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Clustering in a Data Envelopment Analysis Using Bootstrapped Efficiency Scores

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  • Joseph G. Hirschberg
  • Jenny N. Lye

Abstract

This paper explores the insight from the application of cluster analysis to the results of a Data Envelopment Analysis of productive behaviour. Cluster analysis involves the identification of groups among a set of different objects (individuals or characteristics). This is done via the definitions of a distance matrix that defines the relationship between the different objects, which then allows the determination of which objects are most similar into clusters. In the case of DEA, cluster analysis methods can be used to determine the degree of sensitivity of the efficiency score for a particular DMU to the presence of the other DMUs in the sample that make up the reference technology to that DMU. Using the bootstrapped values of the efficiency measures we construct two types of distance matrices. One is defined as a function of the variance covariance matrix of the scores with respect to each other. This implies that the covariance of the score of one DMU is used as a measure of the degree to which the efficiency measure for a single DMU is influenced by the efficiency level of another. An alternative distance measure is defined as a function of the ranks of the bootstrapped efficiency. An example is provided using both measures as the clustering distance for both a one input one output case and a two input two output case.

Suggested Citation

  • Joseph G. Hirschberg & Jenny N. Lye, 2001. "Clustering in a Data Envelopment Analysis Using Bootstrapped Efficiency Scores," Department of Economics - Working Papers Series 800, The University of Melbourne.
  • Handle: RePEc:mlb:wpaper:800
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    File URL: http://www.economics.unimelb.edu.au/downloads/wpapers-00-01/800.pdf
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    References listed on IDEAS

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    1. Gary Ferrier & Joseph Hirschberg, 1997. "Bootstrapping Confidence Intervals for Linear Programming Efficiency Scores: With an Illustration Using Italian Banking Data," Journal of Productivity Analysis, Springer, vol. 8(1), pages 19-33, March.
    2. J. G. Hirschberg, 2000. "Modelling time of day substitution using the second moments of demand," Applied Economics, Taylor & Francis Journals, vol. 32(8), pages 979-986.
    3. Gary Ferrier & Joseph Hirschberg, 1999. "Can We Bootstrap DEA Scores?," Journal of Productivity Analysis, Springer, vol. 11(1), pages 81-92, February.
    4. Mei Xue & Patrick T. Harker, 1999. "Overcoming the Inherent Dependency of DEA Efficiency Scores: A Bootstrap Approach," Center for Financial Institutions Working Papers 99-17, Wharton School Center for Financial Institutions, University of Pennsylvania.
    5. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    6. Mickael Lothgren & Magnus Tambour, 1999. "Bootstrapping the data envelopment analysis Malmquist productivity index," Applied Economics, Taylor & Francis Journals, vol. 31(4), pages 417-425.
    7. Hirschberg, Joseph G. & Slottje, Daniel J., 1994. "An empirical Bayes approach to analyzing earnings functions for various occupations and industries," Journal of Econometrics, Elsevier, vol. 61(1), pages 65-79, March.
    8. Joseph G. Hirschberg & Esfandiar Maasoumi & Daniel J. Slottje, 2001. "Clusters of attributes and well-being in the USA," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 445-460.
    9. Hirschberg, J.G. & Maasoumi, E. & Slottje, D.J., 1998. "The Environment and the Quality of Life in the United States Over Time," Department of Economics - Working Papers Series 654, The University of Melbourne.
    10. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    11. G.D. Ferrier & J. G. Hirschberg, 1992. "Climate Control Efficiency," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 37-54.
    12. Hirschberg, Joseph G. & Slottje, D. J., 1989. "Remembrance of things past the distribution of earnings across occupations and the kappa criterion," Journal of Econometrics, Elsevier, vol. 42(1), pages 121-130, September.
    13. Uwe Jensen, 2000. "Is it efficient to analyse efficiency rankings?," Empirical Economics, Springer, vol. 25(2), pages 189-208.
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    Cited by:

    1. Sethi, Amarjit Singh, 2016. "Sources of Growth in India: Evidence from Punjab and Haryana," Journal of Regional Development and Planning, JRDP, vol. 5(1), pages 15-34.
    2. Fuad Aleskerov & Vsevolod Petrushchenko, 2016. "DEA by sequential exclusion of alternatives in heterogeneous samples," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 5-22, January.
    3. Samoilenko, Sergey & Osei-Bryson, Kweku-Muata, 2010. "Determining sources of relative inefficiency in heterogeneous samples: Methodology using Cluster Analysis, DEA and Neural Networks," European Journal of Operational Research, Elsevier, vol. 206(2), pages 479-487, October.

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