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June 23, 2014
Torturing CPI Data until They Confess: Observations on Alternative Measures of Inflation (Part 1)
On May 30, the Federal Reserve Bank of Cleveland generously allowed me some time to speak at their conference on Inflation, Monetary Policy, and the Public. The purpose of my remarks was to describe the motivations and methods behind some of the alternative measures of the inflation experience that my coauthors and I have produced in support of monetary policy.
In this, and the following two blogs, I'll be posting a modestly edited version of that talk. A full version of my prepared remarks will be posted along with the third installment of these posts.
The ideas expressed in these blogs and the related speech are my own, and do not necessarily reflect the views of the Federal Reserve Banks of Atlanta or Cleveland.
Part 1: The median CPI and other trimmed-mean estimators
A useful place to begin this conversation, I think, is with the following chart, which shows the monthly change in the Consumer Price Index (CPI) (through April).
The monthly CPI often swings between a negative reading and a reading in excess of 5 percent. In fact, in only about one-third of the readings over the past 16 years was the monthly, annualized seasonally adjusted CPI within a percentage point of 2 percent, which is the FOMC's longer-term inflation target. (Officially, the FOMC's target is based on the Personal Consumption Expenditures price index, but these and related observations hold for that price index equally well.)
How should the central bank think about its price-stability mandate within the context of these large monthly CPI fluctuations? For example, does April's 3.2 percent CPI increase argue that the FOMC ought to do something to beat back the inflationary threat? I don't speak for the FOMC, but I doubt it. More likely, there were some unusual price movements within the CPI's market basket that can explain why the April CPI increase isn't likely to persist. But the presumption that one can distinguish the price movements we should pay attention to from those that we should ignore is a risky business.
The Economist retells a conversation with Stephen Roach, who in the 1970s worked for the Federal Reserve under Chairman Arthur Burns. Roach remembers that when oil prices surged around 1973, Burns asked Federal Reserve Board economists to strip those prices out of the CPI "to get a less distorted measure. When food prices then rose sharply, they stripped those out too—followed by used cars, children's toys, jewellery, housing and so on, until around half of the CPI basket was excluded because it was supposedly 'distorted'" by forces outside the control of the central bank. The story goes on to say that, at least in part because of these actions, the Fed failed to spot the breadth of the inflationary threat of the 1970s.
I have a similar story. I remember a morning in 1991 at a meeting of the Federal Reserve Bank of Cleveland's board of directors. I was welcomed to the lectern with, "Now it's time to see what Mike is going to throw out of the CPI this month." It was an uncomfortable moment for me that had a lasting influence. It was my motivation for constructing the Cleveland Fed's median CPI.
I am a reasonably skilled reader of a monthly CPI release. And since I approached each monthly report with a pretty clear idea of what the actual rate of inflation was, it was always pretty easy for me to look across the items in the CPI market basket and identify any offending—or "distorted"—price change. Stripping these items from the price statistic revealed the truth—and confirmed that I was right all along about the actual rate of inflation.
Let me show you what I mean by way of the April CPI report. The next chart shows the annualized percentage change for each component in the CPI for that month. These are shown on the horizontal axis. The vertical axis shows the weight given to each of these price changes in the computation of the overall CPI. Taken as a whole, the CPI jumped 3.2 percent in April. But out there on the far right tail of this distribution are gasoline prices. They rose about 32 percent for the month. If you subtract out gasoline from the April CPI report, you get an increase of 2.1 percent. That's reasonably close to price stability, so we can stop there—mission accomplished.
But here's the thing: there is no such thing as a "nondistorted" price. All prices are being influenced by market forces and, once influenced, are also influencing the prices of all the other goods in the market basket.
What else is out there on the tails of the CPI price-change distribution? Lots of stuff. About 17 percent of things people buy actually declined in price in April while prices for about 13 percent of the market basket increased at rates above 5 percent.
But it's not just the tails of this distribution that are worth thinking about. Near the center of this price-change distribution is a very high proportion of things people buy. For example, price changes within the fairly narrow range of between 1.5 percent and 2.5 percent accounted for about 26 percent of the overall CPI market basket in the April report.
The April CPI report is hardly unusual. The CPI report is commonly one where we see a very wide range of price changes, commingled with an unusually large share of price increases that are very near the center of the price-change distribution. Statisticians call this a distribution with a high level of "excess kurtosis."
