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

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  • Lee, Lung-Fei

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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  • 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.
  • Handle: RePEc:cup:etheor:v:9:y:1993:i:03:p:413-430_00
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    1. repec:gam:jecnmx:v:6:y:2018:i:1:p:8-:d:132670 is not listed on IDEAS
    2. 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.
    3. Liu, Ming & Zhang, Harold H., 1998. "Overparameterization in the seminonparametric density estimation," Economics Letters, Elsevier, vol. 60(1), pages 11-18, July.
    4. Jacob A. Bikker, 2001. "Efficiency in the European banking industry: an exploratory analysis to rank contries," Brussels Economic Review, ULB -- Universite Libre de Bruxelles, vol. 17.
    5. 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.
    6. Althaler, Karl S. & Slavova, Tatjana, 2000. "DEA Problems under Geometrical or Probability Uncertainties of Sample Data," Economics Series 89, Institute for Advanced Studies.

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