Is core inflation an artefact?

Headline inflation (total CPI inflation) has been above core inflation since last June. That's for Canada, but it's roughly the same in most other countries too.

Most central banks, and most economists, pay more attention to core inflation than total inflation as an indicator of underlying inflationary pressures. Core inflation has inertia, and so is a better measure of the underlying trend because it is stripped of the more volatile components of the total CPI. Are they right?

One month ago, Steve Williamson presented a simple 2-good model in which the prices of both goods were perfectly flexible. If the central bank targeted the price of apples, apple inflation would look like core inflation; but if the central bank targeted the price of bananas, banana inflation would look like core inflation. Core inflation is an artefact of monetary policy targeting core inflation, in other words. Nature copies art.

For example, if a central bank were on the gold standard, and targeted some fixed price of gold, then the price of gold would look very sticky, and would be part of core inflation.

I'm going to propose a way to come up with an empirical definition of core inflation that gets around the problem Steve has identified. In general, my method will create a definition of core inflation that may not be independent of the central bank's target. But that doesn't mean it is merely a useless artefact of that target.

The question of how best to define "core inflation" empirically, and whether or not core inflation even exists as an empirically useful concept, can be examined under the general framework of target, instrument, and indicators. What definition of core inflation, if any, makes core inflation a useful indicator for the central bank to respond to when it chooses its instrument setting to hit its target? (Whether or not core inflation is a better target than total inflation is a related but different question.)

Assume the Bank of Canada is targeting 2% total inflation at a 2-year horizon. That means that the Bank looks at the available information, and sets monetary policy, such that the Bank's 2-year ahead forecast of inflation, conditional on that information, and conditional on its monetary policy, equals 2%. If the Bank has rational expectations we know that its forecast errors (deviations of actual inflation from the 2% target) must be uncorrelated with anything in the Bank's information set 2 years ago.

So it is totally useless to try to see whether core inflation gives a better forecast than total inflation of 2-year ahead total inflation. If the Bank is doing what it says it is doing, all deviations of total inflation from the 2% target should be unforecastable noise, 2 years prior. Nothing should forecast 2-year ahead total inflation. Not core inflation, not total inflation, not anything in the bank's information set. The best forecast of 2 year ahead total inflation should be 2%.

Which is a paradox. If the Bank seeks to hit its target, it needs to know what indicators are useful to look at when it chooses monetary policy, and how it should respond to those indicators. Should it look at core inflation or total inflation or both, and how should it respond to each? But if the Bank is responding correctly to those indicators, then all indicators will appear to be useless.

Here's how to escape the paradox. First you look at what indicators the Bank is actually responding to, and how it responds to them. You estimate the Bank's monetary policy reaction function, in other words. Second you use possible indicators to try to forecast 2-year ahead inflation. You test to see if the Bank is making systematic mistakes and violating rational expectations, in other words. Then you put the two together, and draw the appropriate conclusions.

Suppose, for example, that you estimated the reaction function and found that the Bank was responding to core inflation but ignoring total inflation as an indicator. And you also found that neither core inflation nor total inflation would help you forecast 2-year ahead total inflation. Then you could conclude that the Bank was responding correctly to both core and total inflation. Which means that core inflation must be a good indicator for the Bank to respond to, and total inflation adds no value to core inflation as an indicator.

On the other hand, if you found the Bank was ignoring total inflation, but that total inflation could forecast 2-year ahead total inflation, you would conclude that the Bank should pay more attention to total inflation as an indicator.

On the third hand, if you found that the Bank was responding strongly to core inflation, but that core inflation was negatively correlated with 2-year ahead total inflation, you would conclude that the Bank was responding too strongly to core inflation.

And so on.

In general, a good indicator X has the property that either the Bank responds to X or X is good at forecasting the Bank's future mistakes. You estimate the Bank's reaction function to see what the Bank is responding to, then you estimate an inflation forecasting equation to see what mistakes the Bank is making. The value of any indicator is some sort of weighted sum of its values in those two equations. (For example, if the Bank were responding to the roll of a die, and so the roll of the die would forecast future inflation, then the sum of those two values should cancel out to zero.)

Comments

[Max]

"If the central bank targeted the price of apples, apple inflation would look like core inflation; but if the central bank targeted the price of bananas, banana inflation would look like core inflation."

