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Normal-beta exponential stochastic frontier model: Maximum simulated likelihood approach

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  • Misgan Desale Nigusie

    (Bahir Dar University
    Lund University)

Abstract

This paper considers the beta exponential distribution as a distribution function of inefficacy score in a stochastic frontier model. The beta exponential distribution is a three-parameter distribution, and it is more flexible than commonly used probability density functions in a stochastic frontier model (SFM). This new model, a “Normal-Beta Exponential SFM”, nests another five SFMs. This paper presents a simulated log-likelihood function and simulated inefficiency estimator of a normal-beta exponential SFM, a closed form log-likelihood function and closed form inefficiency estimator of a normal-weighted exponential SFM, and an empirical study using a normal-beta exponential SFM. In our empirical study, we have used a likelihood ratio test to compare the performance of SFMs and a normal-beta exponential SFM fits the data better than other nested special case SFMs. Furthermore, the empirical result shows that parameters of a normal-beta exponential SFM can be estimated with less standard error or high certainty than a normal-gamma SFM.

Suggested Citation

  • Misgan Desale Nigusie, 2024. "Normal-beta exponential stochastic frontier model: Maximum simulated likelihood approach," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 23(3), pages 489-504, September.
    • Handle: RePEc:spr:portec:v:23:y:2024:i:3:d:10.1007_s10258-023-00247-0
    DOI: 10.1007/s10258-023-00247-0
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    References listed on IDEAS

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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. William Greene, 2003. "Simulated Likelihood Estimation of the Normal-Gamma Stochastic Frontier Function," Journal of Productivity Analysis, Springer, vol. 19(2), pages 179-190, April.
    3. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    4. M. Jones, 2004. "Families of distributions arising from distributions of order statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 1-43, June.
    5. Alecos Papadopoulos, 2021. "Stochastic frontier models using the Generalized Exponential distribution," Journal of Productivity Analysis, Springer, vol. 55(1), pages 15-29, February.
    6. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
    7. Hung-pin Lai & Cliff Huang, 2010. "Likelihood ratio tests for model selection of stochastic frontier models," Journal of Productivity Analysis, Springer, vol. 34(1), pages 3-13, August.
    8. Geweke, John F. & Keane, Michael P. & Runkle, David E., 1997. "Statistical inference in the multinomial multiperiod probit model," Journal of Econometrics, Elsevier, vol. 80(1), pages 125-165, September.
    9. J. Griffin & M. Steel, 2008. "Flexible mixture modelling of stochastic frontiers," Journal of Productivity Analysis, Springer, vol. 29(1), pages 33-50, February.
    10. Gholamreza Hajargasht, 2015. "Stochastic frontiers with a Rayleigh distribution," Journal of Productivity Analysis, Springer, vol. 44(2), pages 199-208, October.
    11. 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.
    12. 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.
    13. 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.
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    More about this item

    Keywords

    Beta exponential distribution; Stochastic frontier model; Simulated likelihood; Halton sequences;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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