Which Measure of Inflation is Best for Monetary Policy?

Once again, here is an article complaining about using core inflation as the target for monetary policy. I've said this before, but it's worth repeating. There are both theoretical and empirical ways to define the price index to use in monetary policy. However, most of the discussion about policy involves only the empirical definition.

The empirical definition searches for the the price index that best predicts future inflation or best represents the inflation rate faced by a typical consumer. Almost always, the discussion revolves around whether core inflation properly measures the underlying inflation rate faced by consumers, and its usefulness for predicting future inflation rates, an essential component of policy.¹ But the reason why we look to inflation at all comes from theory, so it is useful to ask what theory says about which price index is the most useful to policymakers.

What is the theoretical definition? In models with price and wage sluggishness, it is the failure of prices to move quickly to clear markets that causes output to deviate from target. Thus, monetary policy makers need not be concerned with highly flexible prices, it is the sluggish prices that are the problem. The solution is to keep the problem (sluggish) prices as predictable as possible so that even if prices are set far in advance, they will remain optimal.

To do this, the sluggish prices must be stabilized - the flexible prices can take care of themselves. For policymakers, this implies that highly flexible prices such as food and energy can be removed from the index to isolate and highlight the problematic sluggish prices. The goal is not to find the index that best represents the cost of living, rather, the goal is to learn about current and expected future values of the index most useful for stabilization. All of the criticism about the index misrepresenting the actual cost of living misses this point entirely.

Here is an example of commentary that only talks about the empirical approach:

Strawberries out of the basket, by Wolfgang Munchau, Commentary, Financial Times: A former central banker once told the story of a French prime minister during the fourth republic who had asked why inflation always rose in late spring. His statisticians told him that this was due to the price of strawberries, a seasonal food. The prime minister then instructed his officials to take the strawberries out of the index and to include them in the winter months instead – when you could not buy strawberries anywhere in France.

I am not sure how true this story is, but it seems plausible. Taking inconvenient items out of the inflation index has a long tradition. Today, many central banks still take the strawberries out of the inflation index, along with all other food items and energy. The index you end up with is known as core inflation.

There is a prima facie case for a central bank to target core inflation. Core inflation is a far less noisy indicator than monthly headline inflation. ... There are several ways of constructing core indicators. The traditional way is to strip out the most volatile categories of the index permanently; for example, food and energy. There are alternative methods, such as the trimmed-mean method, used by the Federal Reserve Bank of Dallas among others, which strips only the most volatile items off the index each month.

In the US, core-inflation indicators have turned out to be reasonable measures of underlying inflation – but not always and probably not now. Core inflation was a particularly bad indicator in the 1970s when inflation rose sharply in response to the first and second oil crises...

Generally speaking, core inflation is a misleading indicator in times of protracted increases in energy prices. In such times, core inflation lags behind headline inflation. A monetary policy that follows a lagging indicator risks being too slow – “behind the curve”, as they say in the financial markets. ... One reason why core inflation may be a lagging indicator are the so-called second-round effects of energy prices – the pass-through to non-energy prices or to higher wages. ...

Another problem with core inflation is the impact of the unsuspected volatility of some of its components. In the US, the biggest single component of core inflation is owners’ equivalent rent (OER) – an imputed number that measures the cost of house ownership. ... As the housing boom has subsided, OER inflation has risen back to more normal levels. Last week’s sudden increase in US core inflation was due largely to the jump in the OER component in the core index...

Some private sector economists made the preposterous suggestion that housing should also be excluded from the core index. If you go down this route, you end up with a core inflation index that no longer bears any relationship to reality. ... A forward-looking central bank ignores headline inflation at its peril. ...

The test of whether it is permissible to use core inflation is not only whether the two indicators converge within a reasonable period of time, but whether they converge in the right direction. In both the US and the eurozone we are seeing core inflation catching up with headline inflation and not the other way round.

It seemed outrageous that the aforementioned French prime minister took the strawberries out of the inflation basket. But compared with what some central banks are doing today, those strawberries are peanuts.

By the theoretical argument, it is not "prepostorous" to take asset prices out if the index or "outrageous" to remove food prices as these are highly flexible, and within this theoretical structure, non-problematic prices. That the "core inflation index ... no longer bears any relationship to reality" is beside the point. The point of targeting an index is stabilization, it has little to do with accurately measuring the price of some market basket of goods. It would be nice, agree or not, if people writing on this topic would at least recognize the theoretical side of the problem. For anyone who wants to follow up, there is nice NBER research summary of Woodford's work on these issues.
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¹In general, the empirical approach would search for the price index most highly correlated with future economic activity (or someother variable of interest) so I'm not sure the term "empirical approach" is the best label to use here, but it will do for now.