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.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Farrell efficiency, Index Aggregation
• Subjects: D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity

References

Aczél, J., 1990, “Determining Merged Relative Scores,” Journal of Mathematical Analysis and Applications,150:1.

Eichhorn, W., 1978, Functional Equations in Economics, (Addison-Wesley, Reading, MA).

Farrell, M.J., 1957, “The Measurement of Productive Efficiency,” Journal of Royal Statistical Society, Series A, General, 120:3.

Färe, R., S. Grosskopf and V. Zelenyuk (2004) "Aggregation of Cost Efficiency Indicators and Indexes Across Firms,” Academia Economic Papers, 32:2, pp. 395-411.

Färe, R. and V. Zelenyuk (2003), “On Aggregate Farrell Efficiency Scores,” European Journal of Operational Research 146:3, 615-620.

Koopmans, T.C. (1957), Three Essays on the State of Economic Analysis, New York: McGraw-Hill.