Targeting the stickiest price.

Suppose the price of apples is sticky, but the price of everything else adjusts instantly to its equilibrium value. There is then an old, and strong, argument that monetary policy should target the price of apples. The economy performs best when all prices are at equilibrium. If the price of apples won't move (quickly) to equilibrium, then use monetary policy to move the equilibrium price to where the actual price is. The price of apples doesn't want to change, so don't make it have to change. Don't wait years for the price of apples to move to where it should be; move where it should be to where it is. Mahommed, mountain.

The Bank of Canada's 2% inflation target comes up for renewal in 2011. And Scott Sumner has written a persuasive case for targeting nominal GDP rather than inflation. David Beckworth adds his support to NGDP targeting. It's persuasive, but I'm not fully convinced, in large part because Scott ignores the argument that we should target the stickiest price. (Karl Smith has also put forward a (to me) quite novel and interesting argument against NGDP targeting, based on the idea that prices respond with a longer lag than real GDP to monetary policy, so keeping NGDP stable might cause instability in both the price level and real GDP).

There are two important questions: should the target variable be the CPI or NGDP; and should we target the growth rate of that variable or a level path? Those two questions create four serious candidates:

1. inflation targeting (what we have now in Canada);

2. price level path targeting (like inflation targeting, except that if you come in below/above target one year you aim for slightly higher/lower inflation the next year to get back on path);

3. NGDP growth targeting (like inflation targeting, only you aim for (say) 5% growth in NGDP rather than (say) 2% growth in CPI);

4. NGDP level path targeting.

Of course, there's also the question of the numerical value of the target (would 1% or 3% be better than 2% inflation?), and maybe other target variables should be considered too (like asset prices or monetary aggregates). But I'm going to leave those aside.

The argument that monetary policy should target the stickies price argues strongly for the current policy of inflation targeting against any of the other three options.

The CPI is a price (or, at least, an index of prices). NGDP is not a price. It's an index of prices (the GDP deflator) times a real quantity of goods produced (real GDP). That means the CPI should be the target variable, not NGDP. If real GDP changed path, targeting NGDP would mean the price level would need to change path. And it doesn't want to, so the economy as a whole would be forced off its equilibrium path, and we don't want that.

What does the "target the stickiest price" argument imply for inflation targeting vs. price level path targeting? That's trickier.

An embarrassing fact about macroeconomics is that really crude stupid economically illiterate ways of predicting the impact of indirect taxes on the CPI actually work very well in practice.

Suppose the GST (that's a Value Added Tax) applied to 60% of the goods that make up the CPI. Suppose you increased the GST by 1% (one percentage point). How would that affect the CPI? Any economically illiterate person would immediately answer "0.6%" without giving it any thought. And would be roughly right, as we have just seen again with the introduction of the HST (Harmonised Sales Tax, if non-Canadians want to know, but you don't need to).

Why is 0.6% an economically illiterate answer? There are two reasons: micro and macro. At the micro level, we know that the incidence of a tax (how much is passed up in higher prices to buyers and how much is passed down in lower prices to sellers) depends on the elasticity of demand and supply. And at the macro level we know that you can't do that stupid sort of partial equilibrium micro analysis when you are talking about a general equilibrium experiment like the GST, where taxes are changing across the economy. And we also know that the general level of prices is a monetary phenomenon, and so you can't use stupid micro barter models to talk about CPI determination, you need a monetary model. How will the GST increase affect the demand and supply of money?

But if you are economically illiterate and ignore all of the above paragraph, and use a really stupid model, or non-model, you get the right answer. Why does stupid work, in this case?

It's the same with oil prices. Every economic illiterate knows that an increase in oil prices should cause a rise in the price level. It's an immediate implication of the "adding up" theory of inflation. The overall inflation rate is determined by a weighted average of apple price inflation, plus banana price inflation, plus carrot price inflation... So it stands to reason that if the price of gas goes up because oil prices go up that will cause the CPI to go up too. Obvious, innit? But the adding up theory of inflation, despite its hopeless logical flaws (it's not just economically illiterate, it makes the logical mistake of confusing an accounting identity with a causal relation), actually works quite well in predicting inflation in the short run.

Why do stupid, economically illiterate predictions work?

