IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v61y2024i2d10.1007_s11123-023-00708-w.html
   My bibliography  Save this article

The wrong skewness problem in stochastic frontier analysis: a review

Author

Listed:
  • Alecos Papadopoulos

    (Athens University of Economics and Business)

  • Christopher F. Parmeter

    (University of Miami)

Abstract

We provide a review of the literature related to the “wrong skewness problem” in stochastic frontier analysis. We identify two distinct approaches, one treating the phenomenon as a signal from the data that the underlying structure has some special characteristics that allow inefficiency to co-exist with “wrong” skewness, the other treating it as a sample-failure problem. Each leads to different treatments, while siding with either raises certain methodological issues, and we explore them. We offer simulation evidence that the wrong skewness as a sample problem likely comes from how the noise component of the composite error term has been realized in the sample, which points towards a new way to handle the problem. We also investigate the issues that arise when attempting to use the unconstrained Normal-Half Normal (Skew Normal) likelihood.

Suggested Citation

  • Alecos Papadopoulos & Christopher F. Parmeter, 2024. "The wrong skewness problem in stochastic frontier analysis: a review," Journal of Productivity Analysis, Springer, vol. 61(2), pages 121-134, April.
    • Handle: RePEc:kap:jproda:v:61:y:2024:i:2:d:10.1007_s11123-023-00708-w
    DOI: 10.1007/s11123-023-00708-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11123-023-00708-w
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11123-023-00708-w?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. El Mehdi, Rachida & Hafner, Christian M., 2014. "Inference in stochastic frontier analysis with dependent error terms," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 102(C), pages 104-116.
    2. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
    3. Tsionas, Mike G. & Assaf, A. George & Andrikopoulos, Athanasios, 2020. "Quantile stochastic frontier models with endogeneity," Economics Letters, Elsevier, vol. 188(C).
    4. Massimo Filippini & Lester C. Hunt, 2011. "Energy Demand and Energy Efficiency in the OECD Countries: A Stochastic Demand Frontier Approach," The Energy Journal, , vol. 32(2), pages 59-80, April.
    5. Mester, Loretta J., 1997. "Measuring efficiency at U.S. banks: Accounting for heterogeneity is important," European Journal of Operational Research, Elsevier, vol. 98(2), pages 230-242, April.
    6. Yulia V. Marchenko & Marc G. Genton, 2010. "A suite of commands for fitting the skew-normal and skew-t models," Stata Journal, StataCorp LP, vol. 10(4), pages 507-539, December.
    7. Graziella Bonanno & Filippo Domma, 2022. "Analytical Derivations of New Specifications for Stochastic Frontiers with Applications," Mathematics, MDPI, vol. 10(20), pages 1-17, October.
    8. Alecos Papadopoulos & Christopher F. Parmeter, 2022. "Quantile Methods for Stochastic Frontier Analysis," Foundations and Trends(R) in Econometrics, now publishers, vol. 12(1), pages 1-120, November.
    9. Jun Cai & Qu Feng & William C. Horrace & Guiying Laura Wu, 2021. "Wrong skewness and finite sample correction in the normal-half normal stochastic frontier model," Empirical Economics, Springer, vol. 60(6), pages 2837-2866, June.
    10. Seunghwa Rho & Peter Schmidt, 2015. "Are all firms inefficient?," Journal of Productivity Analysis, Springer, vol. 43(3), pages 327-349, June.
    11. Leamer, Edward E., 1983. "Model choice and specification analysis," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 5, pages 285-330, Elsevier.
    12. Timo Kuosmanen & Mogens Fosgerau, 2009. "Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(2), pages 351-367, June.
    13. Murray D. Smith, 2008. "Stochastic frontier models with dependent error components," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 172-192, March.
    14. J. Griffin & M. Steel, 2008. "Flexible mixture modelling of stochastic frontiers," Journal of Productivity Analysis, Springer, vol. 29(1), pages 33-50, February.
    15. Efthymios G. Tsionas, 2007. "Efficiency Measurement with the Weibull Stochastic Frontier," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 69(5), pages 693-706, October.
    16. William C. Horrace & Ian A. Wright, 2020. "Stationary Points for Parametric Stochastic Frontier Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 516-526, July.
    17. Wang, Hung-Jen, 2003. "A Stochastic Frontier Analysis of Financing Constraints on Investment: The Case of Financial Liberalization in Taiwan," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 406-419, July.
    18. Alecos Papadopoulos, 2023. "The noise error component in stochastic frontier analysis," Empirical Economics, Springer, vol. 64(6), pages 2795-2829, June.
    19. Waldman, Donald M., 1982. "A stationary point for the stochastic frontier likelihood," Journal of Econometrics, Elsevier, vol. 18(2), pages 275-279, February.
    20. Richard E. Caves, 1992. "Industrial Efficiency in Six Nations," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262031930, December.
    21. Boris Bravo-Ureta & Daniel Solís & Víctor Moreira López & José Maripani & Abdourahmane Thiam & Teodoro Rivas, 2007. "Technical efficiency in farming: a meta-regression analysis," Journal of Productivity Analysis, Springer, vol. 27(1), pages 57-72, February.
    22. Lee, Lung-Fei, 1993. "Asymptotic Distribution of the Maximum Likelihood Estimator for a Stochastic Frontier Function Model with a Singular Information Matrix," Econometric Theory, Cambridge University Press, vol. 9(3), pages 413-430, June.
    23. Christopher F. Parmeter & Shirong Zhao, 2023. "An alternative corrected ordinary least squares estimator for the stochastic frontier model," Empirical Economics, Springer, vol. 64(6), pages 2831-2857, June.
    24. Cheol-Keun Cho & Peter Schmidt, 2020. "The wrong skew problem in stochastic frontier models when inefficiency depends on environmental variables," Empirical Economics, Springer, vol. 58(5), pages 2031-2047, May.
    25. Olson, Jerome A. & Schmidt, Peter & Waldman, Donald M., 1980. "A Monte Carlo study of estimators of stochastic frontier production functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 67-82, May.
    26. Alecos Papadopoulos, 2021. "Measuring the effect of management on production: a two-tier stochastic frontier approach," Empirical Economics, Springer, vol. 60(6), pages 3011-3041, June.
    27. Carree, Martin A., 2002. "Technological inefficiency and the skewness of the error component in stochastic frontier analysis," Economics Letters, Elsevier, vol. 77(1), pages 101-107, September.
    28. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    29. 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.
    30. Luis Orea, 2012. "Entry deterrence through regional regulation and strict licensing policy: an analysis of the large retail establishments in Spain," Oxford Economic Papers, Oxford University Press, vol. 64(3), pages 539-562, July.
    31. Monica Chiogna, 2005. "A note on the asymptotic distribution of the maximum likelihood estimator for the scalar skew-normal distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 14(3), pages 331-341, December.
    Full references (including those not matched with items on IDEAS)

