So sánh phương pháp

	Laspeyres and Paasche Index	Törnqvist Index
Lĩnh vực	Kinh tế học	Kinh tế học
Họ	Process / pipeline	Process / pipeline
Năm ra đời	1871	1936
Người khởi xướng	Étienne Laspeyres (1871); Hermann Paasche (1874)	Leo Törnqvist; superlative theory by W. Erwin Diewert
Loại	Bilateral price and quantity index numbers	Superlative index number for aggregating prices or quantities
Công trình gốc	Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4(2), 115–145.	Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4(2), 115–145.
Tên gọi khác	Laspeyres Index, Paasche Index, Base-Weighted Index, Current-Weighted Index	Tornqvist Index, Tornqvist-Theil Index, Translog Index, Tornqvist Price Index
Liên quan	3	3
Tóm tắt	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 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.