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Stationary Points for Parametric Stochastic Frontier Models

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Abstract

The results of Waldman (1982) on the Normal-Half Normal stochastic frontier model are generalized using the theory of the Dirac delta (Dirac, 1930), and distribution-free conditions are established to ensure a stationary point in the likelihood as the variance of the inefficiency distribution goes to zero. Stability of the stationary point and "wrong skew" results are derived or simulated for common parametric assumptions on the model. Identification is discussed.

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  • William C. Horrace & Ian A. Wright, 2016. "Stationary Points for Parametric Stochastic Frontier Models," Center for Policy Research Working Papers 196, Center for Policy Research, Maxwell School, Syracuse University.
    • Handle: RePEc:max:cprwps:196
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    File URL: https://surface.syr.edu/cpr/228/
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    1. Christian Ritter & Léopold Simar, 1997. "Pitfalls of Normal-Gamma Stochastic Frontier Models," Journal of Productivity Analysis, Springer, vol. 8(2), pages 167-182, May.
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    14. Jondrow, James & Knox Lovell, C. A. & Materov, Ivan S. & Schmidt, Peter, 1982. "On the estimation of technical inefficiency in the stochastic frontier production function model," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 233-238, August.
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    16. Robin C. Sickles & William C. Horrace (ed.), 2014. "Festschrift in Honor of Peter Schmidt," Springer Books, Springer, edition 127, number 978-1-4899-8008-3, January.
    17. Qu Feng & William Horrace & Guiying Laura Wu, 2013. "Wrong Skewness and Finite Sample Correction in Parametric Stochastic Frontier Models Abstract: In parametric stochastic frontier models, the composed error is specified as the sum of a two-sided noise," Center for Policy Research Working Papers 154, Center for Policy Research, Maxwell School, Syracuse University.
    18. 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.
    19. 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.
    20. William Horrace, 2015. "Moments of the truncated normal distribution," Journal of Productivity Analysis, Springer, vol. 43(2), pages 133-138, April.
    21. Kobayashi, Masahito, 1991. "Testing for Autocorrelated Disturbances in Nonlinear Regression Analysis," Econometrica, Econometric Society, vol. 59(4), pages 1153-1159, July.
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    Cited by:

    1. 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.
    2. Christopher F. Parmeter & Léopold Simar & Ingrid Van Keilegom & Valentin Zelenyuk, 2024. "Inference in the nonparametric stochastic frontier model," Econometric Reviews, Taylor & Francis Journals, vol. 43(7), pages 518-539, August.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. Zangin Zeebari & Kristofer Månsson & Pär Sjölander & Magnus Söderberg, 2023. "Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market," Journal of Productivity Analysis, Springer, vol. 59(1), pages 79-97, February.
    8. 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.
    9. Tsionas, Mike G., 2021. "Optimal combinations of stochastic frontier and data envelopment analysis models," European Journal of Operational Research, Elsevier, vol. 294(2), pages 790-800.
    10. 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.
    11. William C. Horrace & Christopher F. Parmeter & Ian A. Wright, 2024. "On asymmetry and quantile estimation of the stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 61(1), pages 19-36, February.
    12. 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.
    13. Parmeter, Christopher F. & Simar, Léopold & Van Keilegom, Ingrid & Zelenyuk, Valentin, 2024. "Inference in the nonparametric stochastic frontier model," LIDAM Reprints ISBA 2024013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

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    Keywords

    Neighborhood Effects; Crime; Academic Performance; Racial Disparities; Educational Outcomes;
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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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