Focal Points and the Short Run Phillips Curve; NGDPLPT beats PLPT

Suppose every firm gets surprising news: after having been flat for years, the central bank will raise Nominal GDP by 10% next period, and hold NGDP constant thereafter. How will firms respond?

The Calvo Phillips Curve says that 90% of firms will hold their prices fixed, because the Calvo fairy won't give them permission to raise prices this period. They will expect increased demand for their products and increased sales. And 10% of firms will raise their prices by 10% and expect reduced sales. So the average price level will rise by 1%, and RGDP will rise by the remaining 9%, adding up to 10% increased NGDP in total. [Update: that's only approximately true, but it doesn't matter for this post.]

Does that sound right? Or might an individual firm's willingness to change price depend, in part, on whether it expects other firms to change prices too?

Suppose every firm expects all other firms to raise prices by 10%. That would increase the individual firm's incentive to raise its price by 10% too. And suppose instead that every firm expects all other firms to hold prices constant. That would reduce the individual firm's incentive to raise its price by 10%.

There is an old New Keynesian literature on "strategic complementarity" and "real rigidity" that says the above paragraph is true.

If all prices were perfectly flexible, then, unless those strategic complementarities were very strong (and they probably aren't) we still get a unique Nash equilibrium in which all firms raise prices by 10% and output doesn't increase.

If a randomly chosen 10% of firms have perfectly flexible prices this period, and the remaining 90% of firms have perfectly fixed prices this period, then we get the unique Nash equilibrium of the Calvo Phillips Curve result above.

The Calvo fairy is an all-or-nothing-fairy at the individual firm level. She either lets your firm change price for free, or else she makes it prohibitively costly for your firm to change price.

If instead we had a wimpy Calvo fairy, who only punished you a little bit if you changed prices without her permission, it would be very easy to get multiple Nash equilibria in the above game. If each firm thinks that every other firm will disobey the Calvo fairy, then every firm will disobey the Calvo fairy. If each firm thinks that every other firm will obey the Calvo fairy, then every firm will obey the Calvo fairy. We get two Nash equilibria: one like the Calvo equilibrium; and a second like the perfectly flexible price equilibrium.

Or if firms thought "Hey, if we all disobey her, the Calvo fairy won't punish us all!" we also get two Nash Equilibria.

It is really not that hard to make minor changes to the Calvo model and get multiple Nash Equilibria with self-fulfilling expectations in the Short Run Phillips Curve.

And that looks empirically right to me. When there's a currency reform, or where indirect taxes are changed, and all firms change prices at the same time, it really does look like an outbreak of mass disobedience to the Calvo fairy.

If there are strategic complementarities, and multiple Nash Equilibria, then focal points matter. Like when we all put the clocks back in Fall. Or where a US State Governor changes the date of Halloween. Somebody says we will do something, and we all do it, because we expect everyone else to do it too, and we all want to do what everyone else is doing.

OK. Here's the punchline/policy implication of all this:

There are two ways that central banks can loosen monetary policy at the Zero Lower Bound: they can announce a 10% higher Price Level Path Target; they can announce a 10% higher NGDP Level Path Target. They both shift the AD curve vertically up by the same amount. Announcing a 10% higher PLPT is like announcing a focal point in which all firms raise prices by 10%. That is not the focal point we want firms to converge on, if the economy is in a recession. Announcing a 10% higher NGDPLPT does not create this very undesirable focal point.

Maybe Inflation Targeting has created a bad focal point too.

(Yes, announcing a 10% higher Real GDP Level Path Target would, if feasible and credible, create the right focal point for an economy in recession at the ZLB. But the unknown position of the Long Run Phillips Curve, plus the well-understood problem of instability of equilibrium, even if by a fluke equilibrium exists, under such a target, creates its own problems.)

[This is partly a response to Simon Wren-Lewis' good post. I had been mulling this over for months, trying to figure out how to how best to say it, and reading Simon was a tipping point. Stick to your NGDPLPT first-best guns, Simon!]

Comments

[JCE]

nick i know it's unrelated, but you should respond to this. http://www.economist.com/blogs/freeexchange/2012/12/business-cycles-0

Lay out your view once again

[david]

Don't we want raised prices in a sticky-price model?

[Min]

I know this is off topic, but I have been getting really, really slow response times at the WCI site lately. Is it just me?

Thanks.

Is my demand curve too elastic? ;)

[Nick Rowe]

JCE: thanks. I may have a go at it.

david: if we are in recession, we want firms to respond to an increase in AD by increasing Y rather than P. Yep, in that bit I was assuming we are in the current recession, and thinking about how best to get out of it.

Min: sometimes I get a slow response too. I don't know why.

[Min]

Thanks, Nick. :)

Could it be this tweet stuff on the right?

[david]

Surely in a canonically microfoundational NK model, firms set their Y given prevailing/Calvo'd P? And the elasticity is generally assumed to be fixed? It is the increased P that induces increased Y, so to speak.

[Nick Rowe]

david: I disagree. In the standard New Keynesian model firms set P, and Y is determined by AD given that P. And at the individual firm level, the same is true.

[david]

Three-equation NK macro, the one with Calvo in it, has firms just take what P they are given. You can sustain the multiple equilibria with pure demand externalities and no adjustment costs - a la, a wimpy Calvo fairy - since the externalities first increase and then decline back to zero as the proportion of adjusting firms increases, so the stable equilibria are (as you describe) that no firms adjust or that all firms do.

But then why talk about Calvo? And the Calvo fairy doesn't even do much punishing here; adjustment costs are all pretty small for the argument to work at all, envelope theorem and all. There is no situation where the loss of market-share under mispricing is immense and yet firms remain monopolistically-competitive price-setters. It would certainly be Nash for all firms at one equilibrium to stay there, but their losses from deviating slightly are small - businesses do take GST hikes and so forth as opportunities to adjust relative prices. And real rigidities would weaken the multiple equilibria result (it becomes unambiguously harder to sustain the no-adjustment nominal anchor equilibrium).

[Nick Rowe]

david:

"Three-equation NK macro, the one with Calvo in it, has firms just take what P they are given."

You lost me there. The Calvo Phillips Curve is based on the assumption that each period a fraction of firms can change their prices, and the remaining fraction can't. For firm i that can change this period, it chooses Pi taking the general price level P as given. That is how P changes over time.

"You can sustain the multiple equilibria with pure demand externalities and no [price?] adjustment costs - a la, a wimpy Calvo fairy..."

I agree. You *can* do that, if you assume the strategic complementarities are big enough, but I don't want to assume they are that big.

(I prefer "strategic complementarities" to "demand externalities", because externality means that my firm benefits if your firm increases output, but complementarity means that my firm's *marginal* benefit from increasing output increases if your firm increases output.)

I understand the "small menu costs" idea under monopolistic competition. A first order small deviation of relative price from the profit-maximising relative price causes a second order small loss of profit for an individual firm. In fact, my implicit model here is based on small costs of changing prices plus strategic complementarities. But you lost me on the rest of that paragraph.