FisherIndex

Fisherindex is a price index named after Irving Fisher. It is used to measure changes in the price level over time and aims to balance the biases of alternative index formulas. The Fisher price index is defined as the geometric mean of the Laspeyres and Paasche price indices: F = sqrt(L × P). Here L is the Laspeyres index, computed with base-period quantities, and P is the Paasche index, computed with current-period quantities. Concretely, L = sum(p1 q0) / sum(p0 q0) and P = sum(p1 q1) / sum(p0 q1), where p1 and p0 are current and base prices, and q0 and q1 are base and current quantities. The resulting Fisherindex often lies between L and P.

The Fisherindex is a popular choice in price statistics because it reduces substitution bias compared with either Laspeyres or Paasche alone. It is also regarded as a superlative index, providing a close approximation to a true cost-of-living index for a wide class of consumer preferences. It can be extended to quantity indices by applying the same idea in reverse, and it can be computed for various baskets of goods and services.

Historically, Fisher introduced the index in the early 20th century, and it has since been widely used in national accounts and academic research. Limitations include data requirements for quantities and prices across periods and potential sensitivity to quality changes. See also Laspeyres index, Paasche index, Fisher ideal index, and superlative index theory.