Munich Personal RePEc Archive

On Mr. Farrell's Decomposition and Aggregation

Fare, Rolf and Zelenyuk, Valentin (2002): On Mr. Farrell's Decomposition and Aggregation. Published in: International Journal of Business and Economics , Vol. 4, No. 2 (2005): pp. 167-171.

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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.

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