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.)