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Efficiency analysis with ratio measures

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  • Olesen, Ole Bent
  • Petersen, Niels Christian
  • Podinovski, Victor V.

Abstract

In applications of data envelopment analysis (DEA) data about some inputs and outputs is often available only in the form of ratios such as averages and percentages. In this paper we provide a positive answer to the long-standing debate as to whether such data could be used in DEA. The problem arises from the fact that ratio measures generally do not satisfy the standard production assumptions, e.g., that the technology is a convex set. Our approach is based on the formulation of new production assumptions that explicitly account for ratio measures. This leads to the estimation of production technologies under variable and constant returns-to-scale assumptions in which both volume and ratio measures are native types of data. The resulting DEA models allow the use of ratio measures “as is”, without any transformation or use of the underlying volume measures. This provides theoretical foundations for the use of DEA in applications where important data are reported in the form of ratios.

Suggested Citation

  • Olesen, Ole Bent & Petersen, Niels Christian & Podinovski, Victor V., 2015. "Efficiency analysis with ratio measures," European Journal of Operational Research, Elsevier, vol. 245(2), pages 446-462.
    • Handle: RePEc:eee:ejores:v:245:y:2015:i:2:p:446-462
    DOI: 10.1016/j.ejor.2015.03.013
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    References listed on IDEAS

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    1. B. Hollingsworth & P. Smith, 2003. "Use of ratios in data envelopment analysis," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 733-735.
    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.
    3. Golany, Boaz & Thore, Sten, 1997. "The Economic and Social Performance of Nations: Efficiency and Returns to Scale," Socio-Economic Planning Sciences, Elsevier, vol. 31(3), pages 191-204, September.
    4. Joseph Paradi & Mette Asmild & Paul Simak, 2004. "Using DEA and Worst Practice DEA in Credit Risk Evaluation," Journal of Productivity Analysis, Springer, vol. 21(2), pages 153-165, March.
    5. O. Olesen & N. Petersen, 2009. "Target and technical efficiency in DEA: controlling for environmental characteristics," Journal of Productivity Analysis, Springer, vol. 32(1), pages 27-40, August.
    6. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    7. Podinovski, V. V., 2005. "Selective convexity in DEA models," European Journal of Operational Research, Elsevier, vol. 161(2), pages 552-563, March.
    8. Simar, Leopold & Wilson, Paul W., 2002. "Non-parametric tests of returns to scale," European Journal of Operational Research, Elsevier, vol. 139(1), pages 115-132, May.
    9. Olesen, O. B. & Petersen, N. C., 1995. "Incorporating quality into data envelopment analysis: a stochastic dominance approach," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 117-135, April.
    10. Martin Gaynor & Harald Seider & William B. Vogt, 2005. "The Volume–Outcome Effect, Scale Economies, and Learning-by-Doing," American Economic Review, American Economic Association, vol. 95(2), pages 243-247, May.
    11. 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.
    12. Thanassoulis, E. & Boussofiane, A. & Dyson, R. G., 1995. "Exploring output quality targets in the provision of perinatal care in England using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 80(3), pages 588-607, February.
    13. Dyson, R. G. & Allen, R. & Camanho, A. S. & Podinovski, V. V. & Sarrico, C. S. & Shale, E. A., 2001. "Pitfalls and protocols in DEA," European Journal of Operational Research, Elsevier, vol. 132(2), pages 245-259, July.
    14. Rajiv D. Banker & Richard C. Morey, 1986. "Efficiency Analysis for Exogenously Fixed Inputs and Outputs," Operations Research, INFORMS, vol. 34(4), pages 513-521, August.
    15. Ruggiero, John, 1996. "On the measurement of technical efficiency in the public sector," European Journal of Operational Research, Elsevier, vol. 90(3), pages 553-565, May.
    16. Rajiv D. Banker & Richard C. Morey, 1986. "The Use of Categorical Variables in Data Envelopment Analysis," Management Science, INFORMS, vol. 32(12), pages 1613-1627, December.
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