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Specification and estimation of primal production models

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  • Kumbhakar, Subal C.

Abstract

While estimating production technology in a primal framework production function, input and output distance functions and input requirement functions are widely used in the empirical literature. This paper shows that these popular primal based models are algebraically equivalent in the sense that they can be derived from the same underlying transformation (production possibility) function. By assuming that producers maximize profit, we show that in all cases, except one, the use of ordinary least squares (OLS) gives inconsistent estimates irrespective of whether the production, input distance and input requirement functions are used. Based on several specifications of the production and input distance function models, we conclude that one can estimate the input elasticities and returns to scale consistently using instruments on only one regressor. No instruments are needed if either it is assumed that producers know the technology entirely (including the so-called error term) or a system approach is used. We used Norwegian timber harvesting data to illustrate workings of various model specifications.

Suggested Citation

  • Kumbhakar, Subal C., 2012. "Specification and estimation of primal production models," European Journal of Operational Research, Elsevier, vol. 217(3), pages 509-518.
  • Handle: RePEc:eee:ejores:v:217:y:2012:i:3:p:509-518
    DOI: 10.1016/j.ejor.2011.09.043
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    References listed on IDEAS

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    1. Perelman, Sergio & Santín, Daniel, 2009. "How to generate regularly behaved production data? A Monte Carlo experimentation on DEA scale efficiency measurement," European Journal of Operational Research, Elsevier, vol. 199(1), pages 303-310, November.
    2. COELLI, Tim, 2000. "On the econometric estimation of the distance function representation of a production technology," CORE Discussion Papers 2000042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. 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.
    5. Kumbhakar, Subal C., 2011. "Estimation of production technology when the objective is to maximize return to the outlay," European Journal of Operational Research, Elsevier, vol. 208(2), pages 170-176, January.
    6. James Levinsohn & Amil Petrin, 2003. "Estimating Production Functions Using Inputs to Control for Unobservables," Review of Economic Studies, Oxford University Press, vol. 70(2), pages 317-341.
    7. Subal C. Kumbhakar & Efthymios G. Tsionas, 2011. "Stochastic error specification in primal and dual production systems," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(2), pages 270-297, March.
    8. Boussemart, Jean-Philippe & Briec, Walter & Peypoch, Nicolas & Tavéra, Christophe, 2009. "[alpha]-Returns to scale and multi-output production technologies," European Journal of Operational Research, Elsevier, vol. 197(1), pages 332-339, August.
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    1. repec:aen:journl:ej38-5-lien is not listed on IDEAS
    2. Abhiman Das & Subal C. Kumbhakar, 2016. "Markup and efficiency of Indian banks: an input distance function approach," Empirical Economics, Springer, vol. 51(4), pages 1689-1719, December.
    3. 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.
    4. Subal Kumbhakar & Roar Amundsveen & Hilde Kvile & Gudbrand Lien, 2015. "Scale economies, technical change and efficiency in Norwegian electricity distribution, 1998–2010," Journal of Productivity Analysis, Springer, vol. 43(3), pages 295-305, June.
    5. Ren, Lan Tian & Liu, Zu Xin & Wei, Tong Yang & Xie, Guang Hui, 2012. "Evaluation of energy input and output of sweet sorghum grown as a bioenergy crop on coastal saline-alkali land," Energy, Elsevier, vol. 47(1), pages 166-173.

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