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Measuring the Robustness of Empirical Efficiency Valuations

Author

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  • Ludwig Kuntz

    () (University Hospital Hamburg, 20246 Hamburg, Germany, and Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, 76128 Karlsruhe, Germany)

  • Stefan Scholtes

    () (Judge Institute of Management Studies, University of Cambridge, Cambridge CB2 1AG, England)

Abstract

We study the robustness of empirical efficiency valuations of production processes in an extended Farrell model. Based on input and output data, an empirical efficiency status---efficient or inefficient---is assigned to each of the processes. This status may change if the data of the observed processes change. As illustrated by a capacity planning problem for hospitals in Germany, the need arises to gauge the robustness of empirical efficiency valuations. The example suggests to gauge the robustness of the efficiency valuation for a process with respect to perturbations of prespecified elements of the data. A natural measure of robustness is the minimal perturbation, in terms of a suitable distance function, of the chosen data elements that is necessary to change the efficiency status of the process under investigation. Farrell's (1957) efficiency score is an example of such a robustness measure. We give further examples of relevant data perturbations for which the robustness measure can be computed efficiently. We then focus on weighted maximum norm distance functions, such as the maximal absolute or percentage deviation, but allow for independent perturbations of the elements of an arbitrary a priori fixed subset of the data. In this setting, the robustness measure is naturally related to a certain threshold value for a linear monotone one-parameter family of perturbations and can be calculated by means of a linear programming--based bisection method. Closed form solutions in terms of Farrell's efficiency score are obtained for specific perturbations. Following the theoretical developments, we revisit the hospital capacity planning problem to illustrate the managerial relevance of our techniques.

Suggested Citation

  • Ludwig Kuntz & Stefan Scholtes, 2000. "Measuring the Robustness of Empirical Efficiency Valuations," Management Science, INFORMS, vol. 46(6), pages 807-823, June.
  • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:6:p:807-823
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    File URL: http://dx.doi.org/10.1287/mnsc.46.6.807.11937
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    References listed on IDEAS

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    1. 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.
    2. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
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    Citations

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    Cited by:

    1. Gary Ferrier & Hervé Leleu & Vivian Valdmanis, 2009. "Hospital capacity in large urban areas: is there enough in times of need?," Journal of Productivity Analysis, Springer, vol. 32(2), pages 103-117, October.
    2. Ludwig Kuntz & Stefan Scholtes & Antonio Vera, 2007. "Incorporating efficiency in hospital-capacity planning in Germany," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 8(3), pages 213-223, September.
    3. Wheelock, David C. & Wilson, Paul W., 2008. "Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations," Journal of Econometrics, Elsevier, vol. 145(1-2), pages 209-225, July.
    4. Kuosmanen, Timo & Post, Thierry & Scholtes, Stefan, 2007. "Non-parametric tests of productive efficiency with errors-in-variables," Journal of Econometrics, Elsevier, vol. 136(1), pages 131-162, January.
    5. Michaela-Maria Schaffhauser-Linzatti & Achim Zeileis & Marion Rauner, 2009. "Effects of the Austrian performance-oriented inpatient reimbursement system on treatment patterns: illustrated on cases with knee-joint problems," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(3), pages 293-314, September.
    6. Kuosmanen, T. & Post, G.T., 2001. "Testing for Productive Efficiency with Errors-in-Variables: with an application to the Dutch electricity sesctor," ERIM Report Series Research in Management ERS-2001-22-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. David C. Wheelock & Paul W. Wilson, 2009. "Robust, dynamic nonparametric benchmarking: the evolution of cost-productivity and efficiency among U.S. credit unions," Working Papers 2009-008, Federal Reserve Bank of St. Louis.
    8. Troutt, Marvin D. & Ehie, Ike C. & Brandyberry, Alan A., 2007. "Maximally productive input-output units," European Journal of Operational Research, Elsevier, vol. 178(2), pages 359-373, April.
    9. Post, G.T., 2001. "Testing for Stochastic Dominance with Diversification Possibilities," ERIM Report Series Research in Management ERS-2001-38-F&A, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.

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