The Transformation Function, Technical Efficiency, and the CCR Ratio
Charnes, Cooper, and Rhodes define the ratio of the virtual output to the virtual input as a measure of the technical efficiency of a multiple output multiple input firm. The aggregation weights used in constructing the virtual output and the virtual input may be arbitrarily chosen so long as the weights are non-negative and using these weights no firm’s input-output bundle shows efficiency exceeding 100%. In production economics, the ratio of aggregate output to aggregate input is a measure of total factor productivity and a direct link of the CCR ratio to technical efficiency is not obvious. Usually the CCR ratio is rationalized as efficiency by showing its equivalence to the Farrell efficiency measure. This paper offers a direct derivation of the CCR ratio measure of efficiency from a Transformation Function. We also show how the Banker, Charnes, Cooper (BCC) measure under variable returns to scale can be derived from the Transformation Function.
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- Banker, Rajiv D. & Thrall, R. M., 1992. "Estimation of returns to scale using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 62(1), pages 74-84, October.
- Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
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