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Maximum likelihood estimation of seemingly unrelated stochastic frontier regressions

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  • Hung-pin Lai
  • 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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    References listed on IDEAS

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    1. 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.
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    9. Wang, Hung-Jen & Ho, Chia-Wen, 2010. "Estimating fixed-effect panel stochastic frontier models by model transformation," Journal of Econometrics, Elsevier, vol. 157(2), pages 286-296, August.
    10. 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.
    11. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    12. Manoranjan Pal, 2004. "A Note on a Unified Approach to the Frontier Production Function Models With Correlated Non-Normal Error Components: The Case of Cross Section Data," Indian Economic Review, Department of Economics, Delhi School of Economics, vol. 39(1), pages 7-18, January.
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    2. Kexin Li & Jianxu Liu & Yuting Xue & Sanzidur Rahman & Songsak Sriboonchitta, 2022. "Consequences of Ignoring Dependent Error Components and Heterogeneity in a Stochastic Frontier Model: An Application to Rice Producers in Northern Thailand," Agriculture, MDPI, vol. 12(8), pages 1-17, July.
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    4. Tai-Hsin Huang & Nan-Hung Liu & Subal C. Kumbhakar, 2018. "Joint estimation of the Lerner index and cost efficiency using copula methods," Empirical Economics, Springer, vol. 54(2), pages 799-822, March.
    5. Hung-pin Lai, 2021. "Maximum simulated likelihood estimation of the seemingly unrelated stochastic frontier regressions," Empirical Economics, Springer, vol. 60(6), pages 2943-2968, June.
    6. 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.
    7. Huang, Tai-Hsin & Lin, Chung-I & Wu, Ruei-Cian, 2019. "Assessing the marketing and investment efficiency of Taiwan’s life insurance firms under network structures," The Quarterly Review of Economics and Finance, Elsevier, vol. 71(C), pages 132-147.
    8. Tai-Hsin Huang & Yi-Huang Chiu & Chih-Ying Mao, 2021. "Imposing Regularity Conditions to Measure Banks’ Productivity Changes in Taiwan Using a Stochastic Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 28(2), pages 273-303, June.
    9. Orea, Luis & Álvarez, Inmaculada C. & Wall, Alan, 2021. "Estimating the propagation of the COVID-19 virus with a stochastic frontier approximation of epidemiological models: a panel data econometric model with an application to Spain," Efficiency Series Papers 2021/01, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    10. Schmidt, Rouven & Kneib, Thomas, 2023. "Multivariate distributional stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    11. Hung-pin Lai & Meng-Chi Tang, 2018. "Hospital efficiency under global budgeting: evidence from Taiwan," Empirical Economics, Springer, vol. 55(3), pages 937-963, November.
    12. 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.
    13. 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.
    14. Tai-Hsin Huang & Yi-Chun Lin & Kuo-Jui Huang & Yu-Wei Liao, 2022. "Comparing Cost Efficiency Between Financial and Non-financial Holding Banks and Insurers in Taiwan Under the Framework of Copula Methods and Metafrontier," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(4), pages 735-766, December.
    15. Jianxu Liu & Mengjiao Wang & Ji Ma & Sanzidur Rahman & Songsak Sriboonchitta, 2020. "A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry," Mathematics, MDPI, vol. 8(2), pages 1-23, February.
    16. Arabinda Das, 2021. "Copula-based Stochastic Cost Frontier with Correlated Technical and Allocative Inefficiency," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(2), pages 207-222, June.
    17. Huang, Tai-Hsin & Chen, Kuan-Chen & Lin, Chung-I, 2018. "An extension from network DEA to copula-based network SFA: Evidence from the U.S. commercial banks in 2009," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 51-62.
    18. Huang, Tai-Hsin & Hu, Chu-Nan & Chang, Bao-Guang, 2018. "Competition, efficiency, and innovation in Taiwan’s banking industry — An application of copula methods," The Quarterly Review of Economics and Finance, Elsevier, vol. 67(C), pages 362-375.
    19. Huang, Tai-Hsin & Chiang, Dien-Lin & Chao, Shih-Wei, 2017. "A new approach to jointly estimating the Lerner index and cost efficiency for multi-output banks under a stochastic meta-frontier framework," The Quarterly Review of Economics and Finance, Elsevier, vol. 65(C), pages 212-226.
    20. Inmaculada C. Álvarez & Luis Orea & Alan Wall, 2023. "Estimating the propagation of both reported and undocumented COVID-19 cases in Spain: a panel data frontier approximation of epidemiological models," Journal of Productivity Analysis, Springer, vol. 59(3), pages 259-279, June.

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    More about this item

    Keywords

    Maximum likelihood estimation; Copula; Seemingly unrelated stochastic frontier regressions; C3; C5; R3;
    All these keywords.

    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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