    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. E. Fusco & R. Benedetti & F. Vidoli, 2023. "Stochastic frontier estimation through parametric modelling of quantile regression coefficients," Empirical Economics, Springer, vol. 64(2), pages 869-896, February.
    2. 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.
    3. Papadopoulos, Alecos & Parmeter, Christopher F., 2021. "Type II failure and specification testing in the Stochastic Frontier Model," European Journal of Operational Research, Elsevier, vol. 293(3), pages 990-1001.
    4. William C. Horrace & Yulong Wang, 2022. "Nonparametric tests of tail behavior in stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 537-562, April.
    5. Christian M. Hafner & Hans Manner & Léopold Simar, 2018. "The “wrong skewness” problem in stochastic frontier models: A new approach," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 380-400, April.
    6. 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.
    7. Jun Cai & Qu Feng & William C. Horrace & Guiying Laura Wu, 2021. "Wrong skewness and finite sample correction in the normal-half normal stochastic frontier model," Empirical Economics, Springer, vol. 60(6), pages 2837-2866, June.
    8. William C. Horrace & Christopher F. Parmeter, 2018. "A Laplace stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 37(3), pages 260-280, March.
    9. Cheol-Keun Cho & Peter Schmidt, 2020. "The wrong skew problem in stochastic frontier models when inefficiency depends on environmental variables," Empirical Economics, Springer, vol. 58(5), pages 2031-2047, May.
    10. Zhao, Shirong & Parmeter, Christopher F., 2022. "The “wrong skewness” problem: Moment constrained maximum likelihood estimation of the stochastic frontier model," Economics Letters, Elsevier, vol. 221(C).
    11. Deng, Yaguo, 2024. "A Bayesian semi-parametric approach to stochastic frontier models with inefficiency heterogeneity," DES - Working Papers. Statistics and Econometrics. WS 43837, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Shirong Zhao & Jeremy Losak, 2024. "Two-tiered stochastic frontier models: a Bayesian perspective," Journal of Productivity Analysis, Springer, vol. 61(2), pages 85-106, April.
    13. Hafner, Christian & Manner, Hans & Simar, Leopold, 2013. "The “wrong skewnessâ€Ω problem in stochastic frontier models: A new approach," LIDAM Discussion Papers ISBA 2013046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Alecos Papadopoulos, 2023. "The noise error component in stochastic frontier analysis," Empirical Economics, Springer, vol. 64(6), pages 2795-2829, June.
    15. Rouven E. Haschka, 2024. "Endogeneity in stochastic frontier models with 'wrong' skewness: copula approach without external instruments," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 33(3), pages 807-826, July.
    16. Christopher F. Parmeter & Shirong Zhao, 2023. "An alternative corrected ordinary least squares estimator for the stochastic frontier model," Empirical Economics, Springer, vol. 64(6), pages 2831-2857, June.
    17. Adugna Lemi & Ian Wright, 2020. "Exports, foreign ownership, and firm-level efficiency in Ethiopia and Kenya: an application of the stochastic frontier model," Empirical Economics, Springer, vol. 58(2), pages 669-698, February.
    18. Stead, Alexander D. & Wheat, Phill & Greene, William H., 2023. "Robust maximum likelihood estimation of stochastic frontier models," European Journal of Operational Research, Elsevier, vol. 309(1), pages 188-201.
    19. Mark Andor & Christopher Parmeter, 2017. "Pseudolikelihood estimation of the stochastic frontier model," Applied Economics, Taylor & Francis Journals, vol. 49(55), pages 5651-5661, November.
    20. Alexander D. Stead & Phill Wheat & William H. Greene, 2023. "On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model," Journal of Productivity Analysis, Springer, vol. 60(1), pages 37-48, August.

    More about this item

    Keywords

    Stochastic frontier; Wrong skewness; Non-representative sample; Skew Normal; Data mining; Singular Information matrix;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

    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:61:y:2024:i:2:d:10.1007_s11123-023-00708-w. 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.