Part of the answer is that the stupid prediction works because the Bank of Canada makes it work. Even though tax changes are known well in advance, so the Bank of Canada could lean against them if it chose to, it chooses to let the CPI increase by the amount of the average tax change. It says it is targeting CPI inflation, but makes it quite clear in this particular case that it is targeting net of indirect direct tax CPI. And core inflation, the Bank's "operational guide", is calculated net of "the effect of" indirect taxes. (As though you could talk about "the effect of" indirect taxes or anything else on the CPI regardless of the Bank's policy!).

The Bank accomodates the "first round effects" of tax changes, or gas price changes, and only tries to stop "second round effects". So we get a very predictable one-time jump in the level of the CPI.

But why does the Bank do this? Because it knows full well that there would be bad consequences if it didn't. The CPI "wants" to jump up with taxes, and then keep on rising thereafter at the same rate it did before. And if you try to stop the CPI doing what it "wants" to do, actual prices will be different from equilibrium prices. which causes real problems. If you tried to stop the CPI jumping when indirect taxes increase, there would be a recession immediately before and after the jump, but you wouldn't eliminate the jump, only add a short downward slope on top of it.

What do prices "want" to do, and why?

Start with a simple model. There are 100 firms. Each day, one firm changes its price, and holds its price fixed for the next 99 days. Each firm wants to keep it's price as close as possible to some equilibrium price, called P*. Assume for simplicity that all firms have the same P*, and that the central bank can control P* perfectly.

Suppose P* is initially growing at 0.1% per day, so 10% every 100 days. And it's been growing at 10% per 100 days forever. Every day one firm sets a new price 5% above P*, and watches P* rise until it is 5% above the firm's price just before it changes price again. The average price of all firms, P, is always equal to P*, so the economy is in equilibrium at the macroeconomic level, even if relative prices of each firm is only at equilibrium 50 days after it changed price.

Suppose the central bank decides to stop inflation. So it suddenly holds P* constant. What happens to the price level P? Actual inflation does not instantly fall to zero. Instead, it falls to 5% per 100 days. Because the firm that changes its price immediately the new policy is implemented increases its price by 5% rather than the 10% it would have chosen under the old policy. Since one firm raises its price by 5%, and all the other firms hold theirs constant, and there are 100 firms, inflation must be 5% per 100 days. It takes 50 days after the policy change for inflation to fall to 0%, and another 50 days of falling P for P to equal P* again. (Consider the firm that last changed its price 99 days before the policy change; it would have a price slightly above the new constant P*.)

Because P is above P* for 99 days, we get a 99 day long recession. The average price level is above the equilibrium price level. There is inflation inertia in this simple model. It's not just the price level that doesn't want to change; the inflation rate doesn't want to change to the new equilibrium either.

That simple model explains what happened in 1982, even if you assume the new monetary policy was immediately understood and fully credible.

If we add some real rigidities, so that each firm wants to set a price that is a weighted average of P and P*, we can get even more inflation inertia. Because each firm knows P will keep rising even after P* stops rising, firms that change their price immediately after the policy change will set a price above P*. As the weight on P approaches one, inflation approaches pure inertia.

Add in some slowness of information and expectations to adjust to the new policy, and we get even more inflation inertia.

That seems to be roughly how the world works. A change in the GST gives a firm "permission" to change price other than every 100 days, provided it just passes on the tax increase, and doesn't take the opportunity to adjust P to P*. And if it expects all other firms to do the same, the structure of relative prices stays the same. And some prices, like gas prices, adjust much more frequently, so are always much closer to their own personal P*'s. The central bank can ignore those prices, in the short run, and focus on core inflation. It's the prices that can't change it needs to concentrate on. Since P doesn't adjust to P*, P* must adjust to P.

It's not just the price level that doesn't want to change, the inflation rate doesn't want to change. So don't try to make it change. Target inflation, not the price level.

There are other considerations of course, but we ignore this one at our peril. The primary reason why monetary policy matters is sticky prices. And it's not really the price level that is sticky; it's the inflation rate.

Comments

[Andrew F]

I'm not sure I understand why that is an argument against price level path targeting, especially when the price level is following the expected rate we're currently using. Doesn't it just serve to remove some of the noise and make the price level less of a random walk in the long run?

[Paul Friesen]

Makes sense to me.

Another factor creating inflation inertia in the 70's and early 80's was, I think, inflation compensation clauses built into union contracts. Then the wage costs of firms tend to go up according to inflation in previous periods (when the inflation that is being compensated for in this period was measured).

