Signature
J = (p1_t / p1_0 * p2_t / p2_0 * p3_t / p3_0)^(1 / 3)
| Inputs | Definition | Unit |
|---|---|---|
p1_t | Price of the same first product in month t | currency per unit, above zero |
p1_0 | Price of the first matched product in the base month | currency per unit, above zero |
p2_t | Price of the same second product in month t | currency per unit, above zero |
p2_0 | Price of the second matched product in the base month | currency per unit, above zero |
p3_t | Price of the same third product in month t | currency per unit, above zero |
p3_0 | Price of the third matched product in the base month | currency per unit, above zero |
J | Jevons index of the elementary aggregate as a ratio, 1 when prices are unchanged | none |
|---|
Function
Consumer price index from a fixed basket with Jevons elementary aggregates, chain-linking and average inflation rates
Maps the base-period and current prices of a fixed basket, with the quantities or expenditure of an earlier weight reference period, to a Lowe-type index level, and combines the matched prices of one elementary aggregate by the Jevons geometric mean. It also joins yearly links into a long series on the 2015 = 100 reference and maps two index values and the months between them to an average annual inflation rate. The ratio of two index values is the I_b / I_a input of the live price-year adjustment HE-FM-COST-002 under HE-FN-COST-001, which is not repeated here, and a ratio of the US CPI for all urban consumers enters the Medicaid additional rebate of HE-FM-340B-002. Currency conversion and purchasing power parities are left to the Basket of Countries page. Notation follows the Consumer Price Index article.
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Implementations
Excel
Jevons elementary aggregate from named matched price ranges
With base-month prices in ElemPriceBase and month t prices of the same products in ElemPriceCurrent, a helper column named ElemRelative holds each current price divided by its base price, and GEOMEAN, a classic Excel function, returns the Jevons index; name its cell JevonsOut.
=GEOMEAN(ElemRelative)
Assumptions
Equal weights for the prices in a Jevons elementary aggregate
At the lowest level of aggregation detailed weights are not available, so the manual uses unweighted formulae that treat all the products as equally important, each price taking a weight equal to the reciprocal of the number of prices in the stratum (section 3.4). Differences in spending between the outlets or varieties priced are not reflected.
Matched products with positive prices in a Jevons elementary aggregate
Each relative compares the same product at both dates. The manual states that if a product has no price matching one in the base month, that price must be excluded from the calculation or a quality adjustment made (section 3.4). The geometric mean also needs every price to be above zero.
Worked examples
Jevons aggregate of three illustrative matched prices
Illustrative prices of 1.00, 2.00 and 4.00 in the base month and 1.10, 2.00 and 3.60 now give relatives of 1.1, 1 and 0.9. Their geometric mean is 0.996655, a fall of about 0.33%, while their arithmetic mean is exactly 1 (computed here for illustration).
p1_0 = 1; p2_0 = 2; p3_0 = 4; p1_t = 1.1; p2_t = 2; p3_t = 3.6; J = 0.996655
Jevons aggregate when all matched prices rise by 2%
Equal relatives of 1.02 give a Jevons index of 1.02 whatever the price levels, a limiting case that checks an implementation.
p1_0 = 1; p2_0 = 2; p3_0 = 4; p1_t = 1.02; p2_t = 2.04; p3_t = 4.08; J = 1.02
Common errors
Carli arithmetic mean of relatives in place of the Jevons index
The arithmetic mean of the worked example relatives is 1, no change, against a Jevons fall of about 0.33%, and an arithmetic mean is never below the geometric mean of the same relatives (computed here for illustration). The manual records that Eurostat regulations forbid the Carli index and that in certain circumstances, combined with chain-linking of the within-year indices, it introduces an upward bias known as chain drift (section 3.4).
Unmatched replacement product entered as a Jevons price change
Replacing the third product, priced 4.00 in the base month, with a different product at 3.00 and treating it as the same item gives a Jevons index of 0.937889, a spurious fall of about 6.2% (illustrative, computed here for illustration). The manual excludes such a price or makes a quality adjustment (sections 3.4 and 9).
Sources
ONS technical manual on elementary aggregates and the Jevons index
Office for National Statistics. Consumer Prices Indices Technical Manual, 2019. Newport, Office for National Statistics, 2019, page last revised 26 March 2025. Section 3.4, elementary aggregates, which states that unweighted formulae are used at the lowest level, treating all products as equally important with a weight equal to the reciprocal of the number of prices, defines the Jevons index as the geometric mean of price relatives, the Dutot index as the ratio of average prices and the Carli index as the arithmetic mean of price relatives, names the Jevons index as the elementary aggregate formula primarily used in UK consumer price indices, gives it as the n-th root of the product of the relatives p_i^t / p_i^0 and as the ratio of geometric means of prices, requires prices for matching products, and records that Eurostat regulations forbid the Carli index and that it can introduce chain drift. The page carries a notice dated 25 March 2026 that the manual has been replaced by the ONS technical guidance, whose article Traditional data aggregates in consumer prices (last revised 25 March 2026, section 12) states that the CPI and CPIH use the Jevons index for local collection items and a mixture of the Dutot and Jevons formulations for central items, and gives the same two forms of the Jevons index.
Canonical Identity
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