International Journal of Business and Economics Volume 4, No. 2 August, 2005

On Farrell's Decomposition and Aggregation

Rolf Färe

Department of Economics and Department of Agricultural and Resource Economics, Oregon State University, U.S.A.

Valentin Zelenyuk

Institut de Statistique, Université Catholique de Louvain, Belgium and UPEG at EROC-EERC-Kyiv, Ukraine

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 theoretically justified way of aggregation of Farrell-type efficiency scores.

Keywords：Farrell efficiency, index aggregation.

JEL Classifications：D24.

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