Turning that around once it got moving was tough.

[Paul Friesen]

On the other hand, someone (I think it is Jeffry Sachs but I can't find the book) gives examples of cases where hyperinflation has been stopped in days or weeks just by halting the money creation process. Perhaps inflation needs to be a moderate enough to be institutionalized to exhibit such momentum.

[Ian Lippert]

Isnt targetting NGDP a bad idea since it would have different effects depending on if real GDP is growing or shrinking? If you targeted NGDP to be 5% but we were in recession and RGDP was falling by 3% wouldnt that be an inflation rate of 8%? Seems like it misses the point of managing inflation expectations.

[George Selgin]

I don't know whether you're aware of it, Nick, but your idea of targeting the stickiest prices resembles Gunnar Myrdal's in his book on _Monetary Equilibrium_. He however (logically, in my view) sees it as implying the stabilization of _factor_ prices, rather than output prices (the usual idea). Factor prices, and wage rates especially, would seem to be relatively more sticky today than output prices, just as was the case when Myrdal wrote (in the '30s). So why not carry your argument to a similar, logical conclusion? That would, of course, mean letting output prices _fall_ when there's rapid productivity growth. So, are you willing to go there?

[jsalvati]

Have you read Selgin's work on the productivity norm (roughly targeting NGDP per capita)? It has a somewhat different perspective, and has some discussion about how firms change their prices and why they might be nominally sticky (http://www.cato.org/pubs/journal/cj10n1/cj10n1-14.pdf). The basic idea is that firms like to change their prices about when their costs change. This is a theme I have also seen elsewhere. This kind of theory seems to me significantly more plausible as a source of nominal rigidity than staggered price changes (calvo models, right?).

[Nick Rowe]

Andrew: the argument that price level path targeting makes the long run price level more predictable than inflation targeting (where you get a random walk) is a good one. There are lots of good arguments I have ignored here. I just wanted to focus narrowly on one argument. Inflation inertia is an argument for inflation targeting, and I wanted to spell it out.

Paul: I have never managed to get my head around the argument that wage indexation creates inflation inertia. That's because the alternative to formal indexation is not spelled out. The idea that firms and workers would keep nominal wages fixed during inflation doesn't seem plausible as an alternative, since both care about real, not nominal wages.

Ian: I think it depends on what causes the shocks to real GDP. If they are supply-side shocks, then presumably you want GDP to vary, but don't want inflation to vary, so why target NGDP? If they are demand-side shocks, then does real GDP fluctuate because P diverges from P*? If so, then is that because P has inflation inertia? If so, it's presumably best to target inflation, to prevent P* diverging from P.

George: the idea that monetary policy should target the price that is sticky is an old one. I don't know where it came from originally. Maybe Gunnar Myrdal? If you think wages are stickier than prices then targeting wage inflation would be better. (Though it would be politically tricky, given economic illiteracy; "The BoC is trying to stop workers getting a better wage!!") I'm not sure if wages or prices are stickier.

jsalvati: No I haven't. I should. Thanks for the link. There are two types of staggered price setting: Calvo and Taylor. Calvo has firms change prices at random; it does not generate inflation inertia. Taylor has the oldest price change first; it generates inflation inertia. My little model is a Taylor model. Nearly all NK models use Calvo, because it's analytically tractable. The Bank of Canada uses Taylor in its main model, and uses a very large computer to solve it! The BoC is right to do this.

Too much Fed: you are totally off-topic, again.

[David Beckworth]

Nick,

Building upon Selgin's point, if you target wages then one ends stabilizing income and you are back at something like a nominal income target or nominal GDP target. Scott Sumner has said ideally he would target wages, but given the diffficulties in doing he favors targeting NGDP instead. For this reason and the one I mentioned in my post--the central bank should only respond to AD shocks, not AS shocks--I favor a nominal income type rule.

[Bill Woolsey]

On a micro level, when a sales tax directly paid by the seller is increased, the supply curve shifts to the left, and the gross price rises and the quantity falls.

Money expenditure targeting would allow this to appear at the macro level--the price level rises (gross prices) and real output falls.

It seems to me that you advocate having the central bank increase the quantity of money enough so that the equilibrium price level rises enough so that the net prices consumers pay remain the same. The equilibrium gross price level rises, and the net price level is unchanged. The demands of everything increase enough to keep quantities unchanged.

