In any discussion of “recent” inflation, you’ll invariably see a chart or table showing the 12-month trends of the inflation data. What’s special about a 12-month trend? Why is this a more useful perspective than, say, the latest monthly inflation number, or the read over the past three months? The answer is simple and intuitive: the 12-month trend inflation rate is used to smooth over distracting data fluctuations. That is, the 12-month trend improves the inflation signal relative to the noise in the data.

Seasonal fluctuations are one specific type of noise in the data, but thankfully there are statistical techniques called “seasonal adjustments” that reduce this noise without having to resort to a 12-month trend. In fact, seasonal adjustment eliminates about one-third of the monthly variation in aggregate consumer prices. But that still leaves a lot of variation in consumer prices that aren’t part of the current inflation trend, and so the people drawing the charts smooth over the variations by way of a 12-month trend line.

If a 12-month trend is good, why not 24 months or 36 months? Here we confront the trade-off involved in using time trends: they are backward looking. People who have to make decisions about inflation don’t get much “new” information each month from a 12-month trend and, of course, the new information gets proportionately less as the time trend extends further back into the past.

So, the trade off is this: How much backward-looking data are you willing to accept in order to reduce the noise inherent in the most recent inflation number?  Evidently the answer is 12 months, given the ubiquitousness of the 12-month average. To be clear, however, I haven’t any idea what makes a 12-month trend special.  

Wouldn’t it be useful to have a statistical method, not unlike seasonal adjustment, that could reduce the noise in the inflation measure while preserving its timeliness? This is precisely what the trimmed-mean inflation statistics attempt to do. Recognizing the unusual nature of price-change distributions that underlie an inflation statistic, these measures can reduce the monthly volatility in the inflation measure by a substantial amount without the use of time trends.  

What does this mean in terms of the trade-off we face when evaluating current inflation? Cecchetti and Schoenholtz weigh in on this in a recent blog post at moneyandbanking.com. (Their data was for the PCE price index, which I’ve created on the following table for the CPI.)  

We can think of these average deviations (RMSEs) as the amount of noise in the inflation measure. Note that the monthly trimmed-mean and median CPI measures reduce the noise relative to the CPI by about 68% (a RMSE of near 1.03 compared to 3.24 for the ordinary CPI.)  At a three-month trend, the noise in the trimmed inflation measures are reduced a bit further, and the trimmed-mean CPI is still about 62% less noisy than the headline CPI. But also notice that at longer time trends, that is, time trends longer than 3 months, the trimmed mean and median measures no longer show noise reduction. Moreover, at a twelve-month trend, these measures perform only modestly better than the ordinary CPI. 

There are two key takeaways from this exercise.  First, you can eliminate a lot of noise from the CPI using these measures while preserving the timeliness of the data.  I would think that’s an important benefit to people who are interested in knowing what inflation is NOW. Seen in this light, the trimmed-mean estimators are more akin to seasonal adjustment, than as “core” inflation measures. 

The second important takeaway is that you don’t get much additional noise reduction from the trimmed-mean estimators for time averages longer than three months.  And at 12 months, the time averaging has sufficiently reduced the noise in the regular CPI such that its performance isn’t substantially different from the others.

The bottom line: If you want to know what the current inflation trend is, you can either look at the past three months of trimmed-mean or median CPI data, or wait 12 months to see what the CPI says.