relative prices. And the central bank will observe that apple prices are sticky, and banana prices are flexible, and will feel justified in targeting the stickiest price. But apple prices will only change if the central bank misses its apple price target. Banana prices will be a noisy signal of monetary disequilibrium, because they reflect real shocks too, but will be better than none at all.

Fluctuations in inflation are a noisy signal of monetary disequilibrium, because the firms that do change prices are not always representative of the firms that don't. And by targeting inflation the central bank makes inflation stickier, and this reduces inflation's signal/noise ratio. Fluctuations in output are also a noisy signal of monetary disequilibrium. NGDP targeting means targeting the sum of two noisy signals. NGDP targeting is unlikely to be exactly optimal, but may well be better than inflation targeting, which puts all the weight on one noisy signal and ignores the other.

The big puzzle of the recent recession is why the inflation guard dogs failed to bark, to warn central banks of recession. Even in those countries where inflation did fall, it only fell a little. In others it stayed on target, or even rose above target. The NGDP guard dogs barked loud and clear, giving a consistent and correct signal. That is what we need to model. And if we can model that, we may also have a model in which targeting NGDP can do better than targeting inflation.

But we will need to move away from the Calvo Phillips Curve to build that model. Which is going to make it harder.

Comments

[Min]

"Fluctuations in inflation are a noisy signal of monetary disequilibrium,"

Do you have an operational definition of monetary equilibrium?

[Lord]

OT, Michael Pettis offers that whether an economy is conventional or unconventional (neofisherite) with respect to interest rates is whether consumers are largely debtors or creditors.

[psummers]

Great post, Nick!

One semester I told my undergrad students about the Calvo fairy & how she's a central figure in state-of-the-art macro models (ok, not the fairy bit, but the random-ability-to-change-prices bit; no math). The stares than ensued weren't exactly blank, but more like "on what planet is that a sensible model?"

PS

[Nick Rowe]

Min: "Do you have an operational definition of monetary equilibrium?"

If I did have an operational definition of monetary disequilibrium (that could be observed in close to real time), I would just tell the central bank to target that operational definition to equal 0 at all times. Which would make monetary policy much simpler.

Lord: I will take a look. But it sounds wrong.

PS: Thanks!

[Min]

Moi: "Do you have an operational definition of monetary equilibrium?"

Nick Rowe: "If I did have an operational definition of monetary disequilibrium (that could be observed in close to real time), I would just tell the central bank to target that operational definition to equal 0 at all times."

Oh, I did not expect to have an operational definition that would be cheap and easy to observe. But it would be nice to know what we are talking about. :) If there are only "noisy signals" then there is a lot of room to fudge.

[Nick Rowe]

Min: a non-operational (and crude) definition: monetary disequilibrium is when output deviates from what it would be if all prices were perfectly flexible.

[Lord]

I'm oversimplifying as there are many considerations, but it is intriguing from what might improve demand under different circumstances, though the whole consumer/producer, creditor/debtor division can be ambiguous under different income distributions.

[anon]

The Calvo assumption might be reasonable if the cost of changing prices was noisy, such that most firms would seek to wait for a low-cost period. Nevertheless, George Selgin (in Less than Zero) suggests that firms are most likely to change prices is response to shifts in their particular sectors, and since these are typically supply shifts that would affect output at the same time, targeting overall nominal output is more appropriate than targeting inflation. Because, in the latter case, firms are being forced to compensate for changes in unrelated sectors. If there is a good year for apples, apple prices have to drop less (or not at all, if we also consider your example), but banana prices must rise, and that's more difficult. (Or vice versa.)

Ultimately, we don't seem to know much about the microeconomic causes of non-neutrality. So it's hard to come up with good models.

[Nick Rowe]

anon: your description of what George Selgin says is roughly what I have in mind. Unfortunately, we need to model it in general equilibrium terms. A good apple harvest only tells us that the relative price of bananas to apples needs to rise. It is silent on whether apple prices should fall or banana prices should rise, in terms of money.

But imagine there were 10 different fruits, and a shock hits one sector relative to the other nine. In a coordination game, it is easier to imagine the one sector changing its price than the other nine sectors changing their prices. But this means that the sectoral skewness of the real shocks is what matters. And coordination games have multiple equilibria. So it gets tricky. Which is why Calvo's fairy is such a temptress.

"Ultimately, we don't seem to know much about the microeconomic causes of non-neutrality. So it's hard to come up with good models."

Agreed. We are always faking it, with these microfoundations. I blame Tony Yates, for saying that NGDP targeting is "faith-based", unless we have a model. I've been trying to build a model to please Tony. But my failed attempt has only taught me that I need to drop the assumption that the firms that do change prices are a representative sample of all firms. Which is something, I guess.

[Min]

Nick Rowe: "Min: a non-operational (and crude) definition: monetary disequilibrium is when output deviates from what it would be if all prices were perfectly flexible."

IOW, the normal state of affairs. ;)

[Min]

Joking aside, thanks, Nick. :)