Looking at inflation calculations in a different way.
These charts show the Consumer Price Index (the primary measure of changes in prices and inflation) compounded in three ways. The usual number reported about inflation is the year-over-year change in CPI. Example 1 shows this value mostly around two percent from 2000 through 2021, with a few excursions higher and lower. (Click charts for larger versions.)
When the rate is steady, this makes sense. Recently, though, the rate has been changing, with a big swing up, and then down.
This means the year-over-year change — the usual measure of the inflation rate — hides some information that is useful.
The Consumer Price Index for All Urban Consumers (CPI-U) was unchanged in October on a seasonally adjusted basis, after increasing 0.4 percent in September, the U.S. Bureau of Labor Statistics reported today. Over the last 12 months, the all items index increased 3.2 percent before seasonal adjustment.
BLS reported two “inflation rates,” the monthly change of zero, and the year-over-year change of 3.2 percent. Which is most meaningful?
Both hold meaning, but the year-over-year measure is based, in part, on events that happened up to one year ago. The monthly change considers just the most recent month. To cast the monthly rate in a form compatible with the scale of the annual rate, we can annualize the monthly rate. That is, what would the year-over-year inflation rate be if the current monthly change continued (compounded) for a year?
The two charts below show this. Chart 4a shows the year-over-year change, along with quarter-over-quarter change and month-over-month change. The year-over-year value is 3.2 percent, as reported by BLS.
Chart 4b shows the month-over-month change expressed as a compound annual rate. It is, for this month, zero (when rounded), as reported by BLS. This is what the year-over-year inflation rate would be if the current value continued for another 11 months.
Of course, we don’t know what will happen in the future, so this annualized rate is only a crude projection, perhaps even a fantasy. Further, since the month-over-month price change varies substantially, the corresponding compounded annual rate does, too. This is easily seen in chart 4b in the monthly series. The quarterly series is less volatile.
For this month, using the monthly compounded rate is advantageous to the current administration, as it can say (with appropriate caveats) inflation is zero instead of 3.2 percent. But in the months in the chart where the monthly line is above the annual line, the reverse holds. In August, for example, the year-over-year rate was 3.7 percent, but the month-over-month rate, if annualized, was 7.8 percent.