A consumer price index (CPI) measures how prices change over time for consumer goods and services covered by a specified household population. Its percentage change measures consumer inflation. For quant work, choosing the right series and comparison interval matters as much as calculating the ratio: an index level, a monthly rate and a twelve-month rate are different inputs.
The OECD's CPI definition describes an aggregate built from sampled prices and weighted component indexes. CPI is an index number, not the dollar price of a universal shopping basket, and it need not match your own spending experience.
A small basket makes the weights visible
Consider a fictional fixed-quantity teaching basket, observed at two dates exactly one year apart. Prices are in USD per unit. Both items retain the same quality, quantities stay fixed, and no seasonal adjustment is applied. This illustrates index arithmetic; it does not reproduce an official CPI production method.
| Item | Fixed quantity | Year 0 unit price | Year 1 unit price | Year 0 spending | Year 1 spending |
|---|---|---|---|---|---|
| A | 2 | 3 USD | 4 USD | 6 USD | 8 USD |
| B | 1 | 4 USD | 4 USD | 4 USD | 4 USD |
| Basket total | 10 USD | 12 USD |
Let be fixed quantities and unit prices. Define basket cost and a Year 0 = 100 index :
Here , , and . The annual change is
Original teaching example with unchanged quantities and quality. Stacked spending bars use a zero baseline; the index is dimensionless. These are fictional annual observations, not official CPI data.
The starting expenditure weights are for A and for B. A's price rises by one third, while B's is unchanged. Thus this basket's inflation is . An equally weighted average of the two item price changes would be about 16.67%, which answers a different question. Two units versus one unit are quantities; they are not the spending weights.
The reference period is a scale choice
The index reference period sets the displayed level to 100. The weight reference period supplies expenditure information for the weights. A price reference period supplies the comparison prices in price relatives. These periods need not coincide; the ABS methodology distinguishes all three.
Changing the reference scale alone does not change inflation. If the toy index were rescaled from 100 and 120 to 200 and 240, the ratio would still give . Reweighting changes the basket's economic representation; rebasing merely changes its numerical scale. Also, two countries' index levels cannot by themselves reveal which country has higher living costs.
Why the official calculation is more involved
An official CPI must choose a population, geography and consumption coverage, then sample prices and combine components. For example, U.S. CPI-U represents urban consumers; its coverage differs from that of CPI-W. BLS explains these population and coverage choices. Neither index measures a stock portfolio's price changes.
Goods disappear, package sizes change and replacement models differ in quality. Statistical agencies need replacement, imputation and quality-adjustment procedures so that a better product is not automatically treated as pure inflation. BLS uses geometric-mean formulas for most basic commodity-and-service strata and other formulas for specified cases; higher-level aggregation is another step. The BLS calculation handbook documents these distinctions.
Consumers also substitute between products as relative prices change. Holding this toy basket unchanged deliberately suppresses that behaviour. Actual methods differ in how they accommodate substitution, and weights are updated rather than frozen forever. The ABS discussion of substitution and linking explains why a permanent fixed basket has limits. A CPI should not be treated as an exact measure of every household's cost of maintaining its living standard.
Read the series label before using the number
For a monthly series, a month-on-month change compares adjacent months; a year-on-year change compares the same month in consecutive years. An annual-average change compares annual averages, which is different again. BLS explains the comparison periods and seasonal basis: seasonal adjustment helps interpret short-term movements, and adjusted observations can be revised.
Record the publisher, series identifier, population, geography, all-items or exclusion coverage, frequency, seasonal basis, index reference and comparison horizon. In historical research, retain the release date and vintage available at the decision time. Using a later revision in an earlier trading signal introduces look-ahead bias.
A rising CPI means positive consumer inflation over the chosen interval. Slower positive growth is disinflation; a falling index indicates deflation. Neither the level 120 nor its increase of 20 index points is, by itself, a general formula for a 20% inflation rate: the denominator determines the percentage.
Practice: does rebasing change inflation?
Question. A fictional index rises from 150 to 156 over one year. An analyst rescales the first observation to 100 without changing the underlying series. What is the new second observation, and what is annual inflation?
Answer. The new second observation is . Inflation is , equivalently . The original increase of six index points was not a 6% increase. Rescaling changes the points, not the percentage change.
Sources
- OECD, Inflation (CPI) — definition, elementary aggregation and annual-growth convention.
- U.S. Bureau of Labor Statistics, CPI Frequently Asked Questions — populations, coverage, index interpretation, comparison periods and seasonal adjustment.
- U.S. Bureau of Labor Statistics, Handbook of Methods: CPI Calculation — basic indexes, aggregation, replacement and quality adjustment.
- Australian Bureau of Statistics, Consumer Price Index: Concepts, Sources and Methods, 2025 edition — reference periods, re-referencing, linking and substitution. Official documentation checked 28 October 2026; the example is fictional.