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Asymptotic Distribution of the Maximum Likelihood Estimator for Stochastic Frontier Function Model with a Singular Information Matrix

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  • Lee, L.F.

Abstract

This paper investigates the asymptotic distribution of the maximum likelihood estimator in a stochastic frontier function when the firms are all technically efficient. For such a situation the true parameter vector is on the boundary of the parameter space, and the scores are linearly dependent. The asymptotic distribution of the maximum likelihood estimator is shown to be a mixture of certain truncated distributions. The maximum likelihood estimates for different parameters may have different rates of stochastic convergence. The model can be reparameterized into one with a regular likelihood function. The likelihood ratio test statistic has the usual mixture of chi-square distributions as in the regular case.
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Suggested Citation

  • Lee, L.F., 1992. "Asymptotic Distribution of the Maximum Likelihood Estimator for Stochastic Frontier Function Model with a Singular Information Matrix," Papers 92-01, Michigan - Center for Research on Economic & Social Theory.
    • Handle: RePEc:fth:michet:92-01
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    Cited by:

    1. Centorrino, Samuele & Pérez-Urdiales, María, 2023. "Maximum likelihood estimation of stochastic frontier models with endogeneity," Journal of Econometrics, Elsevier, vol. 234(1), pages 82-105.
    2. Christian M. Hafner & Hans Manner & Léopold Simar, 2018. "The “wrong skewness” problem in stochastic frontier models: A new approach," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 380-400, April.
    3. Daniel , Betty C & Hafner, Christian & Manner, Hans & Simar, Leopold, 2011. "Asymmetries in Business Cycles and the Role of Oil Production," LIDAM Discussion Papers ISBA 2011032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Kumbhakar, Subal C. & Parmeter, Christopher F. & Tsionas, Efthymios G., 2013. "A zero inefficiency stochastic frontier model," Journal of Econometrics, Elsevier, vol. 172(1), pages 66-76.
    5. Liu, Ming & Zhang, Harold H., 1998. "Overparameterization in the seminonparametric density estimation," Economics Letters, Elsevier, vol. 60(1), pages 11-18, July.
    6. Daniel, Betty C. & Hafner, Christian M. & Simar, Léopold & Manner, Hans, 2019. "Asymmetries In Business Cycles And The Role Of Oil Prices," Macroeconomic Dynamics, Cambridge University Press, vol. 23(4), pages 1622-1648, June.
    7. 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.
    8. Fei Jin & Lung-fei Lee, 2020. "Asymptotic properties of a spatial autoregressive stochastic frontier model," Journal of Spatial Econometrics, Springer, vol. 1(1), pages 1-40, December.
    9. Prosper Dovonon & Alastair Hall & Frank Kleibergen, 2018. "Inference in Second-Order Identified Models," CIRANO Working Papers 2018s-36, CIRANO.
    10. George Karabatsos, 2023. "Approximate Bayesian computation using asymptotically normal point estimates," Computational Statistics, Springer, vol. 38(2), pages 531-568, June.
    11. Samuele Centorrino & María Pérez‐Urdiales & Boris Bravo‐Ureta & Alan Wall, 2024. "Binary endogenous treatment in stochastic frontier models with an application to soil conservation in El Salvador," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 365-382, April.
    12. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    13. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    14. Hafner, Christian & Manner, Hans & Simar, Leopold, 2013. "The “wrong skewnessâ€Ω problem in stochastic frontier models: A new approach," LIDAM Discussion Papers ISBA 2013046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    15. C. Lovell & Shawna Grosskopf & Eduardo Ley & Jesús Pastor & Diego Prior & Philippe Eeckaut, 1994. "Linear programming approaches to the measurement and analysis of productive efficiency," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 2(2), pages 175-248, December.
    16. Philip M. Bodman, 1999. "Labour Market Inefficiency and Frictional Unemployment in Australia and its States: A Stochastic Frontier Approach," The Economic Record, The Economic Society of Australia, vol. 75(2), pages 138-148, June.
    17. Dovonon, Prosper & Hall, Alastair R. & Kleibergen, Frank, 2020. "Inference in second-order identified models," Journal of Econometrics, Elsevier, vol. 218(2), pages 346-372.
    18. Althaler, Karl S. & Slavova, Tatjana, 2000. "DEA Problems under Geometrical or Probability Uncertainties of Sample Data," Economics Series 89, Institute for Advanced Studies.
    19. Alexander D. Stead & Phill Wheat & William H. Greene, 2023. "On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model," Journal of Productivity Analysis, Springer, vol. 60(1), pages 37-48, August.

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