IDEAS home Printed from https://ideas.repec.org/a/kap/jproda/v21y2004i1p25-48.html
   My bibliography  Save this article

Are all Scales Optimal in DEA? Theory and Empirical Evidence

Author

Listed:
  • Finn Førsund
  • Lennart Hjalmarsson

Abstract

Policy recommendations concerning optimal scale of production units may have serious implications for the restructuring of a sector. The piecewise linear frontier production function framework (DEA) is becoming the most popular one for assessing not only technical efficiency of operations, but also for scale efficiency and calculation of optimal scale sizes. The main purpose of the present study is to investigate if neoclassical production theory gives any guidance as to the nature of scale properties in the DEA model, and empirically explore such properties. Theoretical results indicate that the DEA model may have more irregular properties than usually assumed in neoclassical production theory, concerning shape of optimal scale curves and the M-locus. The empirical results indicate that optimal scale may be found over almost the entire size variations in outputs and inputs, thus making policy recommendations about efficient scale difficult. It seems necessary to establish the nature of optimal scale before any practical conclusions can be drawn. Proposals for indexes characterizing the nature of optimal scale are provided. Copyright Kluwer Academic Publishers 2004

Suggested Citation

  • Finn Førsund & Lennart Hjalmarsson, 2004. "Are all Scales Optimal in DEA? Theory and Empirical Evidence," Journal of Productivity Analysis, Springer, vol. 21(1), pages 25-48, January.
  • Handle: RePEc:kap:jproda:v:21:y:2004:i:1:p:25-48
    DOI: 10.1023/B:PROD.0000012451.84910.6e
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1023/B:PROD.0000012451.84910.6e
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1023/B:PROD.0000012451.84910.6e?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hanoch, Giora, 1970. "Homotheticity in joint production," Journal of Economic Theory, Elsevier, vol. 2(4), pages 423-426, December.
    2. Yun Zhang & Robert Bartels, 1998. "The Effect of Sample Size on the Mean Efficiency in DEA with an Application to Electricity Distribution in Australia, Sweden and New Zealand," Journal of Productivity Analysis, Springer, vol. 9(3), pages 187-204, March.
    3. 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.
    4. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    5. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    6. Lawrence Seiford & Joe Zhu, 1999. "Sensitivity and Stability of the Classifications of Returns to Scale in Data Envelopment Analysis," Journal of Productivity Analysis, Springer, vol. 12(1), pages 55-75, August.
    7. Wesley D. Seitz, 1970. "The Measurement of Efficiency Relative to a Frontier Production Function," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 52(4), pages 505-511.
    8. Starrett, David A, 1977. "Measuring Returns to Scale in the Aggregate, and the Scale Effect of Public Goods," Econometrica, Econometric Society, vol. 45(6), pages 1439-1455, September.
    9. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 2, number 2.
    10. Kim, H Youn, 1987. "Economies of Scale in Multi-product Firms: An Empirical Analysis," Economica, London School of Economics and Political Science, vol. 54(214), pages 185-206, May.
    11. 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.
    12. Baumol, William J, 1982. "Contestable Markets: An Uprising in the Theory of Industry Structure," American Economic Review, American Economic Association, vol. 72(1), pages 1-15, March.
    13. Banker, Rajiv D., 1984. "Estimating most productive scale size using data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 17(1), pages 35-44, July.
    14. Simar, Leopold & Wilson, Paul W., 2002. "Non-parametric tests of returns to scale," European Journal of Operational Research, Elsevier, vol. 139(1), pages 115-132, May.
    15. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    16. Jamasb, T. & Pollitt, M., 2000. "Benchmarking and regulation: international electricity experience," Utilities Policy, Elsevier, vol. 9(3), pages 107-130, September.
    17. R. Schmalensee & R. Willig (ed.), 1989. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 1, number 1.
    18. Banker, R. D. & Bardhan, I. & Cooper, W. W., 1996. "A note on returns to scale in DEA," European Journal of Operational Research, Elsevier, vol. 88(3), pages 583-585, February.
    19. Hjalmarsson, Lennart & Veiderpass, Ann, 1992. " Productivity in Swedish Electricity Retail Distribution," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(0), pages 193-205, Supplemen.
