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Stochastic Frontier Analysis with Generalized Errors: inference, model comparison and averaging

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  • Kamil Makie{l}a
  • B{l}a.zej Mazur

Abstract

Contribution of this paper lies in the formulation and estimation of a generalized model for stochastic frontier analysis (SFA) that nests virtually all forms used and includes some that have not been considered so far. The model is based on the generalized t distribution for the observation error and the generalized beta distribution of the second kind for the inefficiency-related term. We use this general error structure framework for formal testing, to compare alternative specifications and to conduct model averaging. This allows us to deal with model specification uncertainty, which is one of the main unresolved issues in SFA, and to relax a number of potentially restrictive assumptions embedded within existing SF models. We also develop Bayesian inference methods that are less restrictive compared to the ones used so far and demonstrate feasible approximate alternatives based on maximum likelihood.

Suggested Citation

  • Kamil Makie{l}a & B{l}a.zej Mazur, 2020. "Stochastic Frontier Analysis with Generalized Errors: inference, model comparison and averaging," Papers 2003.07150, arXiv.org, revised Oct 2020.
  • Handle: RePEc:arx:papers:2003.07150
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    1. van den Broeck, Julien & Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1994. "Stochastic frontier models : A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 61(2), pages 273-303, April.
    2. Christian Ritter & Léopold Simar, 1997. "Pitfalls of Normal-Gamma Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 8(2), pages 167-182, May.
    3. Jean-Pierre Florens & Léopold Simar & Ingrid Van Keilegom, 2020. "Estimation of the Boundary of a Variable Observed With Symmetric Error," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 425-441, January.
    4. Makiela, Kamil & Ouattara, Bazoumana, 2018. "Foreign direct investment and economic growth: Exploring the transmission channels," Economic Modelling, Elsevier, vol. 72(C), pages 296-305.
    5. Griffin, J. E. & Steel, M. F. J., 2004. "Semiparametric Bayesian inference for stochastic frontier models," Journal of Econometrics, Elsevier, vol. 123(1), pages 121-152, November.
    6. Phill Wheat & Alexander D. Stead & William H. Greene, 2019. "Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England," Journal of Productivity Analysis, Springer, vol. 51(1), pages 21-38, February.
    7. Efthymios G. Tsionas, 2006. "Inference in dynamic stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 669-676, July.
    8. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    9. Jim Griffin & Mark Steel, 2007. "Bayesian stochastic frontier analysis using WinBUGS," Journal of Productivity Analysis, Springer, vol. 27(3), pages 163-176, June.
    10. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 1999. "The Components of Output Growth: A Stochastic Frontier Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 455-487, November.
    11. Koop, Gary & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian efficiency analysis through individual effects: Hospital cost frontiers," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 77-105.
    12. Jacek Osiewalski & Mark Steel, 1998. "Numerical Tools for the Bayesian Analysis of Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 10(1), pages 103-117, July.
    13. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
    14. Tata Subba Rao & Granville Tunnicliffe Wilson & Andrew Harvey & Rutger-Jan Lange, 2017. "Volatility Modeling with a Generalized t Distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(2), pages 175-190, March.
    15. Kamil Makiela and Jacek Osiewalski, 2018. "Cost Efficiency Analysis of Electricity Distribution," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4).
    16. Fried, Harold O. & Lovell, C. A. Knox & Schmidt, Shelton S. (ed.), 2008. "The Measurement of Productive Efficiency and Productivity Growth," OUP Catalogue, Oxford University Press, number 9780195183528.
    17. Efthymios G. Tsionas, 2002. "Stochastic frontier models with random coefficients," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 127-147.
    18. Oikawa, Koki, 2016. "A microfoundation for stochastic frontier analysis," Economics Letters, Elsevier, vol. 139(C), pages 15-17.
    19. Alexander D. Stead & Phill Wheat & William H. Greene, 2018. "Estimating Efficiency in the Presence of Extreme Outliers: A Logistic-Half Normal Stochastic Frontier Model with Application to Highway Maintenance Costs in England," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages 1-19, Springer.
    20. Mehdi Farsi & Massimo Filippini & William Greene, 2006. "Application Of Panel Data Models In Benchmarking Analysis Of The Electricity Distribution Sector," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 77(3), pages 271-290, September.
    21. J. Griffin & M. Steel, 2008. "Flexible mixture modelling of stochastic frontiers," Journal of Productivity Analysis, Springer, vol. 29(1), pages 33-50, February.
    22. 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.
    23. William C. Horrace & Christopher F. Parmeter, 2018. "A Laplace stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 37(3), pages 260-280, March.
    24. Gholamreza Hajargasht, 2015. "Stochastic frontiers with a Rayleigh distribution," Journal of Productivity Analysis, Springer, vol. 44(2), pages 199-208, October.
    25. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 2000. "Modeling the Sources of Output Growth in a Panel of Countries," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 284-299, July.
    26. Emmanuel Haven & Philip Molyneux & John O. S. Wilson & Sergei Fedotov & Meryem Duygun (ed.), 2016. "The Handbook of Post Crisis Financial Modeling," Palgrave Macmillan Books, Palgrave Macmillan, number 978-1-137-49449-8.
    27. Subal C. Kumbhakar & Gudbrand Lien, 2017. "Yardstick Regulation of Electricity Distribution Disentangling Short-run and Long-run Inefficiencies," The Energy Journal, International Association for Energy Economics, vol. 0(Number 5).
    28. Alexander D. Stead & Phill Wheat & William H. Greene, 2018. "Erratum to: Estimating Efficiency in the Presence of Extreme Outliers: A Logistic-Half Normal Stochastic Frontier Model with Application to Highway Maintenance Costs in England," Springer Proceedings in Business and Economics, in: William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), Productivity and Inequality, pages E1-E1, Springer.
    29. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    30. Gary Koop & Jacek Osiewalski & Mark F. J. Steel, 1999. "The Components of Output Growth: A Stochastic Frontier Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(4), pages 455-487, November.
    31. Kamil Makieła, 2017. "Bayesian Inference and Gibbs Sampling in Generalized True Random-Effects Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(1), pages 69-95, March.
    32. D J Mayston, 2003. "Measuring and managing educational performance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(7), pages 679-691, July.
    33. William H. Greene & Lynda Khalaf & Paul Makdissi & Robin C. Sickles & Michael Veall & Marcel-Cristia (ed.), 2018. "Productivity and Inequality," Springer Proceedings in Business and Economics, Springer, number 978-3-319-68678-3, February.
    34. 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.
    35. 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.
    36. Beckers, Dominique E. & Hammond, Christopher J., 1987. "A tractable likelihood function for the normal-gamma stochastic frontier model," Economics Letters, Elsevier, vol. 24(1), pages 33-38.
    37. Tsionas, Mike G., 2017. "Microfoundations for stochastic frontiers," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1165-1170.
    38. Parmeter, Christopher F. & Kumbhakar, Subal C., 2014. "Efficiency Analysis: A Primer on Recent Advances," Foundations and Trends(R) in Econometrics, now publishers, vol. 7(3-4), pages 191-385, December.
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    Cited by:

    1. Kamil Makieła & Błażej Mazur, 2020. "Bayesian Model Averaging and Prior Sensitivity in Stochastic Frontier Analysis," Econometrics, MDPI, vol. 8(2), pages 1-22, April.

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