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Further improvements of finite sample approximation of central limit theorems for envelopment estimators

Author

Listed:
  • Léopold Simar

    (Université Catholique de Louvain)

  • Valentin Zelenyuk

    (University of Queensland)

  • Shirong Zhao

    (Dongbei University of Finance and Economics)

Abstract

A simple yet easy to implement method is proposed to further improve the finite sample approximation of the recently developed central limit theorems for aggregates of envelopment estimators. Focusing on the simple mean efficiency, we propose using the bias-corrected individual efficiency estimate to improve the variance estimator. The extensive Monte-Carlo experiments confirm that, for relatively small sample sizes (≤100), with both low dimensions and especially for high dimensions, our new method combined with the data sharpening method generally provides better ‘coverage’ (of the true values by the estimated confidence intervals) than the previously developed approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:jproda:v:59:y:2023:i:2:d:10.1007_s11123-023-00661-8
    DOI: 10.1007/s11123-023-00661-8
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    References listed on IDEAS

    as
    1. Léopold Simar & Valentin Zelenyuk, 2018. "Central Limit Theorems for Aggregate Efficiency," Operations Research, INFORMS, vol. 66(1), pages 137-149, January.
    2. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non‐parametric, two‐stage models of production," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 170-191, June.
    3. Guangshun Qiao & Zhan-ao Wang, 2021. "Vertical integration vs. specialization: a nonparametric conditional efficiency estimate for the global semiconductor industry," Journal of Productivity Analysis, Springer, vol. 56(2), pages 139-150, December.
    4. 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.
    5. 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.
    6. 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.
    7. Caitlin T. O’Loughlin & Paul W. Wilson, 2021. "Benchmarking the performance of US Municipalities," Empirical Economics, Springer, vol. 60(6), pages 2665-2700, June.
    8. 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.
    9. 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.
    10. Léopold Simar & Valentin Zelenyuk, 2018. "Improving Finite Sample Approximation by Central Limit Theorems for DEA and FDH efficiency scores," CEPA Working Papers Series WP072018, School of Economics, University of Queensland, Australia.
    11. Bao Hoang Nguyen & Valentin Zelenyuk, 2021. "Aggregate efficiency of industry and its groups: the case of Queensland public hospitals," Empirical Economics, Springer, vol. 60(6), pages 2795-2836, June.
    12. Daraio, Cinzia & Simar, Leopold & Wilson, Paul, 2018. "Central limit theorems for conditional efficiency measures and tests of the ‘separability’ condition in non-parametric, two-stage models of production," LIDAM Reprints ISBA 2018023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. Simar, Léopold & Zelenyuk, Valentin, 2020. "Improving finite sample approximation by central limit theorems for estimates from Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1002-1015.
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    Cited by:

    1. Sokol, Ondřej & Frýd, Lukáš, 2023. "DEA efficiency in agriculture: Measurement unit issues," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).

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    More about this item

    Keywords

    Efficiency; Non-parametric efficiency estimators; Data envelopment analysis; Free disposal hull;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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