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Piecewise Loglinear Estimation of Efficient Production Surfaces

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  • Rajiv D. Banker

    (School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213)

  • Ajay Maindiratta

    (Graduate School of Business Administration, New York University, New York, New York 10006)

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    Abstract

    Linear programming formulations for piecewise loglinear estimation of efficient production surfaces are derived from a set of basic properties postulated for the underlying production possibility sets. Unlike the piecewise linear model of Banker, Charnes, and Cooper (Banker R. D., A. Charnes, W. W. Cooper. 1984. Models for the estimation of technical and scale inefficiencies in data envelopment analysis. Management Sci. 30 (September) 1078--1092.), this approach permits the identification of increasing marginal products, and estimation of the classical S-shaped production functions. Methods are also provided for estimating technical inefficiencies and other production characteristics, such as rates of substitution and transformation, marginal products, returns to scale and most productive scale sizes on the basis of observed production data. The results of a simulation study are reported to illustrate the usefulness of this estimation method in empirical applications when there are a priori reasons to expect increasing marginal products in some regions of the production function. A modified model is provided to extend this analysis to the situation of non-competing outputs addressed by the bi-extremal model of Banker, Charnes, Cooper, and Schinnar (Banker R. D., A. Charnes, W. W. Cooper, A. Schinnar. 1981. A bi-extremal principle for frontier estimation and efficiency evaluation. Management Sci. 27 (December) 1370--1382.).

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 32 (1986)
    Issue (Month): 1 (January)
    Pages: 126-135

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    Handle: RePEc:inm:ormnsc:v:32:y:1986:i:1:p:126-135

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    Related research

    Keywords: production frontiers; data envelopment analysis;

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    Cited by:
    1. Laurens Cherchye & Knox Lovell & Wim Moesen & Tom Van Puyenbroeck, 2005. "One Market, One Number? A Composite Indicator Assessment of EU Internal Market Dynamics," Public Economics Working Paper Series ces0513, Katholieke Universiteit Leuven, Centrum voor Economische Studiƫn, Working Group Public Economics.
    2. Olesen, Ole Bent & Petersen, Niels Christian, 2013. "Imposing the Regular Ultra Passum law in DEA models," Omega, Elsevier, vol. 41(1), pages 16-27.
    3. W. Cooper & Z. Huang & S. Li & J. Zhu, 2008. "A response to the critiques of DEA by Dmitruk and Koshevoy, and Bol," Journal of Productivity Analysis, Springer, vol. 29(1), pages 15-21, February.
    4. Donthu, Naveen & Hershberger, Edmund K. & Osmonbekov, Talai, 2005. "Benchmarking marketing productivity using data envelopment analysis," Journal of Business Research, Elsevier, vol. 58(11), pages 1474-1482, November.
    5. Barnum, Darold T. & Karlaftis, Matthew G. & Tandon, Sonali, 2011. "Improving the efficiency of metropolitan area transit by joint analysis of its multiple providers," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 1160-1176.
    6. Banker, Rajiv D. & Cooper, William W. & Seiford, Lawrence M. & Thrall, Robert M. & Zhu, Joe, 2004. "Returns to scale in different DEA models," European Journal of Operational Research, Elsevier, vol. 154(2), pages 345-362, April.
    7. Mehdiloozad, Mahmood & Sahoo, Biresh K. & Roshdi, Israfil, 2014. "A generalized multiplicative directional distance function for efficiency measurement in DEA," European Journal of Operational Research, Elsevier, vol. 232(3), pages 679-688.
    8. Murthi, B. P. S. & Choi, Yoon K. & Desai, Preyas, 1997. "Efficiency of mutual funds and portfolio performance measurement: A non-parametric approach," European Journal of Operational Research, Elsevier, vol. 98(2), pages 408-418, April.

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