Скачать или смотреть Part 1 Malmquist efficiency, productivity, DEA for researchers & thesis 2023 FGLR FGNZ Ray & Desli,

The Malmquist productivity change index, as defined by D.W. Caves, L.R. Christensen, W.E. Diewert (1982) in Econometrica, has for decades been commonly used indices to estimate dynamic productivity. R. Färe, S. Grosskopf, M. Norris, Z. Zhang (1994) in American Economic Review proposed to compute the Malmquist index from DEA efficiency scores and first decomposed the constant returns to scale the Malmquist index into its catch-up and frontier shift components; a two-factor decomposition which has been used widely, though not universally, accepted. Their subsequent three-factor decomposition, in which the efficiency change component is further decomposed into a scale change and a pure technical efficiency change component has, however, received a good deal of criticism for being internally inconsistent, and was challenged in (S.C. Ray, E. Desli, 1997), though this decomposition, in turn, has been criticized in (B.M. Balk, 2001, C.A.K. Lovell, 2003, Pastor et al, 2011).

Let's understand this Malmquist from the premises of DEA.