A more accurate statement would be that if the CB targeted the price of apples, everyone would be obsessed with the price of apples since that would predict the CB's behavior. If the CB targeted the price of bananas, then everyone would be obsessed with the price of bananas and wouldn't care at all about the price of apples.

[Mark A. Sadowski]

It's difficult to say what would happen ex ante but if one were to target the price of commodities I would guess you would see violent swings in real output, such as we did in the 19th century.

Core inflation makes sense because it strips out the volatile highly variable components of the price index that tend to move much more than the stickier prices that move together. And there are more sophisticated ways of doing this than "core" such as trimmed mean PCE and median CPI. (Which Stephen Williamson claims to have never heard of. Odd for a monetary economist, no?)

[RSJ]

I think the key point about food and energy is that they are (globally) inelastically supplied, subject to global demand, and the supply/demand disruptions are very volatile.

It would be bad policy for the CB to try to force a rapid internal devaluation in response to a civil war in Libya or in response to a crop failure in Russia. If the price increase is temporary, then the CB should not respond. If it is permanent, it should respond.

How would the CB "know" that there was a temporary increase in the price that did not warrant a response or if there was a permanent increase that warranted a response? It would look at core inflation!

Perhaps a good example would be to think of the interest channel as operating with a lag and having a certain inertia. In that case, the optimal variable to control would one that had an equivalent amount of inertia and operated with an equivalent lag.

[Nick Rowe]

Max: that might also be true, but it's independent of the simpler claim I'm making here.

Mark: if core inflation really did represent prices that were sticky and inertial (i.e. did not want to change level or rate of change) then I agree that would be my ex ante guess too. But we ought to measure price stickiness as something like the high variance of P relative to P*, where P* is the hypothetical flexible price equilibrium for that good. Not by the low variance of P. So it might just be that those goods which have a very high volatility of P* will look like they are flexible price goods, and those with low volatility of P* will look like sticky price goods, even when they aren't.

[Nick Rowe]

RSJ: "How would the CB "know" that there was a temporary increase in the price that did not warrant a response or if there was a permanent increase that warranted a response? It would look at core inflation!"

But how would it know what was included in core? How would it know that core inflation even exists? In Steve Williamson's example, if the central bank targets the price of apples, the current price of apples will be a very good predictor of the future price of apples. And the price of apples will be more stable than the volatile price of bananas. But switch the price to target, and it's the other way around.

[Mark A. Sadowski]

Nick, I (think) I understand what you're saying and it merely seems to reiterate Stephen's point.

But my point is not that we should be measuring variability of individual prices, but that we should be measuring thee variability of individual prices with respect to the central tendency of all prices. And by that standard "core" does fairly well.

[RSJ]

OK, but in Steve's model the CB has magical powers that non-magical CBs do not have.

Imagine that you have a bunch of balls colliding with each other. Some are very heavy (more inertia) and some are light. The heavy balls will tend to stick to their trajectory whereas the lighter balls will bounce around a lot.

All that a non-magical CB can do by raising or lowering borrowing rates is to increase or decrease the overall energy of the system. It wont cause the relative differences in volatility to change a whole lot.

Food and energy has always been more volatile, and if the CB tries to target them, then still Food and Energy will be more volatile. I think Williamson is wrong in not taking price elasticities into account.

Energy is inelastically supplied due to basic physics, not due to CB policy. Same for food. Energy is always going to be more volatile than magazine prices.

A non-magical CB cannot avoid systemic shocks -- e.g. civil wars, crop failures.

But because the CB is not going to reduce the relative inertia of prices, then it is not hard to identify which prices go into the core and which do not. Just look at volatility.

[Nick Rowe]

Mark: "But my point is not that we should be measuring variability of individual prices, but that we should be measuring thee variability of individual prices with respect to the central tendency of all prices. And by that standard "core" does fairly well."

Hang on though, because by that standard total inflation would do even better.

Or, suppose there are 3 goods, all taking up 1/3 of the basket. Apples have a very sticky price. Bananas and carrots have flexible prices. There is a common shock that affects the relative price of apples to bananas and carrots. Assume bananas and carrots are close subsititutes, so their relative price changes little. Then we would see bananas and carrots as being much better proxies than apples for the central tendency of all prices.

