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The transformation function, technical efficiency, and the CCR ratio

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  • Ray, Subhash C

Abstract

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 construction 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 Charnes, Cooper, and Rhodes ratio to technical efficiency is not obvious. Usually the ratio measure is rationalized as efficiency by showing its equivalence to the Farrell efficiency measure. This paper offers a direct derivation of the ratio measure of efficiency from a transformation function. We also show how Banker, Charnes, and Cooper measure under variable returns to scale can be derived from the transformation function.

Suggested Citation

  • Ray, Subhash C, 2019. "The transformation function, technical efficiency, and the CCR ratio," European Journal of Operational Research, Elsevier, vol. 278(2), pages 422-429.
    • Handle: RePEc:eee:ejores:v:278:y:2019:i:2:p:422-429
    DOI: 10.1016/j.ejor.2019.02.014
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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. Leleu, Hervé, 2013. "Inner and outer approximations of technology: A shadow profit approach," Omega, Elsevier, vol. 41(5), pages 868-871.
    3. Finn Førsund, 2013. "Weight restrictions in DEA: misplaced emphasis?," Journal of Productivity Analysis, Springer, vol. 40(3), pages 271-283, December.
    4. Ray,Subhash C., 2012. "Data Envelopment Analysis," Cambridge Books, Cambridge University Press, number 9781107405264, September.
    5. 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.
    6. M. Stone, 2002. "How not to measure the efficiency of public services (and how one might)," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 405-434, October.
    7. Starrett, David A, 1977. "Measuring Returns to Scale in the Aggregate, and the Scale Effect of Public Goods," Econometrica, Econometric Society, vol. 45(6), pages 1439-1455, September.
    8. Subhash Ray, 2007. "Shadow profit maximization and a measure of overall inefficiency," Journal of Productivity Analysis, Springer, vol. 27(3), pages 231-236, June.
    9. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    10. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
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    Cited by:

    1. Subhash C. Ray, 2018. "Data Envelopment Analysis with Alternative Returns to Scale," Working papers 2018-20, University of Connecticut, Department of Economics.

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    More about this item

    Keywords

    Data envelopment analysis; Supporting hyperplane; Convexity; Degree of increasing returns;
    All these keywords.

    JEL classification:

    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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