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Evaluating the CDF of the distribution of the stochastic frontier composed error

Author

Listed:
  • Christine Amsler

    (Michigan State University)

  • Peter Schmidt

    (Michigan State University)

  • Wen-Jen Tsay

    (Academia Sinica)

Abstract

In the stochastic frontier model, the composed error is the sum (or difference) of a normal and a half normal random variable. Often the composed error is linked to other errors using a copula, and evaluation of the copula requires evaluation of the cdf of the composed error. There is no analytical expression for this cdf, though there are several approximations. We propose a computationally efficient simulation based method of evaluation and use it to evaluate the accuracy of these approximations. We also derive the exact cdf of the composed error for the special case that the stochastic frontier relative variance parameter λ equals one, and we use this expression to investigate the accuracy of our evaluations and the existing approximations.

Suggested Citation

  • Christine Amsler & Peter Schmidt & Wen-Jen Tsay, 2019. "Evaluating the CDF of the distribution of the stochastic frontier composed error," Journal of Productivity Analysis, Springer, vol. 52(1), pages 29-35, December.
    • Handle: RePEc:kap:jproda:v:52:y:2019:i:1:d:10.1007_s11123-019-00554-9
    DOI: 10.1007/s11123-019-00554-9
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    References listed on IDEAS

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    1. Wei Wang & Christine Amsler & Peter Schmidt, 2011. "Goodness of fit tests in stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 35(2), pages 95-118, April.
    2. 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.
    3. 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.
    4. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. William Greene, 2010. "A stochastic frontier model with correction for sample selection," Journal of Productivity Analysis, Springer, vol. 34(1), pages 15-24, August.
    11. Genius, Margarita & Stefanou, Spiro E. & Tzouvelekas, Vangelis, 2012. "Measuring productivity growth under factor non-substitution: An application to US steam-electric power generation utilities," European Journal of Operational Research, Elsevier, vol. 220(3), pages 844-852.
    12. Arabinda Das, 2015. "Copula-based Stochastic Frontier Model with Autocorrelated Inefficiency," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 7(2), pages 111-126, June.
    13. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2017. "Endogenous environmental variables in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 199(2), pages 131-140.
    14. Tran, Kien C. & Tsionas, Efthymios G., 2015. "Endogeneity in stochastic frontier models: Copula approach without external instruments," Economics Letters, Elsevier, vol. 133(C), pages 85-88.
    15. 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.
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    Cited by:

    1. Simos G. Meintanis & Christos K. Papadimitriou, 2022. "Goodness--of--fit tests for stochastic frontier models based on the characteristic function," Journal of Productivity Analysis, Springer, vol. 57(3), pages 285-296, June.
    2. Justin Dang & Aman Ullah, 2023. "Generalized kernel regularized least squares estimator with parametric error covariance," Empirical Economics, Springer, vol. 64(6), pages 3059-3088, June.
    3. Shih-Tang Hwu & Tsu-Tan Fu & Wen-Jen Tsay, 2021. "Estimation and efficiency evaluation of stochastic frontier models with interval dependent variables," Journal of Productivity Analysis, Springer, vol. 56(1), pages 33-44, August.
    4. Christine Amsler & Alecos Papadopoulos & Peter Schmidt, 2021. "Evaluating the cdf of the Skew Normal distribution," Empirical Economics, Springer, vol. 60(6), pages 3171-3202, June.

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    More about this item

    Keywords

    Stochastic frontier; Composed error; Skew normal distribution;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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