IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v231y2013i2p465-473.html
   My bibliography  Save this article

Specification and estimation of multiple output technologies: A primal approach

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713004189
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.05.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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. 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.
    4. 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.
    5. 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.
    6. John C. Panzar & Robert D. Willig, 1977. "Economies of Scale in Multi-Output Production," The Quarterly Journal of Economics, Oxford University Press, vol. 91(3), pages 481-493.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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.
    14. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    15. 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.
    16. 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).
    17. Yongseung Han, 2012. "Modelling a stochastic profit system using gauge function," Applied Economics Letters, Taylor & Francis Journals, vol. 19(9), pages 823-827, June.
    18. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kumbhakar, Subal C., 2012. "Specification and estimation of primal production models," European Journal of Operational Research, Elsevier, vol. 217(3), pages 509-518.
    2. Layer, Kevin & Johnson, Andrew L. & Sickles, Robin C. & Ferrier, Gary D., 2020. "Direction selection in stochastic directional distance functions," European Journal of Operational Research, Elsevier, vol. 280(1), pages 351-364.
    3. 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.
    4. Anupriya, & Graham, Daniel J. & Carbo, Jose M. & Anderson, Richard J. & Bansal, Prateek, 2020. "Understanding the costs of urban rail transport operations," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 292-316.
    5. repec:zbw:iamodp:274820 is not listed on IDEAS
    6. Simon Pröll & Giannis Karagiannis & Klaus Salhofer, 2019. "Advertising and Markups: The Case of the German Brewing Industry," Working Papers 732019, University of Natural Resources and Life Sciences, Vienna, Department of Economics and Social Sciences, Institute for Sustainable Economic Development.
    7. Kloss, Mathias & Petrick, Martin, 2014. "The Productivity of Family and Hired Labour in EU Arable Farming," 54th Annual Conference, Goettingen, Germany, September 17-19, 2014 187353, German Association of Agricultural Economists (GEWISOLA).
    8. 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.
    9. 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.
    10. Parrotta, Pierpaolo & Pozzoli, Dario & Pytlikova, Mariola, 2014. "Labor diversity and firm productivity," European Economic Review, Elsevier, vol. 66(C), pages 144-179.
    11. Quang-Thanh Ngo & Canh Thi Nguyen, 2020. "Do export transitions differently affect firm productivity? Evidence across Vietnamese manufacturing sectors," Post-Communist Economies, Taylor & Francis Journals, vol. 32(8), pages 1011-1037, November.
    12. Grieco, Paul & Pinkse, Joris & Slade, Margaret, 2018. "Brewed in North America: Mergers, marginal costs, and efficiency," International Journal of Industrial Organization, Elsevier, vol. 59(C), pages 24-65.
    13. Lena, Daniela & Pasurka, Carl A. & Cucculelli, Marco, 2022. "Environmental regulation and green productivity growth: Evidence from Italian manufacturing industries," Technological Forecasting and Social Change, Elsevier, vol. 184(C).
    14. Autant-Bernard, Corinne & Guironnet, Jean-Pascal & Massard, Nadine, 2011. "Agglomeration and social return to R&D: Evidence from French plant productivity changes," International Journal of Production Economics, Elsevier, vol. 132(1), pages 34-42, July.
    15. Kirill Shakhnov, 2022. "The Allocation of Talent: Finance versus Entrepreneurship," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 46, pages 161-195, October.
    16. Atkinson, Scott E. & Primont, Daniel & Tsionas, Mike G., 2018. "Statistical inference in efficient production with bad inputs and outputs using latent prices and optimal directions," Journal of Econometrics, Elsevier, vol. 204(2), pages 131-146.
    17. 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).
    18. Daniel A. Ackerberg & Kevin Caves & Garth Frazer, 2015. "Identification Properties of Recent Production Function Estimators," Econometrica, Econometric Society, vol. 83, pages 2411-2451, November.
    19. Lien, Gudbrand & Kumbhakar, Subal C. & Alem, Habtamu, 2018. "Endogeneity, heterogeneity, and determinants of inefficiency in Norwegian crop-producing farms," International Journal of Production Economics, Elsevier, vol. 201(C), pages 53-61.
    20. repec:zbw:inwedp:732019 is not listed on IDEAS
    21. Mathias Kloss & Thomas Kirschstein & Steffen Liebscher & Martin Petrick, 2019. "Robust Productivity Analysis: An application to German FADN data," Papers 1902.00678, arXiv.org, revised Feb 2019.
    22. Parrotta, Pierpaolo & Pozzoli, Dario & Pytlikova, Mariola, 2010. "Does Labor Diversity Affect Firm Productivity?," Working Papers 10-12, University of Aarhus, Aarhus School of Business, Department of Economics.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:231:y:2013:i:2:p:465-473. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/eor .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.