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Estimation of Technical and Allocative Inefficiencies in a Cost System: An Exact Maximum Likelihood Approach

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  • Tsionas, Efthymios
  • Kumbhakar, Subal

Abstract

Estimation and decomposition of overall (economic) efficiency into technical and allocative components goes back to Farrell (1957). However, in a cross-sectional framework joint econometric estimation of efficiency components has been mostly confined to restrictive production function models (such as the Cobb-Douglas). In this paper we implement a maximum likelihood (ML) procedure to estimate technical and allocative inefficiency using the dual cost system (cost function and the derivative conditions) in the presence of cross-sectional data. Specifically, the ML procedure is used to estimate simultaneously the translog cost system and cost increase due to both technical and allocative inefficiency. This solves the so-called ‘Greene problem’ in the efficiency literature. The proposed technique is applied to the Christensen and Greene (1976) data on U.S. electric utilities, and a cross-section of the Brynjolfsson and Hitt (2003) data on large U.S. firms.

Suggested Citation

  • Tsionas, Efthymios & Kumbhakar, Subal, 2006. "Estimation of Technical and Allocative Inefficiencies in a Cost System: An Exact Maximum Likelihood Approach," MPRA Paper 20173, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:20173
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    References listed on IDEAS

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    1. Kumbhakar, Subal C. & Wang, Hung-Jen, 2006. "Estimation of technical and allocative inefficiency: A primal system approach," Journal of Econometrics, Elsevier, vol. 134(2), pages 419-440, October.
    2. Greene, William H., 1980. "On the estimation of a flexible frontier production model," Journal of Econometrics, Elsevier, vol. 13(1), pages 101-115, May.
    3. McElroy, Marjorie B, 1987. "Additive General Error Models for Production, Cost, and Derived Demand or Share Systems," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 737-757, August.
    4. Schmidt, Peter & Knox Lovell, C. A., 1979. "Estimating technical and allocative inefficiency relative to stochastic production and cost frontiers," Journal of Econometrics, Elsevier, vol. 9(3), pages 343-366, February.
    5. Erik Brynjolfsson & Lorin M. Hitt, 2003. "Computing Productivity: Firm-Level Evidence," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 793-808, November.
    6. Kumbhakar, Subal C., 1997. "Modeling allocative inefficiency in a translog cost function and cost share equations: An exact relationship," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 351-356.
    7. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "The Joint Measurement of Technical and Allocative Inefficiencies: An Application of Bayesian Inference in Nonlinear Random-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 736-747, September.
    8. Wang, Hung-Jen, 2006. "Stochastic frontier models," MPRA Paper 31079, University Library of Munich, Germany.
    9. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56.
    10. Kumbhakar, Subal C. & Wang, Hung-Jen, 2006. "Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis," Journal of Econometrics, Elsevier, vol. 134(2), pages 317-340, October.
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    Cited by:

    1. Jean-Philippe Boussemart & Herv頌eleu & Vivian Valdmanis, 2015. "A two-stage translog marginal cost pricing approach for Floridian hospital outputs," Applied Economics, Taylor & Francis Journals, vol. 47(38), pages 4116-4127, August.
    2. Kumbhakar, Subal C. & Tsionas, Mike G., 2020. "On the estimation of technical and allocative efficiency in a panel stochastic production frontier system model: Some new formulations and generalizations," European Journal of Operational Research, Elsevier, vol. 287(2), pages 762-775.
    3. Dibyendu Maiti & Chiranjib Neogi, 2024. "Endogeneity-corrected stochastic frontier with market imperfections," Empirical Economics, Springer, vol. 67(3), pages 1149-1183, September.
    4. Mamatzakis, Emmanuel & Tsionas, Mike G. & Kumbhakar, Subal C. & Koutsomanoli-Filippaki, Anastasia, 2015. "Does labour regulation affect technical and allocative efficiency? Evidence from the banking industry," Journal of Banking & Finance, Elsevier, vol. 61(S1), pages 84-98.
    5. repec:ags:aaea22:335541 is not listed on IDEAS
    6. Chen Xue & Fulin Du & Mei Yong, 2024. "Impact of Operating Scale on Factor Inputs in Grassland Animal Husbandry—Intermediary Effects Based on Market Risk," Sustainability, MDPI, vol. 16(17), pages 1-21, August.
    7. Xiaoheng Zhang & Xiaohua Yu & Xu Tian & Xianhui Geng & Yingheng Zhou, 2019. "Farm size, inefficiency, and rice production cost in China," Journal of Productivity Analysis, Springer, vol. 52(1), pages 57-68, December.
    8. Ouyang, Xiaoling & Wei, Xiaoyun & Sun, Chuanwang & Du, Gang, 2018. "Impact of factor price distortions on energy efficiency: Evidence from provincial-level panel data in China," Energy Policy, Elsevier, vol. 118(C), pages 573-583.

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    More about this item

    Keywords

    Technical inefficiency; allocative inefficiency; the Greene problem; translog cost function;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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