RSJ: "Imagine that you have a bunch of balls colliding with each other. Some are very heavy (more inertia) and some are light. The heavy balls will tend to stick to their trajectory whereas the lighter balls will bounce around a lot."

That was exactly the analogy I had in mind when I was thinking about this post!

But the real shocks affect the *relative prices*, which is like a change in the relative position of the balls. So if we assume some balls are heavier, we would expect to see the lighter ball moving in response to the relative shocks, and the heavier ball moving little. But an alternative explanation is that all balls are equally light, but the central bank tilts the table to keep one of the balls rolling in a straight line. So it looks heavy.

[Mark A. Sadowski]

Nick,
I'm sorry to drag you into a tit for tat. But I'm either not understanding your argument or I genuinely disagree with you.

Total inflation is only better if we use the mean as a measure of central tendency, and mean can often be skewed by outliers. Median is a much better measure of central tendency in my opinion.

Let's take your example, and let's further assume that each good has approximately equal total expenditure weight in the basket. Then I would indeed target the price of bananas and carrots, not apples, as that would represent the median. And then apples would have the appearance of being the flexible price.

[Nick Rowe]

Mark: we might be talking at cross purposes.

There are two separate questions:

1. what measure of inflation is the best indicator? (That's what my post is about).

2. What measure of inflation is the best target. (That's what we are arguing about here, I think, and we are both very slightly off-topic, but that's OK.)

On 2, there's a long-standing argument that monetary policy should target the stickiest price. We get business cycles and distortions when a sticky price needs to change to get to equilibrium, but won't. So monetary policy should try to make sure that the stickiest price doesn't need to change. Which means, target the stickiest price. So, if apples are the stickiest price, and bananas and carrots have perfectly flexible prices, target the price of apples, even though that may not be the median or mean price, in some circumstances.

[Mark A. Sadowski]

Nick,
On qQuestion 1:

You wrote:
"What measure of inflation is the best indicator? (That's what my post is about)."

I thought I understood your post but maybe you better clarify what you mean by that statement.

On question 2:

My intuition is that sticky prices are less likely to change with respect to each other. Thus it is very likely that a median price and a sticky price measurement would be very close to each other.

I understand that it is theoretically possible for a sticky price measurment and a median price measurement to not be the same. But empirical reality is a different matter. And I suspect statistical analysis would verify my conjecture.

[Nick Rowe]

Mark:

1. To clarify: suppose, for example, the Bank of Canada is targeting total inflation. Then it gets the news that total inflation has gone up, and core inflation has gone down. (Both were a surprise, and there's no other news). Should it tighten monetary policy, or loosen monetary policy, in response to the news?

2. OK. I understand you now. Good point.

[Buyer]

Hello Nick:

If we accept that inflation is always and everywhere a monetary phenomenon, then simply set a target and stick to it -- K % rule. I understand that you are not really advocating that by any stretch, but it seems to me that you could go in that direction.

And I must say that "inflation" is a difficult concept to measure and grasp. Not only does each individual have changing inflation rates through their lifetimes based on purchased wants and needs, inflation in and of itself causes changes in consumed goods in any basket (core or total). Carrots go up in price and I decide to grow carrots in my parent's garden. They are no longer in the core or total measured "basket".

Anyway, I'm enjoying the blog. I have time to read it post course

[Andy Harless]

I see an argument for core inflation that is somewhat different from the traditional "volatility" argument. The premise is that food and energy (or whatever goods we ought to be excluding from the core index) are largely storable and traded in liquid markets. That being the case, the market prices for these things are approximate indicators of what market participants, on average, expect the prices to be in the future (although this won't always be true if the prices are expected to fall, because you can't short physical commodities). So if the central bank is targeting the inflation rate (as opposed to the price level), it doesn't have to target the non-core portion of the index, because the market has already done it.

[K]

What Andy said. If the market is liquid/efficient, then there is nothing for the central bank to do and the price will look like a martingale. Prices in sticky/inefficient markets, on the other hand, are autoregressive because they are trending towards equilibrium. So it shouldn't be that hard, statistically, to distinguish the prices that need to be targeted from the ones that don't. And though stickiness will repress volatility, volatility itself has nothing to do with whether or not a price is off. Some prices, efficient or not, are intrinsically more volatile than others.

