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Conical FDH Estimators of Directional Distances and Luenberger Productivity Indices for General Technologies

Author

Listed:
  • Daraio, Cinzia

    (Sapienza Univer- sity of Rome)

  • Di Leo, Simone

    (Sapienza Univer- sity of Rome)

  • Simar, Léopold

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

In productivity and efficiency analysis, directional distances are very popular, due to their flexibility for choosing the direction to evaluate the distance of Decision Making Units (DMUs) to the efficient frontier of the production set. The theory and the statistical properties of these measures are today well known in various situations. But so far, the way to measure directional distances to the cone spanned by the attainable set has not been analyzed. In this paper we fill this gap and describe how to define and estimate directional distances to this cone, for general technologies, i.e. without imposing convexity. Their statistical properties are also developed. This allows us to measure distances to non-convex attainable set under Constant Returns to Scale (CRS) but also to measure and estimate Luenberger productivity indices and their decompositions for general technologies. The way to make inference on these indices is also described in details. We propose illustrations with some simulated data, as well as, a practical example of inference on Luenberger productivity indices and their decompositions with a well-known real data set.

Suggested Citation

  • Daraio, Cinzia & Di Leo, Simone & Simar, Léopold, 2024. "Conical FDH Estimators of Directional Distances and Luenberger Productivity Indices for General Technologies," LIDAM Discussion Papers ISBA 2024009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2024009
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    References listed on IDEAS

    as
    1. Simar, Léopold & Vanhems, Anne, 2012. "Probabilistic characterization of directional distances and their robust versions," Journal of Econometrics, Elsevier, vol. 166(2), pages 342-354.
    2. Epure, Mircea & Kerstens, Kristiaan & Prior, Diego, 2011. "Bank productivity and performance groups: A decomposition approach based upon the Luenberger productivity indicator," European Journal of Operational Research, Elsevier, vol. 211(3), pages 630-641, June.
    3. 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.
    4. 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.
    5. Manh D. Pham & Léopold Simar & Valentin Zelenyuk, 2019. "Statistical Inference for Aggregation of Malmquist Productivity Indices," CEPA Working Papers Series WP082019, School of Economics, University of Queensland, Australia.
    6. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    7. Cinzia Daraio & Léopold Simar & Paul W. Wilson, 2020. "Fast and efficient computation of directional distance estimators," Annals of Operations Research, Springer, vol. 288(2), pages 805-835, May.
    8. Léopold Simar & Paul W. Wilson, 2023. "Another look at productivity growth in industrialized countries," Journal of Productivity Analysis, Springer, vol. 60(3), pages 257-272, December.
    9. Simar, Léopold & W. Wilson, Paul, 2019. "Central limit theorems and inference for sources of productivity change measured by nonparametric Malmquist indices," European Journal of Operational Research, Elsevier, vol. 277(2), pages 756-769.
    10. Kevork, Ilias S. & Pange, Jenny & Tzeremes, Panayiotis & Tzeremes, Nickolaos G., 2017. "Estimating Malmquist productivity indexes using probabilistic directional distances: An application to the European banking sector," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1125-1140.
    11. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    12. 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.
    13. Cinzia Daraio & Léopold Simar, 2016. "Efficiency and benchmarking with directional distances: a data-driven approach," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(7), pages 928-944, July.
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    More about this item

    Keywords

    Nonparametric production frontiers ; Cone ; DEA ; FDH ; Directional Distances ; Luenberger productivity indices;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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