Price Level Targeting targets the Stickiest Prices; Inflation Targeting targets the more Flexible Prices

And it's good to target the stickiest prices; and bad to target the more flexible prices.

It means that recessions under inflation targeting can last as long as it takes for the stickiest prices to change. Which is bad. And it's especially bad for us old macroeconomists, who remember that the whole point of New Keynesian macroeconomics, when it began in the 1970's, was to show that a good feedback rule for monetary policy, unlike a k% money growth rule, meant that recessions did not have to last as long as it took firms to change prices.

Some prices are stickier than others. Here's a simple extreme example to illustrate my point:

Half the firms change their prices every n periods; so a fraction 1/n of them change their price each period. Think of n as a big number, so 1/n is a small number. And they have to announce any price changes one period in advance, to warn their customers (this assumption doesn't matter much). The other half the firms change their prices every period, (without advance warning).

The economy is humming along normally, with all prices constant. Then a negative shock hits aggregate demand. The central bank does not have a crystal ball, so does not see the shock coming. It only learns of the shock when it sees all the flexible price firms cut their prices 10%. How does the central bank respond in the following period?

Constant Price Level Target. The central bank wants the price level to go back to where it was before the shock. So it loosens monetary policy just enough to offset the shock fully, so the flexible price firms raise their prices back to where they were before. The sticky price firms, since they know the central bank will do this, don't change their prices at all. The recession is over after one period (as long as it takes for the central bank to recognise the shock and respond to it).

0% Inflation Target. Since half the firms have cut their prices by 10%, the average price level has fallen by 5%. The central bank lets bygones be bygones, and wants the price level to remain at its new lower level, so inflation stays at 0% thereafter. The central bank knows that every period a fraction 1/n of the sticky price firms will cut their prices by 5%, and to offset this it loosens monetary policy just a little so that the flexible price firms raise their prices by (5/n)%. After n periods all firms have prices that are 5% lower than originally. The economy slowly recovers from the recession, but does not fully recover until all firms have adjusted their price to the new level of aggregate demand. Which means the recession lasts for n periods. After n/2 periods, for example, 3/4 of firms's prices are where they want them to be, but 1/4 of firms still have prices that are too high, so their sales and output is too low.

Intuition. Inflation targeting ignores the levels of prices. It only looks at changes in prices. It wants all price changes to average out to 0% (for a 0% inflation target). So firms that change their prices twice as frequently get twice the weight in the average that the central bank targets. But firms who change their prices twice as frequently should only get half the weight; because they can adjust to aggregate demand shocks twice as easily, and have only half the need for the central bank to adjust aggregate demand so they don't have to change prices.

Other off-topic stuff: A Price Level Target also acts as an automatic stabiliser (for a central bank that sets a nominal interest rate). Because the expected inflation in the second period means the real interest rate falls in the first period. So the shock to aggregate demand is partly offset even if the central bank doesn't see it. And an NGDP level path target would be better still, if there are supply shocks, especially if the Short-Run Phillips Curve is flattish. But all that other stuff is beyond this post.

Comments

[Iskander]

Good post. When you put it this way, it's a wonder why inflation targeting was chosen in the first place.

I have an additional worry about inflation targeting:
Suppose the price level is constant (sticky prices) and the CB has a 0% inflation target. A drop in NGDP would cause a recession.
Suppose the price level rises at 2% a year ("sticky inflation") and the CB has a 2% inflation target. A drop in NGDP would cause a recession.
The 2% case would be worse for a given drop in NGDP as the price level gets further from the level consistent with output being at potential.

My point is that the CB will not raise NGDP if inflation remains on target (and in the short run it will as that's the rate price setters initially expect ).
Once the inflation rate starts to fall, the CB will react in an expansionary way which will reduce the problem. But this all looks like it will have a greater time lag than NGDP targeting.

Is this a valid objection to inflation targeting?

