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Robust stochastic frontier analysis: a Student’s t-half normal model with application to highway maintenance costs in England

Author

Listed:
  • Phill Wheat

    (University of Leeds)

  • Alexander D. Stead

    (University of Leeds)

  • William H. Greene

    (New York University)

Abstract

The presence of outliers in the data has implications for stochastic frontier analysis, and indeed any performance analysis methodology, because they may lead to imprecise parameter estimates and, crucially, lead to an exaggerated spread of efficiency predictions. In this paper we replace the normal distribution for the noise term in the standard stochastic frontier model with a Student’s t distribution, which generalises the normal distribution by adding a shape parameter governing the degree of kurtosis. This has the advantages of introducing flexibility in the heaviness of the tails, which can be determined by the data, as well as containing the normal distribution as a limiting case, and we outline how to test against the standard model. Monte Carlo simulation results for the maximum simulated likelihood estimator confirm that the model recovers appropriate frontier and distributional parameter estimates under various values of the true shape parameter. The simulation results also indicate the influence of a phenomenon we term ‘wrong kurtosis’ in the case of small samples, which is analogous to the issue of ‘wrong skewness’ previously identified in the literature. We apply a Student’s t-half normal cost frontier to data for highways authorities in England, and this formulation is found to be preferred by statistical testing to the comparator normal-half normal cost frontier model. The model yields a significantly narrower range of efficiency predictions, which are non-monotonic at the tails of the residual distribution.

Suggested Citation

  • 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.
  • Handle: RePEc:kap:jproda:v:51:y:2019:i:1:d:10.1007_s11123-018-0541-y
    DOI: 10.1007/s11123-018-0541-y
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    4. Parmeter, Christopher F., 2021. "Is it MOLS or COLS?," Efficiency Series Papers 2021/04, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
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    6. 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.
    7. 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.
    8. Subal C. Kumbhakar & Mike G. Tsionas, 2021. "Estimation of costs of technical and allocative inefficiency," Journal of Productivity Analysis, Springer, vol. 55(1), pages 41-46, February.
    9. Badunenko, Oleg & Henderson, Daniel J., 2021. "Production Analysis with Asymmetric Noise," MPRA Paper 110888, University Library of Munich, Germany.
    10. 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.
    11. Jradi, Samah & Parmeter, Christopher F. & Ruggiero, John, 2021. "Quantile estimation of stochastic frontiers with the normal-exponential specification," European Journal of Operational Research, Elsevier, vol. 295(2), pages 475-483.
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