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The Estimation of Meta-Frontiers by Constrained Maximum Likelihood

  • Alexandre Repkine


    (Department of Economics, Korea University, Seoul, Republic of Korea)

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    Existing approaches to the meta-frontier estimation are largely based on the linear programming technique, which does not hinge on any statistical underpinnings. We suggest estimating meta-frontiers by constrained maximum likelihood subject to the constraints that specify the way in which the estimated meta-frontier overarches the individual group frontiers. We present a methodology that allows one to either estimate meta-frontiers using the conventional set of constraints that guarantees overarching at the observed combinations of production inputs, or to specify a range of inputs within which such overarching will hold. In either case the estimated meta-frontier coefficients allow for the statistical inference that is not straightforward in case of the linear programming estimation. We apply our methodology to the world¡¯s FAO agricultural data and find similar estimates of the meta-frontier parameters in case of the same set of constraints. On the contrary, the parameter estimates differ a lot between different sets of constraints.

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    Paper provided by Institute of Economic Research, Korea University in its series Discussion Paper Series with number 1011.

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    Date of creation: 2010
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    Handle: RePEc:iek:wpaper:1011
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    1. Zeitsch, John & Lawrence, Denis & Salerian, John, 1994. "Comparing Like with Like in Productivity Studies: Apples, Oranges and Electricity," The Economic Record, The Economic Society of Australia, vol. 70(209), pages 162-70, June.
    2. Coelli, T. J., 1992. "A computer program for frontier production function estimation : Frontier version 2.0," Economics Letters, Elsevier, vol. 39(1), pages 29-32, May.
    3. George Battese & D. Rao & Christopher O'Donnell, 2004. "A Metafrontier Production Function for Estimation of Technical Efficiencies and Technology Gaps for Firms Operating Under Different Technologies," Journal of Productivity Analysis, Springer, vol. 21(1), pages 91-103, January.
    4. 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.
    5. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    6. Arne Henningsen & Christian Henning, 2009. "Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure," Journal of Productivity Analysis, Springer, vol. 32(3), pages 217-229, December.
    7. Christopher O’Donnell & D. Rao & George Battese, 2008. "Metafrontier frameworks for the study of firm-level efficiencies and technology ratios," Empirical Economics, Springer, vol. 34(2), pages 231-255, March.
    8. Víctor Moreira & Boris Bravo-Ureta, 2010. "Technical efficiency and metatechnology ratios for dairy farms in three southern cone countries: a stochastic meta-frontier model," Journal of Productivity Analysis, Springer, vol. 33(1), pages 33-45, February.
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