[Nick Rowe]

Iskander: thanks!

I don't think that's a valid objection. Because the central bank is choosing the level of NGDP differently when it decides to target inflation vs target the price level. So we would get a different change in NGDP in each case.

[John]

Nick,

Thought experiments like this are great to help clarify thinking on level targeting, so thanks!

Semi off topic question: what are the open economy implications of price level targeting? It seems to me that two countries with a price level target will effectively have a nominal exchange rate target, which could make for interesting interactions between foreign and domestic mon pol.

[Nick Rowe]

John: Hmm. Good question. If Long Run Purchasing Power Parity is true, in levels, then I think you are right. The nominal exchange rate would have to return to its long run value following an aggregate demand shock. But if there are real shocks, the equilibrium real exchange rate would probably change too. So the nominal exchange rate would change too, with both countries holding their price levels constant.

[Majromax]

On the other hand, I think price-level targeting might perform worse if the target itself shifts.

Imagine the central bank unexpectedly changes from a fixed price level target to a crawling 1% price level target, or from 0% inflation to 1% inflation.

In each case, simple rational expectations won't cause the price level or inflation to match the target because only 50%+
1/n firms can respond to the announcement. After observing this in one period the central bank will decide to lower interest rates, inferring from below-target inflation/prices that there has been a negative demand shock. Since the PLT central bank needs to correct for the full undershoot, however, it will apply more stimulus than the bygones-inflation bank.

Since a priori demand didn't shift, all central bank action is "incorrect."

--

> If Long Run Purchasing Power Parity is true, in levels, then I think you are right.

I think that if we have two countries that each perfectly meet price level targets and long-run purchasing power parity is true, then we're necessarily in a world where real interest rate parity is also true. A real-terms shock needs to act symmetrically (perhaps through investment mediation), or it will break either the price level target or purchasing power parity.

[Matthew Young]

Majromax:

"After observing this in one period the central bank will decide to lower interest rates, inferring from below-target inflation/prices that there has been a negative demand shock"

Good point. Take it a step further, in the very period of the demand shock, the central banker notices a bulge in deposits, as do all the member banks in equal error. Under these conditions, each adjustment comes in steps, the step length being a multiples of the error band, the collective 'thermostat' uncertainty. Except in central banking, the assumption is no party has advanced knowledge and interest charges are competitive prices of money already deposited and loaned, ex post. Central banking is a bit different, member banks get better rates but keep regulated and insured. So the restricted members get advanced warning, for a price.

[Pete Bias]

Going to have to disagree on this one Nick. You're making some very heroic assumptions and doing what Keynesians do best: aggregating to triviality a communications process by buyers and sellers (market prices and reactions). To think the recession is over in one period assumes that everybody is on board. Maybe; but it's an assumption not a fact.
The CB loosening "just enough" also assumes that CBs have a clue; also a heroic assumption as shown by real data over the past 50 years everywhere in the world. If it were that easy, we wouldn't need a macroeconomics - just add M or G any time you need it.
I don't think it's that easy at all. I'm skeptical that a CB can handle ANY of the targets properly. Again, support for the skepticism abounds. Little macro-models ain't an economy (btw, this is why we see hysteresis in unemployment figures).
(Still love you though!)

Pete Bias

[Nick Rowe]

Pete: thanks!

You are right that I have made heroic assumptions.

But then the Calvo Fairy is also a heroic assumption, because she flies purely at random, so in every period each firm has exactly the same probability of changing its price. And this means that the firms that do change price are a perfectly representative sample of the rest of the population of firms that cannot change price. And the firms that do change price tell us exactly what the firms that cannot change price would do if they could change price.

The other heroic assumption made by standard models is that the central bank responds instantly a shock hits, and the economy responds instantly to the central bank's response. There is zero lag. So stabilisation in response to aggregate demand shocks can be perfect, if the central bank wants it to be.

