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The Transformation Function, Technical Efficiency, and the CCR Ratio

Listed author(s):
  • Subhash C. Ray

    (University of Connecticut)

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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File URL: http://web2.uconn.edu/economics/working/2017-09.pdf
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Paper provided by University of Connecticut, Department of Economics in its series Working papers with number 2017-09.

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Length: 16 pages
Date of creation: Jun 2017
Handle: RePEc:uct:uconnp:2017-09
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University of Connecticut 365 Fairfield Way, Unit 1063 Storrs, CT 06269-1063

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Web page: http://www.econ.uconn.edu/

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  1. 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.
  2. 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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