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Estimating Nonparametric Conditional Frontiers and Efficiencies: A New Approach

Author

Listed:
  • Mastromarco, Camilla
  • Simar, Léopold

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

  • Van Keilegom, Ingrid
Abstract
In production theory, conditional frontiers and conditional efficiency measures are a flexible and appealing approach to consider the role of environmental variables on the production process. Direct approaches estimate non-parametrically conditional distribution functions requiring smoothing techniques and the use of selected bandwidths. The statistical literature produces way to derive bandwidths of optimal order, by using e.g. least-squares-cross-validation techniques. However, it has been shown that the resulting order may not be optimal when estimating the boundary of the distribution function. As a consequence the direct approaches may suffer from some statistical instability. In this paper we suggest a full nonparametric approach which avoids the problem of estimating these bandwidths, by eliminating in a first step the influence of the environmental factors on the inputs and the outputs. By doing this we produce “pure” inputs and outputs which allow to estimate a “pure” measure of efficiency, more reliable for ranking the firms, since the influence of the external factors have been eliminated. This can be viewed as an extension of the use of location-scale models (implying some semi-parametric structure) to full nonparametric models, based on nonseparable, nonparametric models. We are also able to recover the frontier and efficiencies in original units. We describe the method, its statistical properties and we show in some Monte-Carlo simulations, how our new method dominates the traditional direct approach.

Suggested Citation

  • Mastromarco, Camilla & Simar, Léopold & Van Keilegom, Ingrid, 2022. "Estimating Nonparametric Conditional Frontiers and Efficiencies: A New Approach," LIDAM Discussion Papers ISBA 2022035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2022035
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    References listed on IDEAS

    as
    1. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    2. Daouia, Abdelaati & Gijbels, Irène, 2011. "Robustness and inference in nonparametric partial frontier modeling," Journal of Econometrics, Elsevier, vol. 161(2), pages 147-165, April.
    3. Simar, Léopold & Vanhems, Anne & Van Keilegom, Ingrid, 2016. "Unobserved heterogeneity and endogeneity in nonparametric frontier estimation," Journal of Econometrics, Elsevier, vol. 190(2), pages 360-373.
    4. Guerre, Emmanuel & Sabbah, Camille, 2012. "Uniform Bias Study And Bahadur Representation For Local Polynomial Estimators Of The Conditional Quantile Function," Econometric Theory, Cambridge University Press, vol. 28(1), pages 87-129, February.
    5. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2019. "A bootstrap approach for bandwidth selection in estimating conditional efficiency measures," European Journal of Operational Research, Elsevier, vol. 277(2), pages 784-797.
    6. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    7. 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).
    8. 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.
    9. Qi Li & Juan Lin & Jeffrey S. Racine, 2013. "Optimal Bandwidth Selection for Nonparametric Conditional Distribution and Quantile Functions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 57-65, January.
    10. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    11. Seok-Oh Jeong & Byeong Park & Léopold Simar, 2010. "Nonparametric conditional efficiency measures: asymptotic properties," Annals of Operations Research, Springer, vol. 173(1), pages 105-122, January.
    12. Aragon, Y. & Daouia, A. & Thomas-Agnan, C., 2005. "Nonparametric Frontier Estimation: A Conditional Quantile-Based Approach," Econometric Theory, Cambridge University Press, vol. 21(2), pages 358-389, April.
    13. 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.
    14. Park, B.U. & Simar, L. & Weiner, Ch., 2000. "The Fdh Estimator For Productivity Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 16(6), pages 855-877, December.
    15. Abdelaati Daouia & Irène Gijbels, 2011. "Robustness and inference in nonparametric partial-frontier modeling," Post-Print hal-00796744, HAL.
    16. 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.
    17. Daouia, Abdelaati & Simar, Leopold, 2007. "Nonparametric efficiency analysis: A multivariate conditional quantile approach," Journal of Econometrics, Elsevier, vol. 140(2), pages 375-400, October.
    18. Cazals, Catherine & Florens, Jean-Pierre & Simar, Leopold, 2002. "Nonparametric frontier estimation: a robust approach," Journal of Econometrics, Elsevier, vol. 106(1), pages 1-25, January.
    19. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    20. 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.
    21. Cinzia Daraio & Léopold Simar, 2005. "Introducing Environmental Variables in Nonparametric Frontier Models: a Probabilistic Approach," Journal of Productivity Analysis, Springer, vol. 24(1), pages 93-121, September.
    22. Léopold Simar, 2003. "Detecting Outliers in Frontier Models: A Simple Approach," Journal of Productivity Analysis, Springer, vol. 20(3), pages 391-424, November.
    23. repec:hal:journl:peer-00796744 is not listed on IDEAS
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    More about this item

    Keywords

    Nonparametric frontier models ; Environmental factors ; Conditional efficiency ; Robust estimation of frontiers;
    All these keywords.

    JEL classification:

    • 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
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other

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