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A Bootstrap-Regression Procedure to Capture Unit Specific Effects In Data Envelopment Analysis


  • Evangelia Desli

    (Lloyd’¡Çs of London, London EC3M 7HA, UK.)

  • Subhash C. Ray

    (University of Connecticut, Storrs CT 06269-1063, USA.)


The Data Envelopment Analysis (DEA) efficiency score obtained for an individual firm is a point estimate without any confidence interval around it. In recent years, researchers have resorted to bootstrapping in order to generate empirical distributions of efficiency scores. This procedure assumes that all firms have the same probability of getting an efficiency score from any specified interval within the [0,1] range. We propose a bootstrap procedure that empirically generates the conditional distribution of efficiency for each individual firm given systematic factors that influence its efficiency. Instead of resampling directly from the pooled DEA scores, we first regress these scores on a set of explanatory variables not included at the DEA stage and bootstrap the residuals from this regression. These pseudo-efficiency scores incorporate the systematic effects of unit-specific factors along with the contribution of the randomly drawn residual. Data from the U.S. airline industry are utilized in an empirical application.

Suggested Citation

  • Evangelia Desli & Subhash C. Ray, 2004. "A Bootstrap-Regression Procedure to Capture Unit Specific Effects In Data Envelopment Analysis," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 39(1), pages 89-110, January.
  • Handle: RePEc:dse:indecr:v:39:y:2004:i:1:p:89-110

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    References listed on IDEAS

    1. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
    2. 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.
    3. Subhash C. Ray, 1991. "Resource-Use Efficiency in Public Schools: A Study of Connecticut Data," Management Science, INFORMS, vol. 37(12), pages 1620-1628, December.
    4. Simar, L., 1991. "Estimating efficiencies from frontier models with panel data: a comparison of parametric, non-parametric and semi-parametric methods with boot strapping," CORE Discussion Papers 1991026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," CORE Discussion Papers 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. 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.
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    Cited by:

    1. Mazumdar, Mainak & Rajeev, Meenakshi & Ray, Subhash C., 2012. "Sources of Heterogeneity in the Efficiency of Indian Pharmaceutical Firms," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 47(2), pages 191-221.
    2. Greer, Mark, 2009. "Is it the labor unions' fault? Dissecting the causes of the impaired technical efficiencies of the legacy carriers in the United States," Transportation Research Part A: Policy and Practice, Elsevier, vol. 43(9-10), pages 779-789, November.
    3. Sengupta, Atanu & Kundu, Subrata, 2006. "Scale Efficiency of Indian Farmers: A Non- Parametric Approach," Indian Journal of Agricultural Economics, Indian Society of Agricultural Economics, vol. 61(4).
    4. Petridis, Konstantinos & Malesios, Chrisovalantis & Arabatzis, Garyfallos & Thanassoulis, Emmanuel, 2013. "Efficiency analysis of forestry journals: Suggestions for improving journals’ quality," Journal of Informetrics, Elsevier, vol. 7(2), pages 505-521.
    5. Greer, Mark R., 2008. "Nothing focuses the mind on productivity quite like the fear of liquidation: Changes in airline productivity in the United States, 2000-2004," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(2), pages 414-426, February.
    6. Rajitkanok Puenpatom & Robert Rosenman, 2008. "Efficiency of Thai provincial public hospitals during the introduction of universal health coverage using capitation," Health Care Management Science, Springer, vol. 11(4), pages 319-338, December.

    More about this item


    DEA; Kernel Smoothing; Reflection Method; Empirical Density;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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