手法を比較

	Törnqvist Index	Fisher Ideal Index
分野	経済学	経済学
系統	Process / pipeline	Process / pipeline
提唱年	1936	1922
提唱者	Leo Törnqvist; superlative theory by W. Erwin Diewert	Irving Fisher; superlative theory by W. Erwin Diewert
種類	Superlative index number for aggregating prices or quantities	Superlative index number for aggregating prices or quantities
原典	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
別名	Tornqvist Index, Tornqvist-Theil Index, Translog Index, Tornqvist Price Index	Fisher Index, Fisher's Ideal Index, Ideal Index Number, Fisher Price Index
関連	3	3
概要	The Törnqvist index is a superlative index number used to aggregate many individual prices or quantities into a single measure of overall price change or quantity change between two periods. It is a weighted geometric mean of the individual price (or quantity) relatives, where each item's weight is the average of its value shares in the two periods. Because it is 'exact' for the flexible translog aggregator function, it is the standard tool for constructing productivity indices and is widely used in national accounts, productivity statistics, and price measurement.	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.