Inflation and Consumer Price Index, September 2024

Looking at inflation calculations in a different way.

The usual number reported about inflation is the year-over-year change in CPI. 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.

Recently, Bureau of Labor Statistics, part of the United States Department of Labor, released CPI numbers for September 2024, reporting:

The Consumer Price Index for All Urban Consumers (CPI-U) increased 0.2 percent on a seasonally adjusted basis, the same increase as in August and July, the U.S. Bureau of Labor Statistics reported today. Over the last 12 months, the all items index increased 2.4 percent before seasonal adjustment.

BLS reported two “inflation rates,” the monthly change of 0.2 percent, and the year-over-year change of 2.4 percent. Which is most meaningful? ⁽¹⁾“Year-to-year percentage changes in the CPI purport to show what happened to inflation each month, but they can mislead about both recent news and trends because of base effects and compounding. A more timely and less bewildering alternative is to simply monitor monthly changes over several months. A four to six-month average would be better than twelve. And any temptation to multiply monthly changes by twelve to concoct an annual rate must be resisted – since doing that could make it look as though inflation in June and July of 2020 was 6.2%.” The Mystifying Arithmetic of Year-to-Year Inflation Estimates. https://www.cato.org/blog/mystifying-arithmetic-year-year-inflation-estimates-4 ⁽²⁾WashU Expert: Comparing annual inflation changes each month can distort reality. https://source.wustl.edu/2022/08/washu-expert-comparing-annual-inflation-changes-each-month-can-distort-reality/ ⁽³⁾“… monthly changes, while informative, tend to be too noisy to provide a clear signal of the data’s underlying trend. Yearly changes are better for that purpose, but they can go too far in the other direction: they underweight changes in recent months that give analysts a more up-to-date take on the current trend in inflation.” The Signal and the Noise, Part II: CPI Inflation. https://www.whitehouse.gov/cea/written-materials/2023/05/10/the-signal-and-the-noise-part-ii-cpi-inflation/ ⁽⁴⁾“The monthly inflation data are incredibly volatile, so it’s tough to rely on those readings to construct a trend. To help smooth out that volatility, a common way analysts will look at trends is by measuring the change in prices over the past three months, then annualizing that figure to get a sense of what the increase would look like over a one-year period.” Lose Yourself in the Inflation Data. https://www.schwab.com/learn/story/lose-yourself-inflation-data

Both hold meaning, but the year-over-year measure is based, in part, on events that happened up to one year ago and can’t be changed by current policies or actions. 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 present this. These charts show the Consumer Price Index (the primary measure of changes in prices and inflation) compounded in three ways. 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 2.4 percent, as reported by BLS. Also, the monthly rate is 0.2 percent, also as reported by BLS.

Chart 4b shows the month-over-month change expressed as a compound annual rate. It is, for this month, 2.2 percent. This is what the year-over-year inflation rate would be if the current value continued for another 11 months. (If we project the change during the most recent quarter to the coming year, the value is 1.6 percent.)

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 derived compounded annual rate does, too. This is easily seen in chart 4b in the monthly series. The quarterly series is less volatile.

Because the monthly CPI value is volatile, and because annualizing a monthly rate magnifies small changes, we should be cautious when considering this calculation and projection. Can we say that inflation is now negative? I don’t think so. Also, this calculation can work in favor or disfavor of political advocacy. For example, last November I wrote this:

For this month, using the monthly compounded rate is advantageous to the current administration, as it can say (with appropriate caveats) inflation is 1.2 percent instead of 3.1 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.

For an interactive visualization of this and other CPI data, see Visualization: Consumer Price Index and Inflation.