International Journal of Business and Economics

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
UPEG at EROC-EERC-Kyiv, Ukraine
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.