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	Laspeyres and Paasche Index	マルムクィスト生産性指数
分野	経済学	効率性分析
系統	Process / pipeline	Regression model
提唱年	1871	1994
提唱者	Étienne Laspeyres (1871); Hermann Paasche (1874)	Färe, Grosskopf, Norris & Zhang
種類	Bilateral price and quantity index numbers	Non-parametric productivity index
原典	Diewert, W. E. (1976). Exact and superlative index numbers. Journal of Econometrics, 4(2), 115–145.	Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review, 84(1), 66–83.
別名	Laspeyres Index, Paasche Index, Base-Weighted Index, Current-Weighted Index	MPI, Malmquist Index, Malmquist DEA Productivity Index, Malmquist Verimlilik Endeksi
関連	3	1
概要	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 Malmquist Productivity Index (MPI) is a non-parametric measure of total factor productivity (TFP) change over time. Formally grounded in distance functions by Caves, Christensen, and Diewert (1982) and operationalized using Data Envelopment Analysis by Färe, Grosskopf, Norris, and Zhang (1994), MPI decomposes productivity growth into two components: efficiency change (catching-up to the frontier) and technical change (shift of the frontier itself).