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Improving Finite Sample Approximation by Central Limit Theorems for DEA and FDH efficiency scores

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  • Simar, Leopold
  • Zelenyuk, Valentin
Abstract
We propose an improvement of the finite sample approximation of the central limit theorems (CLTs) that were recently derived for statistics involving production efficiency scores estimated via Data Envelopment Analysis (DEA) or Free Disposal Hull (FDH) approaches. The improvement is very easy to implement since it involves a simple correction of the already employed statistics without any additional computational burden and preserves the original asymptotic results such as consistency and asymptotic normality. The proposed approach persistently showed improvement in all the scenarios that we tried in various Monte-Carlo experiments, especially for relatively small samples or relatively large dimensions (measured by total number of inputs and outputs) of the underlying production model. This approach therefore is expected to be valuable (and at almost no additional computational costs) for practitioners wishing to perform statistical inference about production efficiency using DEA or FDH approaches.
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  • Simar, Leopold & Zelenyuk, Valentin, 2018. "Improving Finite Sample Approximation by Central Limit Theorems for DEA and FDH efficiency scores," LIDAM Discussion Papers ISBA 2018020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2018020
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    References listed on IDEAS

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    1. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
    2. Alois Kneip & Léopold Simar & Paul W. Wilson, 2016. "Testing Hypotheses in Nonparametric Models of Production," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 435-456, July.
    3. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2021. "Inference In Dynamic, Nonparametric Models Of Production: Central Limit Theorems For Malmquist Indices," Econometric Theory, Cambridge University Press, vol. 37(3), pages 537-572, June.
    4. Olesen, O. B., 1995. "Some unsolved problems in data envelopment analysis: A survey," International Journal of Production Economics, Elsevier, vol. 39(1-2), pages 5-36, April.
    5. Simar, Leopold & Wilson, Paul, 2018. "Technical, Allocative and Overall Efficiency: Inference and Hypothesis Testing," LIDAM Discussion Papers ISBA 2018018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Forsund, Finn R. & Sarafoglou, Nikias, 2005. "The tale of two research communities: The diffusion of research on productive efficiency," International Journal of Production Economics, Elsevier, vol. 98(1), pages 17-40, October.
    7. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    8. Atici, Kazim Baris & Podinovski, Victor V., 2015. "Using data envelopment analysis for the assessment of technical efficiency of units with different specialisations: An application to agriculture," Omega, Elsevier, vol. 54(C), pages 72-83.
    9. 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.
    10. 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.
    11. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2015. "When Bias Kills The Variance: Central Limit Theorems For Dea And Fdh Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 31(2), pages 394-422, April.
    12. Alois Kneip & Léopold Simar & Paul Wilson, 2011. "A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 483-515, November.
    13. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2008. "Asymptotics And Consistent Bootstraps For Dea Estimators In Nonparametric Frontier Models," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1663-1697, December.
    14. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
    15. Fukuyama, Hirofumi & Weber, William L., 2010. "A slacks-based inefficiency measure for a two-stage system with bad outputs," Omega, Elsevier, vol. 38(5), pages 398-409, October.
    16. Léopold Simar & Valentin Zelenyuk, 2018. "Central Limit Theorems for Aggregate Efficiency," Operations Research, INFORMS, vol. 66(1), pages 137-149, January.
    17. Jeong, Seok-Oh & Simar, Léopold, 2006. "Linearly interpolated FDH efficiency score for nonconvex frontiers," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2141-2161, November.
    18. Emrouznejad, Ali & Parker, Barnett R. & Tavares, Gabriel, 2008. "Evaluation of research in efficiency and productivity: A survey and analysis of the first 30 years of scholarly literature in DEA," Socio-Economic Planning Sciences, Elsevier, vol. 42(3), pages 151-157, September.
    19. Gorman, Michael F. & Ruggiero, John, 2008. "Evaluating US state police performance using data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 113(2), pages 1031-1037, June.
    20. Cook, Wade D. & Tone, Kaoru & Zhu, Joe, 2014. "Data envelopment analysis: Prior to choosing a model," Omega, Elsevier, vol. 44(C), pages 1-4.
    21. Chowdhury, Hedayet & Zelenyuk, Valentin & Laporte, Audrey & Wodchis, Walter P., 2014. "Analysis of productivity, efficiency and technological changes in hospital services in Ontario: How does case-mix matter?," International Journal of Production Economics, Elsevier, vol. 150(C), pages 74-82.
    22. Cook, Wade D. & Liang, Liang & Zhu, Joe, 2010. "Measuring performance of two-stage network structures by DEA: A review and future perspective," Omega, Elsevier, vol. 38(6), pages 423-430, December.
    23. Joe Zhu, 2014. "Data Envelopment Analysis," International Series in Operations Research & Management Science, in: Quantitative Models for Performance Evaluation and Benchmarking, edition 3, chapter 1, pages 1-9, Springer.
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    Cited by:

    1. Simar, Léopold & Zelenyuk, Valentin & Zhao, Shirong, 2024. "Inference for aggregate efficiency: Theory and guidelines for practitioners," European Journal of Operational Research, Elsevier, vol. 316(1), pages 240-254.
    2. Monge, Juan F. & Ruiz, José L., 2023. "Setting closer targets based on non-dominated convex combinations of Pareto-efficient units: A bi-level linear programming approach in Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 311(3), pages 1084-1096.
    3. Manh Pham & Léopold Simar & Valentin Zelenyuk, 2024. "Statistical Inference for Aggregation of Malmquist Productivity Indices," Operations Research, INFORMS, vol. 72(4), pages 1615-1629, July.
    4. Léopold Simar & Valentin Zelenyuk & Shirong Zhao, 2023. "Further improvements of finite sample approximation of central limit theorems for envelopment estimators," Journal of Productivity Analysis, Springer, vol. 59(2), pages 189-194, April.
    5. Nguyen, Bao Hoang & Simar, Léopold & Zelenyuk, Valentin, 2022. "Data sharpening for improving central limit theorem approximations for data envelopment analysis–type efficiency estimators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1469-1480.
    6. Valentin Zelenyuk, 2021. "Performance Analysis: Economic Foundations and Trends," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(3), pages 153-229, September.

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    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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