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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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Kumbhakar, Subal C. & Badunenko, Oleg & Willox, Michael, 2022. "Do carbon taxes affect economic and environmental efficiency? The case of British Columbia’s manufacturing plants," Energy Economics, Elsevier, vol. 115(C).
    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. Baños-Pino, José F. & Boto-García, David & Zapico, Emma, 2021. "Persistence and dynamics in the efficiency of toll motorways: The Spanish case," Efficiency Series Papers 2021/03, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    4. Liu, Tung, 2021. "Measuring cost inefficiency: A dual approach," Economic Modelling, Elsevier, vol. 99(C).
    5. Sergio Destefanis & Matteo Fragetta & Emanuel Gasteiger, 2024. "Does one size fit all in the Euro Area? Some counterfactual evidence," Empirical Economics, Springer, vol. 67(4), pages 1615-1647, October.
    6. Arandarage Mayura Prasad Arandara & Shingo Takahashi, 2023. "Productivity analysis of Sri Lankan cooperative banks: input distance function approach," Asia-Pacific Journal of Regional Science, Springer, vol. 7(1), pages 93-117, March.
    7. 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.
    8. Scalco, Paulo R. & Tabak, Benjamin M. & Teixeira, Anderson M., 2021. "Prudential measures and their adverse effects on bank competition: The case of Brazil," Economic Modelling, Elsevier, vol. 100(C).
    9. Gianluigi Coppola & Sergio Destefanis & Giorgia Marinuzzi & Walter Tortorella, 2021. "Regional policies and sectoral outputs in the Italian regions. A multi-input multi-output counterfactual approach," Discussion Paper series in Regional Science & Economic Geography 2021-08, Gran Sasso Science Institute, Social Sciences, revised May 2021.
    10. Paulo Roberto Scalco & Benjamin M. Tabak & Anderson Mutter Teixeira, 2019. "The Dark Side of Prudential Measures," Working papers - Textos para Discussao do Curso de Ciencias Economicas da UFG 078, Curso de Ciencias Economicas da Universidade Federal de Goias - FACE.
    11. Baños-Pino, José F. & Boto-García, David & Zapico, Emma, 2022. "Persistence and dynamics in the efficiency of toll motorways: The Spanish case," Economics of Transportation, Elsevier, vol. 31(C).
    12. Subal C. Kumbhakar & Gudbrand Lien, 2017. "Yardstick Regulation of Electricity Distribution Disentangling Short-run and Long-run Inefficiencies," The Energy Journal, International Association for Energy Economics, vol. 0(Number 5).
    13. 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.
    14. 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.

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