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Measuring firm performance using nonparametric quantile-type distances

Author

Listed:
  • Abdelaati Daouia
  • Léopold Simar
  • Paul W. Wilson

Abstract

When faced with multiple inputs and outputs , traditional quantile regression of Y conditional on X = x for measuring economic efficiency in the output (input) direction is thwarted by the absence of a natural ordering of Euclidean space for dimensions q ( p ) greater than one. Daouia and Simar (2007) used nonstandard conditional quantiles to address this problem, conditioning on Y ≥ y ( X ≤ x ) in the output (input) orientation, but the resulting quantiles depend on the a priori chosen direction. This article uses a dimensionless transformation of the ( p + q )-dimensional production process to develop an alternative formulation of distance from a realization of ( X , Y ) to the efficient support boundary, motivating a new, unconditional quantile frontier lying inside the joint support of ( X , Y ), but near the full, efficient frontier. The interpretation is analogous to univariate quantiles and corrects some of the disappointing properties of the conditional quantile-based approach. By contrast with the latter, our approach determines a unique partial-quantile frontier independent of the chosen orientation (input, output, hyperbolic, or directional distance). We prove that both the resulting efficiency score and its estimator share desirable monotonicity properties. Simple arguments from extreme-value theory are used to derive the asymptotic distributional properties of the corresponding empirical efficiency scores (both full and partial). The usefulness of the quantile-type estimator is shown from an infinitesimal and global robustness theory viewpoints via a comparison with the previous conditional quantile-based approach. A diagnostic tool is developed to find the appropriate quantile-order; in the literature to date, this trimming order has been fixed a priori . The methodology is used to analyze the performance of U.S. credit unions, where outliers are likely to affect traditional approaches.

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  • Abdelaati Daouia & Léopold Simar & Paul W. Wilson, 2017. "Measuring firm performance using nonparametric quantile-type distances," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 156-181, March.
  • Handle: RePEc:taf:emetrv:v:36:y:2017:i:1-3:p:156-181
    DOI: 10.1080/07474938.2015.1114289
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    Cited by:

    1. Caitlin O’Loughlin & Léopold Simar & Paul W. Wilson, 2023. "Methodologies for assessing government efficiency," Chapters, in: António Afonso & João Tovar Jalles & Ana Venâncio (ed.), Handbook on Public Sector Efficiency, chapter 4, pages 72-101, Edward Elgar Publishing.
    2. Priscillah Wanjiru Gitau & Robert Abayo & Priscillah Wanjiru Gitau, 2020. "Influence of Organizational Resource Allocation and Strategy Communication on Organizational Performance of Selected Supermarkets in Nairobi County," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 4(8), pages 331-340, August.
    3. 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.
    4. Daraio, Cinzia & Simar, Léopold, 2014. "Directional distances and their robust versions: Computational and testing issues," European Journal of Operational Research, Elsevier, vol. 237(1), pages 358-369.
    5. Daouia, Abdelaati & Florens, Jean-Pierre & Simar, Léopold, 2021. "Robustified Expected Maximum Production Frontiers," Econometric Theory, Cambridge University Press, vol. 37(2), pages 346-387, April.
    6. 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.
    7. Paul W. Wilson & Shirong Zhao, 2023. "Investigating the performance of Chinese banks over 2007–2014," Annals of Operations Research, Springer, vol. 321(1), pages 663-692, February.
    8. Amy Apon & Linh Ngo & Michael Payne & Paul Wilson, 2015. "Assessing the effect of high performance computing capabilities on academic research output," Empirical Economics, Springer, vol. 48(1), pages 283-312, February.
    9. Wei, Xiao & Zhang, Ning, 2020. "The shadow prices of CO2 and SO2 for Chinese Coal-fired Power Plants: A partial frontier approach," Energy Economics, Elsevier, vol. 85(C).
    10. Dai, Sheng & Kuosmanen, Timo & Zhou, Xun, 2023. "Generalized quantile and expectile properties for shape constrained nonparametric estimation," European Journal of Operational Research, Elsevier, vol. 310(2), pages 914-927.
    11. Simar, Léopold & Wilson, Paul W., 2020. "Technical, allocative and overall efficiency: Estimation and inference," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1164-1176.
    12. Léopold Simar & Paul W. Wilson, 2020. "Hypothesis testing in nonparametric models of production using multiple sample splits," Journal of Productivity Analysis, Springer, vol. 53(3), pages 287-303, June.
    13. Caitlin T. O’Loughlin & Paul W. Wilson, 2021. "Benchmarking the performance of US Municipalities," Empirical Economics, Springer, vol. 60(6), pages 2665-2700, June.
    14. Amir Moradi-Motlagh & Ali Emrouznejad, 2022. "The origins and development of statistical approaches in non-parametric frontier models: a survey of the first two decades of scholarly literature (1998–2020)," Annals of Operations Research, Springer, vol. 318(1), pages 713-741, November.
    15. Wilson, Paul W., 2018. "Dimension reduction in nonparametric models of production," European Journal of Operational Research, Elsevier, vol. 267(1), pages 349-367.
    16. 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.
    17. 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).
    18. Kneip, Alois & Simar, Léopold & Wilson, Paul W., 2022. "Conical FDH Estimators of General Technologies, with Applications to Returns to Scale and Malmquist Productivity Indices," LIDAM Discussion Papers ISBA 2022024, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    19. Simar, Léopold & Wilson, Paul, 2022. "Modern Tools for Evaluating the Performance of Health-Care Providers," LIDAM Discussion Papers ISBA 2022006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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