IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v52y2019i1d10.1007_s11123-019-00554-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11123-019-00554-9
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11123-019-00554-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    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. 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. 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.
    6. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2017. "Endogenous environmental variables in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 199(2), pages 131-140.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. 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.
    4. Schmidt, Rouven & Kneib, Thomas, 2023. "Multivariate distributional stochastic frontier models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    5. 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.
    6. 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.
    7. Mamonov Mikhail E. & Parmeter Christopher F. & Prokhorov Artem B., 2022. "Dependence modeling in stochastic frontier analysis," Dependence Modeling, De Gruyter, vol. 10(1), pages 123-144, January.
    8. 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.
    9. 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.
    10. Orea, Luis, 2019. "The Econometric Measurement of Firms’ Efficiency," Efficiency Series Papers 2019/02, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    11. Martini, Gianmaria & Scotti, Davide & Viola, Domenico & Vittadini, Giorgio, 2020. "Persistent and temporary inefficiency in airport cost function: An application to Italy," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 999-1019.
    12. Alexandre Repkine, 2023. "The Estimation of a Polluting By-Production Technology Using Statistical Copulas," Journal of Productivity Analysis, Springer, vol. 60(1), pages 49-62, August.
    13. Mustafa U. Karakaplan & Levent Kutlu, 2019. "School district consolidation policies: endogenous cost inefficiency and saving reversals," Empirical Economics, Springer, vol. 56(5), pages 1729-1768, May.
    14. 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.
    15. 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.
    16. 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.
    17. Levent Kutlu & Ran Wang, 2018. "Estimation of cost efficiency without cost data," Journal of Productivity Analysis, Springer, vol. 49(2), pages 137-151, June.
    18. 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.
    19. Subal C. Kumbhakar & Christopher F. Parmeter & Valentin Zelenyuk, 2022. "Stochastic Frontier Analysis: Foundations and Advances I," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 8, pages 331-370, Springer.
    20. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jproda:v:52:y:2019:i:1:d:10.1007_s11123-019-00554-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.