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Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions

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  • Hung-pin Lai

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  • Cliff Huang

Abstract

In this paper, we propose the copula-based maximum likelihood (ML) approach to estimate the multiple stochastic frontier (SF) models with correlated composite errors. The motivation behind the extension to system of SF regressions is analogous to the classical generalization to system of seemingly unrelated regressions (Zellner in J Am Statist Assoc 57:348–368, 1962 ). A demonstration of the copula approach is provided via the analysis of a system of two SF regressions. The consequences of ignoring the correlation between the composite errors are examined by a Monte Carlo experiment. Our findings suggest that the stronger the correlation between the two SF regressions, the more estimation efficiency is lost in separate estimations. Estimation without considering the correlated composite errors may cause significantly efficiency loss in terms of mean squared errors in estimation of the SF technical efficiency. Finally, we also conduct an empirical study based on Taiwan hotel industry data, focusing on the SF regressions for the accommodation and restaurant divisions. Our results, which are consistent with the findings in simulation, show that joint estimation is significantly different from separate estimation without considering the correlated composite errors in the two divisions. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:40:y:2013:i:1:p:1-14
    DOI: 10.1007/s11123-012-0289-8
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    File URL: http://hdl.handle.net/10.1007/s11123-012-0289-8
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    References listed on IDEAS

    as
    1. William Greene, 2010. "A stochastic frontier model with correction for sample selection," Journal of Productivity Analysis, Springer, vol. 34(1), pages 15-24, August.
    2. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    3. 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.
    4. William Greene, 2003. "Simulated Likelihood Estimation of the Normal-Gamma Stochastic Frontier Function," Journal of Productivity Analysis, Springer, vol. 19(2), pages 179-190, April.
    5. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    6. Pitt, Mark M. & Lee, Lung-Fei, 1981. "The measurement and sources of technical inefficiency in the Indonesian weaving industry," Journal of Development Economics, Elsevier, vol. 9(1), pages 43-64, August.
    7. Wen-Jen Tsay & Cliff Huang & Tsu-Tan Fu & I.-Lin Ho, 2013. "A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 39(3), pages 259-269, June.
    8. Murray D. Smith, 2008. "Stochastic frontier models with dependent error components," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 172-192, March.
    9. Peng Shi & Wei Zhang, 2011. "A copula regression model for estimating firm efficiency in the insurance industry," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2271-2287.
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    Citations

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    Cited by:

    1. Graziella Bonanno & Domenico De Giovanni & Filippo Domma, 2017. "The ‘wrong skewness’ problem: a re-specification of stochastic frontiers," Journal of Productivity Analysis, Springer, vol. 47(1), pages 49-64, February.
    2. repec:eee:quaeco:v:67:y:2018:i:c:p:51-62 is not listed on IDEAS
    3. Huang, Tai-Hsin & Lin, Chung-I & Chen, Kuan-Chen, 2017. "Evaluating efficiencies of Chinese commercial banks in the context of stochastic multistage technologies," Pacific-Basin Finance Journal, Elsevier, vol. 41(C), pages 93-110.
    4. repec:spr:empeco:v:54:y:2018:i:2:d:10.1007_s00181-016-1216-z is not listed on IDEAS
    5. Hung-pin Lai, 2015. "Maximum likelihood estimation of the stochastic frontier model with endogenous switching or sample selection," Journal of Productivity Analysis, Springer, vol. 43(1), pages 105-117, February.
    6. repec:eee:quaeco:v:67:y:2018:i:c:p:362-375 is not listed on IDEAS
    7. repec:eee:quaeco:v:65:y:2017:i:c:p:212-226 is not listed on IDEAS
    8. 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, Publishing House "SINERGIA PRESS", vol. 34(2), pages 3-18.

    More about this item

    Keywords

    Maximum likelihood estimation; Copula; Seemingly unrelated stochastic frontier regressions; C3; C5; R3;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • R3 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Real Estate Markets, Spatial Production Analysis, and Firm Location

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