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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.

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  • 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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    12. 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.
    13. Kumbhakar, Subal C., 2012. "Specification and estimation of primal production models," European Journal of Operational Research, Elsevier, vol. 217(3), pages 509-518.
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    Cited by:

    1. Tsionas, Mike G. & Kumbhakar, Subal C., 2021. "Stochastic frontier models with time-varying conditional variances," European Journal of Operational Research, Elsevier, vol. 292(3), pages 1115-1132.
    2. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    3. Baños-Pino, José F. & Boto-García, David & Zapico, Emma, 2021. "Electricity Sector Reform Performance in Sub-Saharan Africa: A Parametric Distance Function Approach," Efficiency Series Papers 2021/03, University of Oviedo, Department of Economics, Oviedo Efficiency Group (OEG).
    4. Kai Sun & Ruhul Salim, 2020. "A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry," Journal of Productivity Analysis, Springer, vol. 54(2), pages 139-156, December.
    5. Ligia Alba Melo-Becerra & Lucas Wilfried Hahn-De-Castro & Dalma Sofía Ariza-Hernández & Cristian Oswaldo Carmona-Sanchez, 2016. "Efficiency of Public Education in a Multiproduct Context: The Case of Colombian Municipalities," Borradores de Economia 979, Banco de la Republica de Colombia.
    6. Sebastian Lakner & Stefan Kirchweger & Daniel Hoop & Bernhard Brümmer & Jochen Kantelhardt, 2018. "The Effects of Diversification Activities on the Technical Efficiency of Organic Farms in Switzerland, Austria, and Southern Germany," Sustainability, MDPI, vol. 10(4), pages 1-18, April.
    7. Oleg Badunenko & Subal C. Kumbhakar, 2020. "Energy Intensity and Long- and Short-Term Efficiency in US Manufacturing Industry," Energies, MDPI, vol. 13(15), pages 1-21, August.
    8. Tsionas, Mike G. & Andrikopoulos, Athanasios, 2020. "On a High-Dimensional Model Representation method based on Copulas," European Journal of Operational Research, Elsevier, vol. 284(3), pages 967-979.
    9. Baležentis, Tomas & Sun, Kai, 2020. "Measurement of technical inefficiency and total factor productivity growth: A semiparametric stochastic input distance frontier approach and the case of Lithuanian dairy farms," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1174-1188.
    10. 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.
    11. Ligia Alba Melo-Becerra & Lucas Wilfried Hahn-De-Castro & Dalma Sofía Ariza-Hernández & Cristian Oswaldo Carmona-Sanchez, 2016. "El desempeno municipal en el sector educativo: un análisis a partir de una función multiproducto," Documentos de Trabajo Sobre Economía Regional y Urbana 015017, Banco de la República - Economía Regional.
    12. Musau, Andrew & Kumbhakar, Subal C. & Mydland, Ørjan & Lien, Gudbrand, 2021. "Determinants of allocative and technical inefficiency in stochastic frontier models: An analysis of Norwegian electricity distribution firms," European Journal of Operational Research, Elsevier, vol. 288(3), pages 983-991.
    13. Emir Malikov & Gudbrand Lien, 2021. "Proxy Variable Estimation of Multiproduct Production Functions," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(5), pages 1878-1902, October.
    14. Kumbhakar, Subal C. & Li, Mingyang & Zhao, Shunan, 2021. "Estimation of technical change: Direct semi/nonparametric approaches," Economics Letters, Elsevier, vol. 199(C).
    15. Oleg Badunenko & Deni Mazrekaj & Subal C. Kumbhakar & Kristof Witte, 2021. "Persistent and transient inefficiency in adult education," Empirical Economics, Springer, vol. 60(6), pages 2925-2942, June.
    16. 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).
    17. Robin C. Sickles & Kai Sun & Thomas P. Triebs, 2021. "The optimal use of management," Economic Inquiry, Western Economic Association International, vol. 59(3), pages 1346-1363, July.
    18. Efthymios G. Tsionas & Subal C. Kumbhakar & Emir Malikov, 2015. "Estimation of Input Distance Functions: A System Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 97(5), pages 1478-1493.
    19. Destefanis, Sergio & Fragetta, Matteo & Gasteiger, Emanuel, 2021. "Does one size fit all in the Euro Area? Some counterfactual evidence," ECON WPS - Working Papers in Economic Theory and Policy 05/2019, TU Wien, Institute of Statistics and Mathematical Methods in Economics, Economics Research Unit.
    20. Melo-Becerra, Ligia Alba & Hahn-De-Castro, Lucas Wilfried & Ariza, Dalma Sofía & Carmona, Cristian Oswaldo, 2020. "Efficiency of local public education in a decentralized context," International Journal of Educational Development, Elsevier, vol. 76(C).
    21. Badunenko, Oleg & Cordero, Jose M. & Kumbhakar, Subal C., 2021. "Are you slacking? Where do you and your country stand in the happiness pursuit?," MPRA Paper 108316, University Library of Munich, Germany.
    22. Anaya, Karim L. & Pollitt, Michael G., 2017. "Using stochastic frontier analysis to measure the impact of weather on the efficiency of electricity distribution businesses in developing economies," European Journal of Operational Research, Elsevier, vol. 263(3), pages 1078-1094.
    23. Luigi Brighi & Paolo Silvestri, 2019. "Inefficiency in Childcare Production: Evidence from Italian Microdata," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 5(1), pages 103-133, March.
    24. Chaudhuri, Kausik & Kumbhakar, Subal C. & Sundaram, Lavanya, 2016. "Estimation of firm performance from a MIMIC model," European Journal of Operational Research, Elsevier, vol. 255(1), pages 298-307.

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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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