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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.

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File URL: http://www.economics.unimelb.edu.au/downloads/wpapers-00-01/800.pdf
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Bibliographic Info

Paper provided by The University of Melbourne in its series Department of Economics - Working Papers Series with number 800.

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Length: 23 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:mlb:wpaper:800

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References

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  1. 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.
  2. Hirschberg, J.G. & Maasoumi, E. & Slottje, D.J., 2001. "Clusters of Attributes and Well-Being in the US," Department of Economics - Working Papers Series 778, The University of Melbourne.
  3. Uwe Jensen, 2000. "Is it efficient to analyse efficiency rankings?," Empirical Economics, Springer, vol. 25(2), pages 189-208.
  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. Mickael Lothgren & Magnus Tambour, 1999. "Bootstrapping the data envelopment analysis Malmquist productivity index," Applied Economics, Taylor & Francis Journals, vol. 31(4), pages 417-425.
  6. Simar, L. & Wilson, P.W., . "Sensitivity analysis of efficiency scores: how to bootstrap in nonparametric frontier models," CORE Discussion Papers RP -1304, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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.
  8. Ferrier, G.D. & Hirschberg, J.G., 1998. "Can We Bootstrap DEA Scores?," Department of Economics - Working Papers Series 627, The University of Melbourne.
  9. Hirschberg, J.G., 1996. "Modelling Time of Day Sustitution Using the Second Moments of Demand," Department of Economics - Working Papers Series 506, 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. 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.
  12. 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.
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