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Analysis of dependence between the random components of a stochastic production function for the purpose of technical efficiency estimation

Author

Listed:
  • Aivazian, Sergei

    (CEMI RAS, Moscow, Russia)

  • Afanasiev, Mikhail

    (CEMI RAS, Moscow, Russia)

  • Rudenko, Victoria

    (Moscow Engineering Physics Institute (National Research Nuclear University), Russia)

Abstract

In elaboration of the stochastic frontier methodology we offer an approach to test a statistic hypothesis about independence of random components of a stochastic production function for the purpose of estimation of technical efficiency. We describe the dependence between the error components by a copula. For parameters estimation in the econometric model in case of dependent error components the analytical expressions for log-likelihood function and its derivatives are given. The results of an experimental hypothesis test based on simulated data with dependent error components are also provided. We use two approaches for the parameters estimation: statistical package Stata 10.0 under an assumption of independence of the error components and created in MS Excel macro which gives the possibility to analyze models with dependent error components. It is shown that using non-tested assumption of independence of the random components of a stochastic production function may lead to wrong results in estimation of the technical efficiency.

Suggested Citation

  • Aivazian, Sergei & Afanasiev, Mikhail & Rudenko, Victoria, 2014. "Analysis of dependence between the random components of a stochastic production function for the purpose of technical efficiency estimation," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 34(2), pages 3-18.
    • Handle: RePEc:ris:apltrx:0234
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    References listed on IDEAS

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    1. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    2. Christine Amsler & Artem Prokhorov & Peter Schmidt, 2014. "Using Copulas to Model Time Dependence in Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 497-522, August.
    3. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    4. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-396, June.
    5. Carta, Alessandro & Steel, Mark F.J., 2012. "Modelling multi-output stochastic frontiers using copulas," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3757-3773.
    6. Hung-pin Lai & Cliff Huang, 2013. "Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions," Journal of Productivity Analysis, Springer, vol. 40(1), pages 1-14, August.
    7. Murray D. Smith, 2008. "Stochastic frontier models with dependent error components," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 172-192, March.
    8. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
    9. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    10. Penikas, Henry & Simakova, Varvara, 2009. "Interest Rate Risk Management Based on Copula-GARCH Models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 13(1), pages 3-36.
    11. Blagoveschensky, Yury, 2012. "Basics of copula’s theory," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 26(2), pages 113-130.
    12. Aivazian, Sergei & Afanasiev, Mikhail & Rudenko, Victoria, 2012. "Some specification aspects for three-factor models of a company's production potential taking into account intellectual capital," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 27(3), pages 36-69.
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    Cited by:

    1. Nikolskiy, Ilya & Furmanov, Kirill, 2023. "Assessing the accuracy of efficiency rankings obtained from a stochastic frontier model," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 71, pages 128-142.

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    More about this item

    Keywords

    econometric model; production potential; production factors; intellectual capital; copula; normal copula; dependence of error components.;
    All these keywords.

    JEL classification:

    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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