[anon]

Interestingly, what Andy said only applies to commodity prices as such, not to their second-round effects on core inflation. Given rational expectations, one would think that storable goods cannot enter into inflation expectations at all, because expectations of future prices ought to be reflected in current prices. But this is not true empirically: consumer prices respond to economic shocks with a lag. Thus, market measures of expected inflation soar after an oil price spike.

This is somewhat important as it may provide info about the "correct" description of price stickiness, which is relevant because different models of price stickiness give very different macro outcomes.

[Nick Rowe]

Hello Buyer! [Buyer woks as a buyer. Lots of people have jobs selling things; very few people have jobs buying things. I find that an interesting fact. It tells us something about macroeconomics. One day I should do a post on it.]

Milton Friedman once said the optimal monetary policy is to increase the money supply by a constant k% each year. The Bank of Canada tried it for a time in the late 1970's, then abandoned it. Or, "We didn't abandon M1, M1 abandoned us" as Governor Bouey put it. Velocity is now thought to be too unstable for this policy to work well.

Andy: I would tend to lean towards the opposite policy implication. If non-core prices tend to be good measures of people's expectations about future *aggregate* variables, then they are very important indicators and the Bank should pay a lot of attention to them. Both because they convey information about the future, and because they convey information about people's expectations, which matter in their own right even if they are wrong.

K: that's not really right. If all prices are perfectly flexible, the price level will not follow a martingale. The price level will only jump up or down when news arrives, it is true. But a change in the growth rate of the money supply will still affect the inflation rate. Suppose the Bank announced today that it will increase money growth in 2021. Hold everything else constant. P jumps up today on the news, and P will rise, but at a slowly increasing rate, converging to the money growth rate in 2021. The demand for real money M/P is a decreasing function of the inflation rate.

anon: "This is somewhat important as it may provide info about the "correct" description of price stickiness, which is relevant because different models of price stickiness give very different macro outcomes."

Could you clarify/expand on that?

[Phil Koop]

"What Andy said. If the market is liquid/efficient, then there is nothing for the central bank to do and the price will look like a martingale."

I do not understand this argument. If we are going to treat a commodity C as a cash-and-carry asset with spot price C(t), then the numeraire with respect to which it is a martingale is the risk-free nominal rate of return adjusted for convenience yield, so that the forward value that yields the martingale is F(t,T) = C(t).exp{(r-d)(T-t)}, with r the risk-free nominal rate and d the (possibly negative) convenience yield. Assuming d to be zero for the sake of argument is fair enough; doing the same for r is not, because it embeds inflation expectations, which is the heart of the matter we are arguing!

[Phil Koop]

Nick, I was under the impression that in orthodox economic theory, a central bank charged with managing inflation is really targeting inflation expectations? Bygones are bygones, and if realized inflation happened to be 1% or 3%, that only matters to the extent that it affects inflation expectations going forward? (Certainly you commonly hear central banks write off deviations of realized inflation from target as a one-off.) There is an element to "looking for the keys under the streetlight" to focusing on any measure of realized inflation, for as I mentioned in another thread, expectations in the real measure are unknowable.

The point is that it is not as simple as you suggest to measure the errors made by the CB because realized inflation is only a good basis of error measurement to the extent that the inflation expectations of the public are rational. Empirically, there seem to have been extended periods when this was not true.

[Nick Rowe]

Phil: suppose, just suppose, that the Bank of Canada knew that people's inflation expectations were biased upwards by 1%. Would it target 1% inflation rather than 2% inflation? That's not my reading of what the Bank of Canada tries to do. Certainly, in the early days of inflation targeting, before the Bank's target was credible, people's expectations did seem to be biased strongly upwards, from the Bank's POV. Yet it still tried to hit its target for actual inflation.

It recognises that actual inflation depends on expected inflation, and so will respond very strongly to indications that expectations have become "unanchored" from the 2% target. It hopes and believes that by consistently targeting 2% inflation expectations will become anchored at 2% too. You might say that by trying to hit actual inflation of 2%, and by hoping its own expectations are rational, it is targeting a rational expectation of 2% inflation. But, otherwise, it is targeting actual inflation rather than the public's expectation of inflation.