Of course, the point of the tax is to get revenue to spend and shift the allocation of resources from the things people buy to what the government wants.

And as the government spends that revenue the demands for particular goods that the government buys should rise. As resources are reallocated, the quantities of the things government buys increases. Real output should recover.

How does this work with money expenditure targeting? The net prices of the things that the government doesn't want fall, and they rise for the things the government does want. The shift in resources occur.

Your argument is that money expenditure targeting require... I think slower aggregate growth in money wages to return to equilibrium. Is that right?

Wages grow more slowly, the supplies of various goods rise, so that prices, both gross and net drop. The relative prices are still shifted, with the government demanded goods having higher prices and everything else having lower prices. If the trajectory of wages is sticky, then this creates a recession. The expanded government spending creates a smaller demand for output than the resources that are freed until the net prices fall. (The ordinary growth in productivity only allows for lower money prices if wages grow more slowly than productivity for a time.)

Solution? Isn't it obvious? When you measure final sales of domestic product, you measure the funds received by the firms, rather than what the buyers pay. In other words, indirect taxes shouldn't be included. (You know, I don't think they are included.)

By the way, it is _wrongheaded_ to see money expenditures targeting as a target for the product of a price index and a measure of real output. Think about it. Money expenditure targeting targets money expenditures. Now, you can come up with a price index and get an estimate of real expenditures by dividing. But do you really think that real output is determined, and the price level is determined, and then there is some multiplication going on?

If you really think money causes prices and prices cause output, then price level or inflation targeting is great. If money causes nominal expenditure, and money expenditure impacts prices and output at the same time, then stabilizing money expenditure makes sense.

The stickiest prices are surely wages, and I favor stabilizing their equilibrium trajectory. This is suboptimal if there is a shift in the income share between labor and capital. Stabilizing wage growth would work better. The indirect tax story above comes to be the same thing, with the indirect tax being like an increase in equilibrium capital incomes. The growth path of money wages needs to be lower if money expenditures are targeted. But while I think an economy that uses sales tax maybe should stabilize expenditures firms receive net of the tax, (my solution) I don't favor trying to stabilize wages and let profits fluctuate, as flexible as profits may be. I don't see that as creating the best environment for micro adjustment.

If there is a big sales tax that changes a lot, then.. OK, I must admit, having every tax increase result in a recession that requires slower growth in wages, isn't so bad to me. But... I guess I am confusing my support for impediments to excessive government taxation and spending with my improved coordination norm.

Imagine a price is stuck. If you target that price, then that works great. You are always on target. Of course, there are surpluses and shortages. If you target wages and they are really, really sticky, well, you stay on target, but there are surpluses and shortages of labor. So, what do you really do? Target employment? Target unemployment?

Money expenditure targeting is imperfect, but it looks to be the least bad option.

[Nick Rowe]

David: "Building upon Selgin's point, if you target wages then one ends stabilizing income and you are back at something like a nominal income target or nominal GDP target."

Bill: "Imagine a price is stuck. If you target that price, then that works great. You are always on target. Of course, there are surpluses and shortages. If you target wages and they are really, really sticky, well, you stay on target, but there are surpluses and shortages of labor."

No and no. You are both making the same mistake. I think you have both missed the point. (Which makes it my fault, since you are both bright enough to get it ;-) )

Suppose, for example the nominal wage is sticky. It doesn't want to move. It will only move, and then slowly, if there's a difference between the actual wage W and the equilibrium wage W*. Now, the equilibrium nominal wage W* depends on monetary policy. By varying monetary policy the central bank can move W*. If it is targeting nominal wages, it will make sure that W doesn't move, which means the Bank has to move W* to where W is. So the labour market stays in long run equilibrium, with no shortages or surpluses. But wage income, both real and nominal, which is WL, or (W/P)L will certainly vary over time, as the demand and supply of labour changes, and the equilibrium real wage and level of employment, (W/P)* and L* will vary. But by varying W*, the Bank can keep W/P=(W/P)*, and so keep L=L*, even though W is sticky.

[Too Much Fed]

Why is replying to Paul Friesen off topic?

[The Money Demand Blog]

The stickiest price is the contractual interest rate in a long term financial contract. My hunch is that such contracts work best with NGDP level path targeting.