    20. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    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. Førsund, Finn, 2015. "Economic Perspectives on DEA," Memorandum 10/2015, Oslo University, Department of Economics.
    2. F R Førsund & L Hjalmarsson, 2004. "Calculating scale elasticity in DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1023-1038, October.
    3. Rolf Färe & Giannis Karagiannis, 2023. "Translation efficiency and directionally optimal scale," Journal of Economics, Springer, vol. 140(3), pages 259-273, December.
    4. Førsund, Finn R. & Kittelsen, Sverre A. & Krivonozhko, Vladimir E., 2007. "Farrell Revisited: Visualising the DEA Production Frontier," Memorandum 15/2007, Oslo University, Department of Economics.
    5. Olesen, Ole Bent & Petersen, Niels Christian, 2013. "Imposing the Regular Ultra Passum law in DEA models," Omega, Elsevier, vol. 41(1), pages 16-27.
    6. K. Tone & M. Tsutsui, 2015. "How to Deal with Non-Convex Frontiers in Data Envelopment Analysis," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 1002-1028, September.
    7. Cesaroni, Giovanni, 2018. "Industry cost efficiency in data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 37-43.
    8. Forsund, Finn R. & Sarafoglou, Nikias, 2005. "The tale of two research communities: The diffusion of research on productive efficiency," International Journal of Production Economics, Elsevier, vol. 98(1), pages 17-40, October.
    9. Degla, Pamphile, 2015. "Technical Efficiency in Producing Cashew Nuts in Benin’s Savanna Zone, West Africa," Quarterly Journal of International Agriculture, Humboldt-Universitaat zu Berlin, vol. 54(2), pages 1-16, May.
    10. Olesen, Ole B. & Ruggiero, John, 2014. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 235(3), pages 798-809.
    11. Olesen, Ole B. & Ruggiero, John, 2012. "Maintaining the Regular Ultra Passum Law in data envelopment analysis," Discussion Papers on Economics 2/2012, University of Southern Denmark, Department of Economics.
    12. Tone, Kaoru & Sahoo, Biresh K., 2004. "Degree of scale economies and congestion: A unified DEA approach," European Journal of Operational Research, Elsevier, vol. 158(3), pages 755-772, November.
    13. Kaoru Tone & Miki Tsutsui, 2013. "How to deal with S-shaped curve in DEA," GRIPS Discussion Papers 13-10, National Graduate Institute for Policy Studies.
    14. Erbetta, Fabrizio & Rappuoli, Luca, 2008. "Optimal scale in the Italian gas distribution industry using data envelopment analysis," Omega, Elsevier, vol. 36(2), pages 325-336, April.
    15. Førsund, Finn R. & Kittelsen, Sverre A.C & Lindseth, Frode, 2005. "Efficiency And Productivity Of Norwegian Tax Offices," Memorandum 29/2005, Oslo University, Department of Economics.
    16. F R Førsund & S A C Kittelsen & V E Krivonozhko, 2009. "Farrell revisited–Visualizing properties of DEA production frontiers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(11), pages 1535-1545, November.
    17. Asmild, Mette & Paradi, Joseph C. & Reese, David N., 2006. "Theoretical perspectives of trade-off analysis using DEA," Omega, Elsevier, vol. 34(4), pages 337-343, August.
    18. Cesaroni, Giovanni & Giovannola, Daniele, 2015. "Average-cost efficiency and optimal scale sizes in non-parametric analysis," European Journal of Operational Research, Elsevier, vol. 242(1), pages 121-133.
    19. Kaoru Tone & Biresh Sahoo, 2006. "Re-examining scale elasticity in DEA," Annals of Operations Research, Springer, vol. 145(1), pages 69-87, July.
    20. Mehdi Toloo & Mona Barat & Atefeh Masoumzadeh, 2015. "Selective measures in data envelopment analysis," Annals of Operations Research, Springer, vol. 226(1), pages 623-642, March.
    21. Rodrigo Gómez Monge, 2012. "El sector bancario en México, los depósitos a plazo y las cuentas de ahorro: un análisis de eficiencia durante el periodo de internacionalización a través de la envolvente de datos (dea)," Revista Ciencias Estratégicas, Universidad Pontificia Bolivariana, June.
    22. Stefan Seifert, 2016. "Semi-Parametric Measures of Scale Characteristics of German Natural Gas-Fired Electricity Generation," Discussion Papers of DIW Berlin 1571, DIW Berlin, German Institute for Economic Research.
    23. 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.
    24. Nikolay VASILIEV & Elsa SUUSTER & Helis LUIK & Rando VÄRNIK & Eduard MATVEEV & Alar ASTOVER, 2011. "Productivity of Estonian dairy farms decline after the accession to the European Union," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 57(9), pages 457-463.
    25. Olesen, Ole Bent & Petersen, Niels Christian, 2011. "Scale properties in data envelopment analysis," Discussion Papers on Economics 4/2011, University of Southern Denmark, Department of Economics.

