In 2021, Federal Reserve Governor Waller gave a speech at Stanford University called ‘The Economic Outlook and a Cautionary Tale on “Idiosyncratic” Price Changes and Inflation.’  In the talk he laid out a hypothetical example that was critical of the trimmed-mean approach to inflation measurement. Although the talk was quite some time ago, I’m motivated to write about it for a couple of reasons. First, Governor Waller will likely be an influential voice in discussions about the usefulness of various inflation metrics, including trimmed-mean and median inflation estimators. Second, I’ve heard this criticism–indeed, this exact example–repeated more recently on social media, so it has some popular appeal.  

But it’s wrong. 

Here’s his example:

Consider a three-good economy with goods A, B and C, and look at how their prices increase over time.…[C]onsider a world in which there are sharp price changes that are staggered across the goods. In year 1, the price of good A goes up 5 percent, while the price of goods B and C increase 2 percent. If we assume equal weights for each good, the inflation rate for this economy is 3 percent. This repeats in year 2, with the price of good B increasing 5 percent while the other two have increases of 2 percent. In year 3, good C sees the largest increase. In this economy, inflation averages 3 percent each year, which is above the FOMC’s 2 percent inflation target. Now, one could look at this data and manipulate it in several common ways. First, if one used a trimmed-mean measure of inflation, you would throw out the highest and the lowest readings for each year. What do you get? The average inflation rate would be 2 percent every year. Thus, over a three-year period, a trimmed mean measure of inflation would be 2 percent and indicate we are hitting our inflation target when the true measure would be 3 percent per year.” 

What Governor Wallace has stumbled upon isn’t a problem with trimmed-mean estimators; it’s a problem of inappropriately using a symmetric trim when the underlying data distribution is clearly asymmetric.  Let me explain.

I’ve created the underlying distribution that Governor Waller has concocted in the following chart:

In the example, the distribution stays the same from period to period.  What changes is that the particular good rising 5% rotates between the three goods. Pictured is Good A rising 5%, but in the next period it would be Good B, and then Good C in the period after that.  Governor Waller points out, correctly, that if you use a median approach to the data, the inflation rate would always read 2%, when obviously the true inflation rate is 3%.  In other words, if the central banker pays attention to the median inflation rate, they would be misled into thinking inflation was at target (2%), when in fact it is running a percentage point too high.

What’s the problem with Governor Waller’s example? In the example, the underlying distribution is positively skewed, permanently.  In situations like this, the trimmed-mean estimator has to take the persistent skewness of the distribution into account and asymmetrically trim.  Otherwise, the trimmed-mean will be biased (persistently too low.) This is the reason the Dallas Fed uses an asymmetric trimmed-mean for the PCE price data, which are also persistently skewed. (Peter Rupert made this point in a recent U.S. Macro Snapshot post, but I think it’s worth repeating here.) 

What is the asymmetric trim in this hypothetical?  The mean percentile of the distribution is 67%, which means that for every percent you trim from the bottom of the distribution, you only trim ½ of a percent from the top of the distribution. If you do that, you’ll see the resulting average for all the trims, including the median percent change, is 3%, not 2%.  This is the proper, unbiased, estimate of the rate of inflation. 

Let’s continue with Governor Waller’s discussion.

A second way of manipulating the data is to say in year 1, “Look, inflation is being driven by good A, which had an idiosyncratic, outsized price increase. If you throw it out, the underlying inflation rate is 2 percent.” Then in year 2, you say, “Good B had an idiosyncratic price increase, so throw it out.” Repeat for year 3. Again, by selectively throwing out unusually high price increases for individual goods, you would conclude that inflation over the three-year period is 2 percent and we are hitting the inflation target when, in fact, it was 3 percent. 

This, I think, is an appropriate concern.  Analysts look across the component price data and believe they can judge what should, and should not be considered idiosyncratic.  But EVERY price change, in some sense, is special, responding to the characteristics and forces of their particular markets.  The real risk is that an analyst who already has a notion of what the inflation rate is will find some justification for throwing out subsets of the data to fit the inflation rate they had pre-conceived. 

I have my own story to tell in this regard (that I originally told at a 2014 Cleveland Fed conference “Torturing the CPI data until They Confess.”) 

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 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.

The trimmed-mean inflation estimators, when properly constructed, don’t allow analyst bias to creep into the number.  They’re entirely judgment free. Those who believe they can look across the components of the CPI and separate the anomalous data points from the inflationary data points are kidding themselves–whether they realize it or not.  In other words, it’s best to just let the data speak for themselves.