手法を比較

	マルムクィスト生産性指数	ネットワークデータ包絡分析 (Network DEA)
分野	効率性分析	効率性分析
系統	Regression model	Regression model
提唱年	1994	2000
提唱者	Färe, Grosskopf, Norris & Zhang	Färe & Grosskopf
種類	Non-parametric productivity index	Multi-stage nonparametric efficiency model
原典	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.	Färe, R., & Grosskopf, S. (2000). Network DEA. Socio-Economic Planning Sciences, 34(1), 35–49.
別名	MPI, Malmquist Index, Malmquist DEA Productivity Index, Malmquist Verimlilik Endeksi	Network Data Envelopment Analysis, Network Efficiency Analysis, Multi-Stage DEA, Ağ Veri Zarflama Analizi
関連	1	2
概要	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).	Network Data Envelopment Analysis (Network DEA) is a nonparametric efficiency measurement framework introduced by Färe and Grosskopf (2000) that extends classical DEA to multi-stage or multi-division production processes. Rather than treating a decision-making unit as a black box, it explicitly models the internal structure — the divisions and the intermediate products that flow between them — enabling stage-level and overall efficiency scores to be estimated simultaneously within a single coherent model.