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On Mr. Farrell's Decomposition and Aggregation

By Rolf Fare and Valentin Zelenyuk

Abstract

In this paper we show that in order to aggregate individual efficiency scores into a group (e.g., industry) efficiency score, in such a way that the multiplicative structure of further decompositions is preserved with equal weights across components, the weighted geometric mean is required. We also show how the weights can be chosen using a variation of a theorem by Koopmans (1957). In the end, our paper provides a mathematically consistent and economic-theory justified way of aggregation of Farrell-type efficiency scores.

Topics: D24 - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
Year: 2002
DOI identifier: 10.1080/13504850110118165
OAI identifier: oai:mpra.ub.uni-muenchen.de:28005

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