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Specification and estimation of multiple output technologies: A primal approach

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  • Kumbhakar, Subal C.

Abstract

This paper addresses specification and estimation of multiple-outputs and multiple-inputs production technology in the presence of technical inefficiency. The primary focus is on the primal formulations. Several competing specifications such as production function, input (output) distance function, input requirement function are considered. We show that all these specifications come from the same transformation function and are algebraically identical. We also show that: (i) unless the transformation function is separable (i.e., outputs are separable from inputs), the input (output) ratios in the input (output) distance function can not be treated as exogenous (uncorrelated with technical inefficiency) resulting inconsistent estimates of the input (output) distance function parameters. (ii) Even if input (output) ratios are exogenous, estimation of the input (output) distance function will result in inconsistent parameter estimates if outputs (inputs) are endogenous. We address endogeneity and instrumental variable issues in details in the context of flexible (translog) functional forms. Estimation of several specifications using both single and system approaches are discussed using Norwegian dairy farming data.

Suggested Citation

  • Kumbhakar, Subal C., 2013. "Specification and estimation of multiple output technologies: A primal approach," European Journal of Operational Research, Elsevier, vol. 231(2), pages 465-473.
    • Handle: RePEc:eee:ejores:v:231:y:2013:i:2:p:465-473
    DOI: 10.1016/j.ejor.2013.05.019
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    1. McFadden, Daniel, 1978. "Cost, Revenue, and Profit Functions," Histoy of Economic Thought Chapters, in: Fuss, Melvyn & McFadden, Daniel (ed.),Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 1, McMaster University Archive for the History of Economic Thought.
    2. Kumbhakar, Subal C., 2012. "Specification and estimation of primal production models," European Journal of Operational Research, Elsevier, vol. 217(3), pages 509-518.
    3. Yair Mundlak, 1961. "Empirical Production Function Free of Management Bias," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 43(1), pages 44-56.
    4. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    5. Laurens Cherchye & Timo Kuosmanen & Hervé Leleu, 2010. "Technical and Economic Efficiency Measures Under Short Run Profit Maximizing Behavior," Recherches économiques de Louvain, De Boeck Université, vol. 76(2), pages 163-173.
    6. Rafael Cuesta & José Zofío, 2005. "Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks," Journal of Productivity Analysis, Springer, vol. 24(1), pages 31-48, September.
    7. Tim Coelli & Gholamreza Hajargasht & C.A. Knox Lovell, 2008. "Econometric Estimation of an Input Distance Function in a System of Equations," CEPA Working Papers Series WP012008, School of Economics, University of Queensland, Australia.
    8. John C. Panzar & Robert D. Willig, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 91(3), pages 481-493.
    9. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    10. R. G. Chambers & Y. Chung & R. Färe, 1998. "Profit, Directional Distance Functions, and Nerlovian Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 351-364, August.
    11. COELLI, Tim, 2000. "On the econometric estimation of the distance function representation of a production technology," LIDAM Discussion Papers CORE 2000042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Subal Kumbhakar & Frank Asche & Ragnar Tveteras, 2013. "Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers," Journal of Productivity Analysis, Springer, vol. 40(3), pages 307-321, December.
    13. Diewert, W E, 1974. "Functional Forms for Revenue and Factor Requirements Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 119-130, February.
    14. Yongseung Han, 2012. "Modelling a stochastic profit system using gauge function," Applied Economics Letters, Taylor & Francis Journals, vol. 19(9), pages 823-827, June.
    15. Fare, Rolf & Grosskopf, Shawna & Zaim, Osman, 2002. "Hyperbolic efficiency and return to the dollar," European Journal of Operational Research, Elsevier, vol. 136(3), pages 671-679, February.
    16. Caves, Douglas W & Christensen, Laurits R & Swanson, Joseph A, 1981. "Productivity Growth, Scale Economies, and Capacity Utilization in U.S. Railroads, 1955-74," American Economic Review, American Economic Association, vol. 71(5), pages 994-1002, December.
    17. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 70(2), pages 317-341.
    18. Subal C. Kumbhakar & Gudbrand Lien & Ola Flaten & Ragnar Tveterås, 2008. "Impacts of Norwegian Milk Quotas on Output Growth: A Modified Distance Function Approach," Journal of Agricultural Economics, Wiley Blackwell, vol. 59(2), pages 350-369, June.
    19. Wooldridge, Jeffrey M., 2009. "On estimating firm-level production functions using proxy variables to control for unobservables," Economics Letters, Elsevier, vol. 104(3), pages 112-114, September.
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    More about this item

    Keywords

    Production function; Distance function; Input requirement function; Transformation function;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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