Data Note
Inflation comparisons depend on the basket, weights and interval being measured. Explicit index calculations distinguish core inflation, contributions to headline inflation, annualized monthly momentum and the realized change over twelve months.
A monthly rise in consumer prices, its annualized equivalent and a twelve-month inflation rate describe different intervals. Headline and core indexes add another distinction: they cover different baskets. Mixing the interval with the basket can make a statistical comparison appear to reveal a change in underlying inflation that the numbers do not establish.
BLS identifies the all-items Consumer Price Index and its measure excluding food and energy as distinct series. Removing those categories does not remove their importance to household budgets. It changes the statistic used to examine price movements across the remaining items. Neither series is a direct measure of a particular firm's selling prices or input costs.
Take a deliberately simplified, fixed-basket example. Food and energy together receive a weight of 20 percent; other items receive 80 percent. All component index levels initially equal 100. In the next month, the first group rises by 2 percent and the second by 0.3 percent.
| Hypothetical group | Initial expenditure weight | Next index level | Weighted next level |
|---|---|---|---|
| Food and energy | 0.20 | 102.0 | 20.40 |
| Other items | 0.80 | 100.3 | 80.24 |
| All items | 1.00 | — | 100.64 |
Headline inflation is 0.64 percent for this month. The other-items index rises by 0.3 percent. Its weight is normalized within its own basket; it is not reported as the 0.24-percentage-point contribution that those items make to the hypothetical all-items change.
This is an original arithmetic example, not a reconstruction of the published CPI. It assumes fixed weights and a simple aggregation of component indexes. Actual index construction, weight updates and item-level aggregation require the agency's detailed methods. The example isolates why a contribution to an aggregate and the growth rate of a subaggregate are different objects.
Repeating a monthly increase of 0.3 percent for twelve consecutive months produces an annual increase of approximately 3.66 percent:
The corresponding annualization of 0.64 percent is approximately 7.96 percent. These transformations assume repetition of the observed monthly rate. They do not predict that food, energy or other prices will continue at that pace.
A twelve-month rate instead compares the actual current index with its actual level twelve months earlier. It contains eleven other monthly movements as well as the latest one. Consequently, a strong current month can coincide with a falling twelve-month rate if a still larger increase drops out of the comparison. Nothing in that outcome makes the current increase disappear.
Suppose the index was 100 twelve months earlier and is now 104. The twelve-month rate is 4 percent. If the previous month's index was 103.8, the current monthly increase is only about 0.193 percent. Annualizing that single month gives roughly 2.34 percent, not 4 percent. Both answers are consistent because the observations cover different horizons.
Seasonal adjustment addresses recurring calendar patterns; it does not change the economic meaning of annualization. A monthly seasonally adjusted rate should not be spliced into a twelve-month unadjusted comparison without identifying the distinction. BLS publishes both adjusted and unadjusted CPI information, so the table heading and series definition belong with the number.
For a policy assessment, a sequence of monthly readings can provide evidence about recent momentum, while the twelve-month measure summarizes a longer experience. For a purchasing contract, the relevant index may be a specified subcomponent with its own escalation clause. The appropriate measure follows the decision being analyzed. A comparison becomes informative only after the basket, weights, observation interval and adjustment convention have been made consistent.