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Indicators of Ill-Conditioned Data Sets and Model Misspecification in Data Envelopment Analysis: An Extended Facet Approach

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Author Info

  • O. B. Olesen

    (Department of Management, Odense University, Odense, Denmark)

  • N. C. Petersen

    (Department of Management, Odense University, Odense, Denmark)

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    Abstract

    Date Envelopment Analysis (DEA) employs mathematical programming to measure the relative efficiency of Decision Making Units (DMUs). This paper is concerned with development of indicators to determine whether or not the specification of the input and output space is supported by data in the sense that the variation in data is sufficient for estimation of a frontier of the same dimension as the input output space. Insufficient variation in data implies that some inputs/outputs can be substituted along the efficient frontier but only in fixed proportions. Data thus locally supports variation in a subspace of a lower dimension rather than in the input output space of full dimension. Each segment of the efficient frontier is in this sense subject to local collinearity. Insufficient variation in data provides a bound on admissible disaggregations in cases where substitution in fixed proportions is incompatible with a priori information concerning the production process. A data set incapable of estimating a frontier of full dimension will in this case be denoted ill-conditioned. It is shown that the existence of well-defined marginal rates of substitution along the estimated strongly efficient frontier segments requires the existence of Full Dimensional Efficient Facets (FDEFs). A test for the existence of FDEFs is developed, and an operational two-stage procedure for efficiency evaluation relative to an over-all non-fixed technology is developed; the two-stage procedure provides a lower and an upper bound on the efficiency index for each DMU.

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 42 (1996)
    Issue (Month): 2 (February)
    Pages: 205-219

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    Handle: RePEc:inm:ormnsc:v:42:y:1996:i:2:p:205-219

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    Related research

    Keywords: efficiency measurement; data envelopment analysis; facets; virtual multipliers; model misspecification; rates of sustitutions; maintained hypotheses; Frontier estimation;

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    Citations

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    Cited by:
    1. Tone, Kaoru & Sahoo, Biresh K., 2005. "Evaluating cost efficiency and returns to scale in the Life Insurance Corporation of India using data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 39(4), pages 261-285, December.
    2. Allen, R. & Thanassoulis, E., 2004. "Improving envelopment in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 154(2), pages 363-379, April.
    3. Olesen, Ole Bent & Petersen, Niels Christian, 2013. "Imposing the Regular Ultra Passum law in DEA models," Omega, Elsevier, vol. 41(1), pages 16-27.
    4. Bougnol, M.-L. & Dulá, J.H., 2009. "Anchor points in DEA," European Journal of Operational Research, Elsevier, vol. 192(2), pages 668-676, January.
    5. Gitto, Simone & Mancuso, Paolo, 2010. "Airport efficiency: a DEA two stage analysis of the Italian commercial airports," MPRA Paper 34366, University Library of Munich, Germany, revised 10 Oct 2010.
    6. Aparicio, Juan & Pastor, Jesus T., 2014. "Closest targets and strong monotonicity on the strongly efficient frontier in DEA," Omega, Elsevier, vol. 44(C), pages 51-57.
    7. Thanassoulis, Emmanuel & Kortelainen, Mika & Allen, Rachel, 2012. "Improving envelopment in Data Envelopment Analysis under variable returns to scale," European Journal of Operational Research, Elsevier, vol. 218(1), pages 175-185.
    8. Kittelsen,S.A.C., 1999. "Monte Carlo simulations of DEA efficiency measures and hypothesis tests," Memorandum 09/1999, Oslo University, Department of Economics.
    9. Fukuyama, Hirofumi & Sekitani, Kazuyuki, 2012. "Decomposing the efficient frontier of the DEA production possibility set into a smallest number of convex polyhedrons by mixed integer programming," European Journal of Operational Research, Elsevier, vol. 221(1), pages 165-174.
    10. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2009. "An occurrence of multiple projections in DEA-based measurement of technical efficiency: Theoretical comparison among DEA models from desirable properties," European Journal of Operational Research, Elsevier, vol. 196(2), pages 764-794, July.
    11. Seiford, Lawrence M. & Zhu, Joe, 1998. "On alternative optimal solutions in the estimation of returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 108(1), pages 149-152, July.
    12. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    13. Atici, Kazim Baris & Podinovski, Victor V., 2012. "Mixed partial elasticities in constant returns-to-scale production technologies," European Journal of Operational Research, Elsevier, vol. 220(1), pages 262-269.
    14. Athanassopoulos, Antreas D. & Lambroukos, Nikos & Seiford, Lawrence, 1999. "Data envelopment scenario analysis for setting targets to electricity generating plants," European Journal of Operational Research, Elsevier, vol. 115(3), pages 413-428, June.
    15. Hirofumi Fukuyama & Kazuyuki Sekitani, 2012. "An efficiency measure satisfying the Dmitruk–Koshevoy criteria on DEA technologies," Journal of Productivity Analysis, Springer, vol. 38(2), pages 131-143, October.
    16. HOSSEINZADEH LOTFI, Farhad & HATAMI-MARBINI, Adel & AGRELL, Per & GHOLAMI, Kobra, 2013. "Centralized resource reduction and target setting under DEA control," CORE Discussion Papers 2013005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. Dimitrov, Stanko & Sutton, Warren, 2013. "Generalized symmetric weight assignment technique: Incorporating managerial preferences in data envelopment analysis using a penalty function," Omega, Elsevier, vol. 41(1), pages 48-54.
    18. Finn Førsund, 2013. "Weight restrictions in DEA: misplaced emphasis?," Journal of Productivity Analysis, Springer, vol. 40(3), pages 271-283, December.
    19. Silva Portela, Maria Conceicao A. & Thanassoulis, Emmanuel, 2005. "Profitability of a sample of Portuguese bank branches and its decomposition into technical and allocative components," European Journal of Operational Research, Elsevier, vol. 162(3), pages 850-866, May.
    20. Maria Silva Portela & Pedro Borges & Emmanuel Thanassoulis, 2003. "Finding Closest Targets in Non-Oriented DEA Models: The Case of Convex and Non-Convex Technologies," Journal of Productivity Analysis, Springer, vol. 19(2), pages 251-269, April.
    21. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "Measurement of returns to scale using a non-radial DEA model: A range-adjusted measure approach," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1918-1946, February.
    22. Amatatsu, Hirofumi & Ueda, Tohru, 2012. "Measurement of simultaneous scale and mix changes in inputs and outputs using DEA facets and RTS," European Journal of Operational Research, Elsevier, vol. 223(3), pages 752-761.
    23. Zhu, Joe, 2000. "Further discussion on linear production functions and DEA," European Journal of Operational Research, Elsevier, vol. 127(3), pages 611-618, December.
    24. Kao, Chiang, 2010. "Congestion measurement and elimination under the framework of data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 123(2), pages 257-265, February.

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