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Quantile estimation of stochastic frontier models with the normal–half normal specification: A cumulative distribution function approach

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  • Zhao, Shirong
Abstract
In this paper, based on the cumulative distribution function (CDF) method (Jradi et al., 2021) for finding the optimal quantile when estimating stochastic frontier models (SFM) with normal–exponential composite error term, we derive an expression to find the optimal quantile for the SFM with normal–half normal composite error term. We then use Monte-Carlo simulations and the same data set as Jradi et al. (2019) to compare the difference of iteration method (Jradi et al., 2019) and CDF method for the SFM with normal–half normal specification. The simulations and empirical application illustrate that both methods work well.

Suggested Citation

  • Zhao, Shirong, 2021. "Quantile estimation of stochastic frontier models with the normal–half normal specification: A cumulative distribution function approach," Economics Letters, Elsevier, vol. 206(C).
    • Handle: RePEc:eee:ecolet:v:206:y:2021:i:c:s0165176521002755
    DOI: 10.1016/j.econlet.2021.109998
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    References listed on IDEAS

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    1. 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.
    2. Tsionas, Mike G. & Assaf, A. George & Andrikopoulos, Athanasios, 2020. "Quantile stochastic frontier models with endogeneity," Economics Letters, Elsevier, vol. 188(C).
    3. Jradi, Samah & Ruggiero, John, 2019. "Stochastic data envelopment analysis: A quantile regression approach to estimate the production frontier," European Journal of Operational Research, Elsevier, vol. 278(2), pages 385-393.
    4. Jradi, Samah & Parmeter, Christopher F. & Ruggiero, John, 2019. "Quantile estimation of the stochastic frontier model," Economics Letters, Elsevier, vol. 182(C), pages 15-18.
    5. 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.
    6. 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.
    7. 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.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Timothy J. Coelli & D.S. Prasada Rao & Christopher J. O’Donnell & George E. Battese, 2005. "An Introduction to Efficiency and Productivity Analysis," Springer Books, Springer, edition 0, number 978-0-387-25895-9, December.
    10. 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.
    11. Tsionas, Mike G., 2020. "Quantile Stochastic Frontiers," European Journal of Operational Research, Elsevier, vol. 282(3), pages 1177-1184.
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Dai, Sheng & Kuosmanen, Timo & Zhou, Xun, 2023. "Non-crossing convex quantile regression," Economics Letters, Elsevier, vol. 233(C).
    4. 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.
    5. 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.

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    More about this item

    Keywords

    Stochastic frontier models; Quantile regressions; Skewed normal distribution; Efficiency;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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