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Central Limit Theorems for Directional Distance Functions with and without Undesirable Outputs

Author

Listed:
  • Simar, Léopold

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

  • Zelenyuk, Valentin
  • Zhao, Shirong

Abstract

We develop new central limit theorems (CLTs) for the aggregate directional distance functions (DDFs), which embed the CLTs for the aggregate efficiency and simple mean DDFs as special cases. Moreover, we develop new CLTs for the aggregate DDFs in the presence of the weak disposability of undesirable outputs. Our Monte-Carlo simulations confirm the good performance of statistical inference based on the new CLTs we have derived and illustrate how wrong the inference based on the standard CLTs can be. To our knowledge, this is the first study that provides both the asymptotic theory and the simulation evidence for the non-parametric frontier approaches when some outputs are undesirable. Finally, we provide an empirical illustration using a data set from large US banks as well as supply the computational code for alternative applications.

Suggested Citation

  • Simar, Léopold & Zelenyuk, Valentin & Zhao, Shirong, 2024. "Central Limit Theorems for Directional Distance Functions with and without Undesirable Outputs," LIDAM Discussion Papers ISBA 2024010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2024010
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    References listed on IDEAS

    as
    1. David C. Wheelock & Paul W. Wilson, 2018. "The evolution of scale economies in US banking," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 16-28, January.
    2. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    3. Léopold Simar & Valentin Zelenyuk, 2018. "Central Limit Theorems for Aggregate Efficiency," Operations Research, INFORMS, vol. 66(1), pages 137-149, January.
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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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

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