[K]

Nick, Phil: When I used the (weasely) "look like a martingale" I didn't mean literally "is a martingale".  What I meant was "sequence of price changes is not statistically-significantly autoregressive".  

I haven't done empirical work on prices (outside of capital markets).  But here's the model I have in mind: individual equilibrium prices are volatile, but the sum of them (the inflation index) is much less so since they have some independent drivers. Therefore they will be not all be equally far from equilibrium (or even on the same side of equilibrium) and they will be trending at different, sometimes much higher, rates than the index, no matter what the choice of numeraire. For the most liquid ones, however, the trend (serial autocorrelation of changes) will just come from the numeraire but will not be statistically significant except in the extremely long run.  But for the stickiest ones, the existence of serial autocorrelation will be clear, independently of the choice of numeraire.  That is, they have their own internal trends.  I am not saying that you can measure the trend of any one sticky price at any given moment. I am just proposing that maybe you can tell that some price series *do* have their own independent trending behaviour.  Those are the ones that are dangerous and need to be watched and maintained at equilibrium on average.

Some price may even be sticky *and* volatile.  If the equilibrium price is extremely volatile then a smoothed (sticky) price could still be volatile. But it will also be autoregressive, and *that*, not the level of volatility, is the key characteristic that tells us it needs to be managed.

[David Pearson]

I would argue the Fed cannot maintain 2%+ TIPS inflation expectations unless: 1) shelter prices reverse their fall; or 2) commodity prices continue to rise. So as long as the Fed is unsuccessful in creating expectations of house price inflation, its actions will, almost by definition, need to raise commodity prices to be "successful". Shelter is 40% of cpi, and house prices -- a shelter component -- are still DEFLATING at a rate of over 5% annualized (by some measures).

So by unsuccessfully targeting sticky prices (shelter), the Fed ends up relying on non-sticky prices. The problem is that the relative price distortions caused by higher commodity prices reduce real growth.

[Nick Rowe]

K: OK. If all prices were perfectly flexible, and so the price of money (1/P) were perfectly flexible, then in the limit, as the interest elasticity of the demand for money approached infinity, then 1/P would follow a martingale. In this case, it's easy to think of money as a consumer durable like a house or fridge, rather than like a financial asset. There is a downward-sloping demand curve for the services of houses, fridges, and real money balances, because they are imperfect substitutes for other assets, and so the own rate of return will not be independent of the (real) supply.

[david stinson]

As usual, I am a bit confused.

@Nick: "there's a long-standing argument that monetary policy should target the stickiest price."

I don't get that, because:

a) it is frequently contended that sticky prices result in quantity adjustments under monetary disequilibrium;

b) if the contention in a) true, movements in sticky prices cannot be good leading or coincident indicators of the full extent of monetary disequilibrium;

c) monetary policy is a process of achieving either monetary equilibrium or a target level of monetary disequilibrium (i.e., a slight excess supply);

d) therefore, an index of sticky prices cannot be a good indicator for purposes of monetary policy;

e) core inflation has "inertia";

f) core inflation is an index of sticky prices; and

g) therefore core inflation is not a good indicator for purposes of monetary policy.

What part of the above is wrong?

Put another way, if the central bank targets the stickest price, and hits its target, how will the central bank know whether it hit its target a) because they're really smart and got their policy right, or b) because the sticky price is out of equilibrium but hasn't moved yet because it's sticky?

[Nick Rowe]

Both Davids:

Let P be the actual price, and let P* be the equilibrium price, where demand=supply, and where the price would be if it were perfectly flexible. So a deviation of P from P* causes disequilibrium and quantity distortions, which is a bad thing. The Bank can control P* (up to a point) with monetary policy.

For flexible prices, P will equal P* regardless of what the Bank does to P*.

For sticky/inertial prices, P will only slowly adjust to reduce the gap between P and P*. So the Bank should try to keep P* constant (or moving at a steady speed), so that P stays as close as possible to P* the whole time. "Don't make any sudden moves with P* because P won't be able to keep up." If you keep P* constant (or moving at a steady speed), then P will stay equal to P* and so P will stay constant too (or moving at a steady speed).