The following chart shows what an average monthly CPI price report looks like. The point of this chart is to convince you that the unusual distribution of price changes we saw in the April CPI report is standard fare. A very high proportion of price changes within the CPI market basket tends to remain close to the center of the distribution, and those that don't tend to be spread over a very wide range, resulting in what appear to be very elongated tails.
And this characterization of price changes is not at all special to the CPI. It characterizes every major price aggregate I have ever examined, including the retail price data for Brazil, Argentina, Mexico, Columbia, South Africa, Israel, the United Kingdom, Sweden, Canada, New Zealand, Germany, Japan, and Australia.
Why do price change distributions have peaked centers and very elongated tails? At one time, Steve Cecchetti and I speculated that the cost of unplanned price changes—called menu costs—discourage all but the most significant price adjustments. These menu costs could create a distribution of observed price changes where a large number of planned price adjustments occupy the center of the distribution, commingled with extreme, unplanned price adjustments that stretch out along its tails.
But absent a clear economic rationale for this unusual distribution, it presents a measurement problem and an immediate remedy. The problem is that these long tails tend to cause the CPI (and other weighted averages of prices) to fluctuate pretty widely from month to month, but they are, in a statistical sense, tethered to that large proportion of price changes that lie in the center of the distribution.
So my belated response to the Cleveland board of directors was the computation of the weighted median CPI (which I first produced with Chris Pike). This statistic considers only the middle-most monthly price change in the CPI market basket, which becomes the representative aggregate price change. The median CPI is immune to the obvious analyst bias that I had been guilty of, while greatly reducing the volatility in the monthly CPI report in a way that I thought gave the Federal Reserve Bank of Cleveland a clearer reading of the central tendency of price changes.
Cecchetti and I pushed the idea to a range of trimmed-mean estimators, for which the median is simply an extreme case. Trimmed-mean estimators trim some proportion of the tails from this price-change distribution and reaggregate the interior remainder. Others extended this idea to asymmetric trims for skewed price-change distributions, as Scott Roger did for New Zealand, and to other price statistics, like the Federal Reserve Bank of Dallas's trimmed-mean PCE inflation rate.
How much one should trim from the tails isn't entirely obvious. We settled on the 16 percent trimmed mean for the CPI (that is, trimming the highest and lowest 8 percent from the tails of the CPI's price-change distribution) because this is the proportion that produced the smallest monthly volatility in the statistic while preserving the same trend as the all-items CPI.
The following chart shows the monthly pattern of the median CPI and the 16 percent trimmed-mean CPI relative to the all-items CPI. Both measures reduce the monthly volatility of the aggregate price measure by a lot—and even more so than by simply subtracting from the index the often-offending food and energy items.
But while the median CPI and the trimmed-mean estimators are often referred to as "core" inflation measures (and I am guilty of this myself), these measures are very different from the CPI excluding food and energy.
In fact, I would not characterize these trimmed-mean measures as "exclusionary" statistics at all. Unlike the CPI excluding food and energy, the median CPI and the assortment of trimmed-mean estimators do not fundamentally alter the underlying weighting structure of the CPI from month to month. As long as the CPI price change distribution is symmetrical, these estimators are designed to track along the same path as that laid out by the headline CPI. It's just that these measures are constructed so that they follow that path with much less volatility (the monthly variance in the median CPI is about 95 percent smaller than the all-items CPI and about 25 percent smaller than the CPI less food and energy).
I think of the trimmed-mean estimators and the median CPI as being more akin to seasonal adjustment than they are to the concept of core inflation. (Indeed, early on, Cecchetti and I showed that the median CPI and associated trimmed-mean estimates also did a good job of purging the data of its seasonal nature.) The median CPI and the trimmed-mean estimators are noise-reduced statistics where the underlying signal being identified is the CPI itself, not some alternative aggregation of the price data.
This is not true of the CPI excluding food and energy, nor necessarily of other so-called measures of "core" inflation. Core inflation measures alter the weights of the price statistic so that they can no longer pretend to be approximations of the cost of living. They are different constructs altogether.
The idea of "core" inflation is one of the topics of tomorrow's post.
By Mike Bryan, vice president and senior economist in the Atlanta Fed's research department
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