قارن الطرق

	Laspeyres and Paasche Index	Fisher Ideal Index
المجال	الاقتصاد	الاقتصاد
العائلة	Process / pipeline	Process / pipeline
سنة النشأة	1871	1922
صاحب الطريقة	Étienne Laspeyres (1871); Hermann Paasche (1874)	Irving Fisher; superlative theory by W. Erwin Diewert
النوع	Bilateral price and quantity index numbers	Superlative index number for aggregating prices or quantities
المصدر التأسيسي	Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4(2), 115–145.	Fisher, I. (1922). The Making of Index Numbers: A Study of Their Varieties, Tests, and Reliability. Boston: Houghton Mifflin. ISBN: 9780678006597
الأسماء البديلة	Laspeyres Index, Paasche Index, Base-Weighted Index, Current-Weighted Index	Fisher Index, Fisher's Ideal Index, Ideal Index Number, Fisher Price Index
ذات صلة	3	3
الملخص	The Laspeyres and Paasche indices are the two foundational bilateral index numbers used to measure how a basket of prices (or quantities) changes between a base period and a current period. The Laspeyres index weights price changes by base-period quantities — it asks what the original basket costs now relative to then — while the Paasche index weights by current-period quantities, asking what the current basket costs now relative to then. They differ because consumers substitute away from goods whose relative prices rise, and this difference defines the well-known substitution bias: the Laspeyres index tends to overstate, and the Paasche index to understate, the true cost-of-living change, bracketing it between them.	The Fisher ideal index is a superlative index number that aggregates many individual prices or quantities into a single measure of overall change by taking the geometric mean of the Laspeyres (base-weighted) and Paasche (current-weighted) indices. Proposed by Irving Fisher in his 1922 treatise as the 'ideal' formula because it passes a battery of desirable axiomatic tests, it was later shown by W. Erwin Diewert to be exact for a flexible (quadratic) aggregator, giving it both an axiomatic and an economic-theoretic justification. It is the index of choice when a measure must satisfy the time-reversal and factor-reversal tests exactly.