Preliminary evidence from Brent Meyer and Guhan Venkatu of the Cleveland Fed shows that the median CPI is a robust measure of underlying inflation trends:
Trimmed-Mean Inflation Statistics: Just Hit the One in the Middle Brent Meyer and Guhan Venkatu: This paper reinvestigates the performance of trimmed-mean inflation measures some 20 years since their inception, asking whether there is a particular trimmed-mean measure that dominates the median CPI. Unlike previous research, we evaluate the performance of symmetric and asymmetric trimmed-means using a well-known equality of prediction test. We find that there is a large swath of trimmed-means that have statistically indistinguishable performance. Also, while the swath of statistically similar trims changes slightly over different sample periods, it always includes the median CPI—an extreme trim that holds conceptual and computational advantages. We conclude with a simple forecasting exercise that highlights the advantage of the median CPI relative to other standard inflation measures.
In the introduction, they add:
In general, we find aggressive trimming (close to the median) that is not too asymmetric appears to deliver the best forecasts over the time periods we examine. However, these “optimal” trims vary slightly across periods and are never statistically superior to the median CPI. Given that the median CPI is conceptually easy for the public to understand and is easier to reproduce, we conclude that it is arguably a more useful measure of underlying inflation for forecasters and policymakers alike.
And they conclude the paper with:
While we originally set out to find a single superior trimmed-mean measure, we could not conclude as such. In fact, it appears that a large swath of candidate trims hold statistically indistinguishable forecasting ability. That said, in general, the best performing trims over a variety of time periods appear to be somewhat aggressive and almost always include symmetric trims. Of this set, the median CPI stands out, not for any superior forecasting performance, but because of its conceptual and computational simplicity—when in doubt, hit the one in the middle.
Interestingly, and contrary to Dolmas (2005) we were unable to find any convincing evidence that would lead us to choose an asymmetric trim. While his results are based on components of the PCE chain-price index, a large part (roughly 75% of the initial release) of the components comprising the PCE price index are directly imported from the CPI. It could be the case that the imputed PCE components are creating the discrepancy. The trimmed-mean PCE series currently produced by the Federal Reserve Bank of Dallas trims 24 percent from the lower tail and 31 percent from the upper tail of the PCE price-change distribution. This particular trim is relatively aggressive and is not overly asymmetric—two features consistent with the best performing trims in our tests.
Finally, even though we failed to best the median CPI in our first set of tests, it remains the case that the median CPI is generally a better forecaster of future inflation over policy-relevant time horizons (i.e. inflation over the next 2-3 years) than the headline and core CPI.
One note. They are not saying that trimmed or median statistics are the best way to measure the cost of living for a household. They are asking what variable has the most predictive power for future (untrimmed, non-core, i.e. headline) inflation ("specifically the annualized percent change in the headline CPI over the next 36 months," though the results for 24 months are similar). That turns out, in general, to be the median CPI.