Malmquist Productivity Index Decompositions: A Unifying Framework

In two widely cited but unpublished working papers, Simar and Wilson (1998Shephard, R. 1970. Theory of Cost and Production Functions, New Jersey: Princeton University Press. [Google Scholar]) and Zofío and Lovell (1998Wheelock, D and Wilson, PW. 1999. Technical progress, inefficiency, and productivity change in U.S. banking, 1984–1993. Journal of Money, Credit and Banking, 31: 212–34. [Crossref], [Web of Science ®], [Google Scholar]) proposed an alternative decomposition of the Malmquist Productivity Index, which retained what seemed to be the strongholds of previous proposals with regard to the contribution of technological and efficiency change to productivity change. Namely, a technical change term with regard to the best practice variable returns to scale (VRS) technology, which is to be found in Ray and Desli (1997Ray, S. Sept. 2001. “On an extended decomposition of the malmquist productivity index”. In Paper Presented at the Seventh European Workshop on Efficiency and Productivity, Sept., 25–29. Oviedo: Universidad de Oviedo. [Google Scholar]) and a scale efficiency change term that illustrates a firm's situation with regard to optimal scale (benchmark technology), Färe et al . (1994Färe, R, Grosskopf, S and Norris, M. 1997. Productivity growth, technical progress, and efficiency change in industrialized countries: reply. American Economic Review, 87: 1040–43. [Web of Science ®], [Google Scholar]). Attaining this objective required the introduction of an additional term in the Malmquist Productivity Index decomposition, which would reflect the scale bias of technical change. It is our objective to provide economic rationale for this term within a theory of production context, the existing decompositions and recent articles that further elaborate on this issue. The ideas are illustrated using productivity trends in 17 OECD countries.