    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. Finn Førsund & Lennart Hjalmarsson & Vladimir Krivonozhko & Oleg Utkin, 2007. "Calculation of scale elasticities in DEA models: direct and indirect approaches," Journal of Productivity Analysis, Springer, vol. 28(1), pages 45-56, October.
    2. F R Førsund & L Hjalmarsson, 2004. "Calculating scale elasticity in DEA models," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(10), pages 1023-1038, October.
    3. Giancarlo Moschini, 1988. "A Model of Production with Supply Management for the Canadian Agricultural Sector," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 70(2), pages 318-329.
    4. Sara Amoroso, 2015. "Profits, R&D and labour: Breaking the law of diminishing returns to labour," JRC Working Papers on Corporate R&D and Innovation 2015-10, Joint Research Centre.
    5. Hadjicostas, Petros & Soteriou, Andreas C., 2006. "One-sided elasticities and technical efficiency in multi-output production: A theoretical framework," European Journal of Operational Research, Elsevier, vol. 168(2), pages 425-449, January.
    6. Resende, Marcelo, 1999. "Productivity growth and regulation in U.S. local telephony," Information Economics and Policy, Elsevier, vol. 11(1), pages 23-44, March.
    7. Bruno De Borger & Kristiaan Kerstens & Diego Prior & Ignace Van de Woestyne, 2013. "Static efficiency decompositions and capacity utilization: integrating economic and technical capacity notions," Applied Economics, Taylor & Francis Journals, vol. 45(24), pages 3529-3529, August.
    8. Valentin Zelenyuk, 2021. "Performance Analysis: Economic Foundations & Trends," CEPA Working Papers Series WP162021, School of Economics, University of Queensland, Australia.
    9. Giancarlo Moschini, 1988. "The Cost Structure of Ontario Dairy Farms: A Microeconometric Analysis," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 36(2), pages 187-206, July.
    10. Ryu, Sang-Lyul & Won, Jayoun, 2022. "Scale and scope economies in Korean accounting firms around Sarbanes-Oxley regulations," Journal of Asian Economics, Elsevier, vol. 78(C).
    11. Walter Briec & Kristiaan Kerstens & Hervé Leleu & Philippe Eeckaut, 2000. "Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies," Journal of Productivity Analysis, Springer, vol. 14(3), pages 267-274, November.
    12. Ferenc Kiss & Bernard Lefebvre, 1987. "Econometric models of telecommunications firms : a survey," Revue Économique, Programme National Persée, vol. 38(2), pages 307-374.
    13. Gabriele Dono & Luca Giraldo & Simone Severini, 2012. "The Cost of Irrigation Water Delivery: An Attempt to Reconcile the Concepts of Cost and Efficiency," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(7), pages 1865-1877, May.
    14. Tone, Kaoru & Sahoo, Biresh K., 2005. "Evaluating cost efficiency and returns to scale in the Life Insurance Corporation of India using data envelopment analysis," Socio-Economic Planning Sciences, Elsevier, vol. 39(4), pages 261-285, December.
    15. Perekhozhuk, Oleksandr, 2007. "Marktstruktur und Preisbildung auf dem ukrainischen Markt für Rohmilch," Studies on the Agricultural and Food Sector in Transition Economies, Leibniz Institute of Agricultural Development in Transition Economies (IAMO), volume 41, number 92322.
    16. Sueyoshi, Toshiyuki & Sekitani, Kazuyuki, 2007. "The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane," European Journal of Operational Research, Elsevier, vol. 181(2), pages 549-570, September.
    17. Tone, Kaoru & Sahoo, Biresh K., 2004. "Degree of scale economies and congestion: A unified DEA approach," European Journal of Operational Research, Elsevier, vol. 158(3), pages 755-772, November.
    18. Tone, Kaoru & Sahoo, Biresh K., 2003. "Scale, indivisibilities and production function in data envelopment analysis," International Journal of Production Economics, Elsevier, vol. 84(2), pages 165-192, May.
    19. Mwabu, Germano, 2007. "Health Economics for Low-Income Countries," Center Discussion Papers 10118, Yale University, Economic Growth Center.
    20. Dono, Gabriele & Giraldo, Luca, 2011. "Cost Analysis for Water Distribution in Agriculture," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114435, European Association of Agricultural Economists.

    More about this item

    Keywords

    optimal scale; scale elasticity; efficiency; Regular Ultra Passum (RUP) law; data envelopment analysis (DEA); efficiency frontier; M-locus;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D20 - Microeconomics - - Production and Organizations - - - General
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L52 - Industrial Organization - - Regulation and Industrial Policy - - - Industrial Policy; Sectoral Planning Methods

    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:kap:jproda:v:21:y:2004:i:1:p:25-48. See general information about how to correct material in RePEc.

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.