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The “wrong skewness” problem in stochastic frontier models: a new approach

Author

Listed:
  • Hafner, Christian

    () (Université catholique de Louvain, CORE, Belgium)

  • Manner, H.

    (University of Cologne)

  • Simar, L.

    () (Université catholique de Louvain, CORE, Belgium)

Abstract

Stochastic frontier models are widely used to measure, e.g., technical efficiencies of firms. The classical stochastic frontier model often suffers from the empirical artefact that the residuals of the production function may have a positive skewness, whereas a negative one is expected under the model, which leads to estimated full efficiencies of all firms. We propose a new approach to the problem by generaliz- ing the distribution used for the inefficiency variable. This generalized stochastic frontier model allows the sample data to have the wrong skewness while estimating well-defined and non-degenerate efficiency measures. We discuss the statistical properties of the model and we discuss a test for the symmetry of the error term (no inefficiency). We provide a simulation study to show that our model delivers estimators of efficiency with smaller bias than those of the classical model even if the population skewness has the correct sign. Finally, we apply the model to data of the U.S. textile industry for 1958-2005, and show that for a number of years our model suggests technical efficiencies well below the frontier, while the classical one estimates no inefficiency in those years.

Suggested Citation

  • Hafner, Christian & Manner, H. & Simar, L., 2015. "The “wrong skewness” problem in stochastic frontier models: a new approach," CORE Discussion Papers 2015014, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2015014
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    References listed on IDEAS

    as
    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.
    2. Eric J. Bartelsman & Wayne Gray, 1996. "The NBER Manufacturing Productivity Database," NBER Technical Working Papers 0205, National Bureau of Economic Research, Inc.
    3. Stevenson, Rodney E., 1980. "Likelihood functions for generalized stochastic frontier estimation," Journal of Econometrics, Elsevier, vol. 13(1), pages 57-66, May.
    4. Greene, William H., 1990. "A Gamma-distributed stochastic frontier model," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 141-163.
    5. Timo Kuosmanen & Mogens Fosgerau, 2009. "Neoclassical versus Frontier Production Models? Testing for the Skewness of Regression Residuals," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(2), pages 351-367, June.
    6. Waldman, Donald M., 1982. "A stationary point for the stochastic frontier likelihood," Journal of Econometrics, Elsevier, vol. 18(2), pages 275-279, February.
    7. Lee, Lung-Fei, 1993. "Asymptotic Distribution of the Maximum Likelihood Estimator for a Stochastic Frontier Function Model with a Singular Information Matrix," Econometric Theory, Cambridge University Press, vol. 9(03), pages 413-430, June.
    8. Olson, Jerome A. & Schmidt, Peter & Waldman, Donald M., 1980. "A Monte Carlo study of estimators of stochastic frontier production functions," Journal of Econometrics, Elsevier, vol. 13(1), pages 67-82, May.
    9. Carree, Martin A., 2002. "Technological inefficiency and the skewness of the error component in stochastic frontier analysis," Economics Letters, Elsevier, vol. 77(1), pages 101-107, September.
    10. 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.
    11. 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.
    12. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
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    More about this item

    Keywords

    Stochastic frontier model; production efficiency; skewness; testing symmetry preferences;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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