I have assumed heterogeneity in price flexibility/stickiness. Admittedly, I have assumed a bimodal distribution, with half the firms having perfectly flexible prices, which is extreme heterogeneity. But less extreme than assuming homogeneity.

I have assumed the Central Bank gets it exactly right, but only after a one-period lag. Less extreme than zero lag.

[Scott Sumner]

Excellent, this post clarifies a lot of things for me.

I'm going to give you the argument I've always used on NGDPLT, and I'd be curious as to whether you think it's right. One criticism of NGDPLT is that while it would be helpful in a recession, central banks would not want to use level targeting if the economy overheated. The critics claim that if the target were 4%, and NGDP suddenly rose by 6%, then under level targeting you'd have to aim for 2% NGDP growth over the next year. That's true, but where I disagree with the critics is the implication they draw from this fact. They seem to treat the 2% NGDP growth as a sort of recessionary policy. My response is that it would be recessionary if you started from the natural rate of output. But if you have previously just experienced a year of 6% NGDP growth, then the economy has overheated. In that case, a year of 2% NGDP growth actually just brings you back to the natural rate, back to macroeconomic equilibrium.

I think my intuition is similar to yours, but I didn't really know how you'd model it. Your approach seems correct.

[Nick Rowe]

Scott: Thanks!

Your argument sounds right to me. Taking the economy down from an unsustainable boom, because output is above the natural rate, because NGDP is above trend, is not the same as creating a recession.

[Jussi]

"unsustainable boom"

This is a common expression but not sure what it means. How does unsustainable boom look at the micro level? What are the firms or economic activities that are "excess" supply? I'm not sure what is the qualitative difference of cutting an unsustainable boom and creating a recession?

I think Nick once made a post with a jigsaw diagram where the economy always touched its full potential before plunging to recession but I couldn't find it.

[Nick Rowe]

Jussi: In an "unsustainable boom" the average firm is trying to raise its price above the average price. Which is impossible of course. But firms' attempts to raise their prices above other firms' prices results in ever-accelerating inflation and eventual collapse of money.

[Jussi]

Thanks Nick but isn't that just inflation? I thought you were referring something else by "because output is above the natural rate". I wonder how that is possible. Do we some day look back and say that we cannot produce as much we did yesterday?

[Nick Rowe]

Jussi: There is nothing *physically* unsustainable about output being above the natural rate (or there needn't be). It's just that demand is too high, so firms decide they can increase profits by raising their prices above other firms' prices rather than continuing to produce enough output to meet demand at existing prices.

[Jussi]

Thanks Nick. I appreciate and I still struggle.

The level targeting means after a positive AD shock that the CB needs deliberately cut the demand below the potential supply (AD deficiency). So can you please elaborate the case where the AD shock is positive (instead negative like in your post), is it also in this case that the level targeting is preferable? I mean I do not fully get the statement "a year of 2% NGDP growth actually just brings you back to the natural rate, back to macroeconomic equilibrium" as I think targeting the change (0 %) here seems to be enough to tame the shock slowly without AD deficiency?

[Nick Rowe]

Jussi: it would be nice if we only had positive shocks to AD. But in this class of models, an "AD shock" is a difference between actual AD and expected AD. So unless you can fool people all the time in the same direction, the average shock must be zero (as much positive as negative on average). The best you can do is minimise the variance of the shock.

[Jussi]

Nick: The question Scott brought up was

"One criticism of NGDPLT is that while it would be helpful in a recession, central banks would not want to use level targeting if the economy overheated"

You said

"Taking the economy down from an unsustainable boom, because output is above the natural rate, because NGDP is above trend, is not the same as creating a recession."

which I do not get because

"I think targeting the change (0 %) here seems to be enough to tame the shock slowly without AD deficiency?"

I get your post and I think level targeting makes, given the model, sense if the AD shock is negative. But can you elaborate why do you think it is preferable to target the level if the economy experience "unsustainable boom"?