If P is inertial, then you have a problem with price level path targeting. If the Bank makes a mistake one period, so P* accidentally falls, and P falls too, but not as much, then the Bank will try to get P* back up to where it would have been otherwise, or even higher, which means P must rise but won't rise enough to equal P*. Inflation targeting, by contrast, says that P has fallen, but don't try to push it back up, just keep P* equal to where P is now, so that P doesn't have to move again.

[Nick Rowe]

david stinson: "Put another way, if the central bank targets the stickest price, and hits its target, how will the central bank know whether it hit its target a) because they're really smart and got their policy right, or b) because the sticky price is out of equilibrium but hasn't moved yet because it's sticky?"

If prices were really sticky, i.e. stuck, this would be a problem. But if there is some flexibility, if P is falling relative to the target trend, then the Bank knows P* must be below P, so it must raise P*. But it can get tricky if there's enough intertia, because P might be falling because P* was below P in the past, even though P* is above P now, and P hasn't had enough time to change direction.

[david stinson]

Hi Nick.

Thanks for your explanation. Not to belabour the point but......

I understand why minimizing monetary-policy-induced movements in P* is a good thing - to my mind, it's another way of saying monetary equilibrium is a good thing. I guess what I don't understand is the notion that a good way to to do that is by observing P or an index of sticky prices and using those as a determinant for action or inaction, whether engaging in price level targeting or inflation targeting. Either sticky prices are sticky enough to create quantity adjustments, and therefore necessarily distort price-based signals of monetary disequilibrium, or they're not.

Why wouldn't it make more sense to use a much broader index of prices, as they would presumably be a better early indicator of monetary disequilibrium and therefore a better way to minimize monetary-policy-induced changes in P*? Even then, the presence of sticky prices and the potential for quantity adjustments suggest that even a broad price index could well understate the true extent of monetary discequilibrium.

[Nick Rowe]

david: "Why wouldn't it make more sense to use a much broader index of prices, as they would presumably be a better early indicator of monetary disequilibrium and therefore a better way to minimize monetary-policy-induced changes in P*?"

It's not obvious to me that it wouldn't be better to do just as you say, for exactly that reason. It would depend on the nature of the shocks. If the only price shocks are relative shocks, and the Bank has very good information on P*, then the Bank should ignore non-core prices. But if the Bank has bad information on P* because P*=M+V where M is monetary policy and V is a large persistent shock, then non-core prices would give good information on V and P*.

That's why I think it's an empirical question, whether core or total is a better *indicator* (as distinct from *target*).

[jesse]

While CBs concentrate on core inflation doesn't mean they don't ignore the volatile components. Core inflation is useful because adding in the more volatile components would produce too many false positives. Carney et al are not ignoring the price of oil and wheat when it comes to inflation targeting but must not devote the lion's share of their efforts to analysing what is likely noise.

[Jacques René Giguère]

But the problem is why do we want to measure core inflation ( or any inflation0
To measure the tightness of monetary policy? You could look at employment figures ( Not NGDP as it depends on the index).
To measure purchasing power? You cannot empirically disentangle monetary from real-and-relative prices changes. And you have to choose your reference, the least sticky one. How can you choose the reference since the stickyness is measured against the basket whose price are measured against the stil-to-define-index?
But as soon as you recognize that essentially you must first target an arbitrary reference, you are into something more sinister: essentially a small local version of Gödel's second theorem. No axiomatic system can be defined within himself. Your problem is unsolvable by the very structure of mathematics.

[amv]

I'm surprised that nobody brings in the Mankiw/Reis Stability Price Index (2003): http://mattrognlie.com/2011/05/01/why-target-the-cpi/

[sarge]

Quick question for those in the know:

Would a 10% consumption tax increase result in an immediate increase in nominal GDP (assuming the same number of products are purchased, e.g. because income taxes were lowered at the same time), assuming GDP is measured using C+I+G+X-M? And then would real GDP be pretty well unchanged because the GDP deflator would rise to offset the new consumption tax?

[Andy Harless]

Nick: "If non-core prices tend to be good measures of people's expectations about future *aggregate* variables, then they are very important indicators and the Bank should pay a lot of attention to them."

Non-core prices are good measures of people's expectations about their own future values, not necessarily about future aggregate variables.