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Nonparametric Least Squares Methods for Stochastic Frontier Models

Author

Listed:
  • Leopold Simar

    () (Institut de statistique, biostatistique et sciences actuarielles, Universite catholique de Louvain)

  • Ingrid Van Keilegom

    () (Institut de statistique, biostatistique et sciences actuarielles, Universite catholique de Louvain)

  • Valentin Zelenyuk

    () (School of Economics, The University of Queensland)

Abstract

When analyzing productivity and efficiency of firms, stochastic frontier models are very attractive because they allow, as in typical regression models, to introduce some noise in the Data Generating Process. Most of the approaches so far have been using very restrictive fully parametric specified models, both for the frontier function and for the components of the stochastic terms. Recently, local MLE approaches were introduced to relax these parametric hypotheses. However, the high computational complexity of the latter makes them difficult to use, in particular if bootstrap-based inference is needed. In this work we show that most of the benefits of the local MLE approach can be obtained with less assumptions and involving much easier, faster and numerically more robust computations, by using nonparametric least-squares methods. Our approach can also be viewed as a semi-parametric generalization of the so-called “modified OLS†that was introduced in the parametric setup. If the final evaluation of individual efficiencies requires, as in the local MLE approach, the local specification of the distributions of noise and inefficiencies, it is shown that a lot can be learned on the production process without such specifications. Even elasticities of the mean inefficiency can be analyzed with unspecified noise distribution and a general class of local one-parameter scale family for inefficiencies. This allows to discuss the variation in inefficiency levels with respect to explanatory variables with minimal assumptions on the Data Generating Process. Our method is illustrated and compared with other methods with a real data set.

Suggested Citation

  • Leopold Simar & Ingrid Van Keilegom & Valentin Zelenyuk, 2014. "Nonparametric Least Squares Methods for Stochastic Frontier Models," CEPA Working Papers Series WP032014, School of Economics, University of Queensland, Australia.
  • Handle: RePEc:qld:uqcepa:94
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    File URL: https://economics.uq.edu.au/files/5133/WP032014.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Xu Guo & Gao-Rong Li & Michael McAleer & Wing-Keung Wong, 2018. "Specification Testing of Production in a Stochastic Frontier Model," Sustainability, MDPI, Open Access Journal, vol. 10(9), pages 1-10, August.
    2. repec:kap:jproda:v:47:y:2017:i:3:d:10.1007_s11123-016-0479-x is not listed on IDEAS
    3. Xu Guo & Tao Wang & Lixing Zhu, 2016. "Model checking for parametric single-index models: a dimension reduction model-adaptive approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1013-1035, November.
    4. repec:eee:ejores:v:265:y:2018:i:2:p:748-764 is not listed on IDEAS
    5. 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.
    6. Christopher F. Parmeter & Valentin Zelenyuk, 2016. "A Bridge Too Far? The State of the Art in Combining the Virtues of Stochastic Frontier Analysis and Data Envelopement Analysis," Working Papers 2016-10, University of Miami, Department of Economics.
    7. Guo, Xu & Li, Gao Rong & Wong, Wing Keung, 2014. "Specification Testing of Production Frontier Function in Stochastic Frontier Model," MPRA Paper 57999, University Library of Munich, Germany.

    More about this item

    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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