IDEAS home Printed from https://ideas.repec.org/a/eee/ecmode/v99y2021ics0264999321000468.html
   My bibliography  Save this article

Measuring cost inefficiency: A dual approach

Author

Listed:
  • Liu, Tung

Abstract

Total cost inefficiency comprises technical inefficiency and allocative inefficiency. Measuring cost inefficiency with these two components has been challenging both theoretically and empirically. Current literature has provided some solutions. However, these solutions are restricted to specific functions and their empirical estimations are complicated to implement, which lead to limited applications. Using the duality between production and cost functions, this paper proposes a new approach that is simple for estimation and applicable to general cases. Firstly, we define two types of allocative inefficiency and derive their input cost share inequalities. Secondly, a three-stage procedure is developed to estimate total cost inefficiency and its two components. Finally, an empirical presentation based on the existing data supplements the theory. Our results show that this solution can identify the inefficiency for each input and derive robust estimates of economies of scale, which are important for both policy implications and managerial decisions.

Suggested Citation

  • Liu, Tung, 2021. "Measuring cost inefficiency: A dual approach," Economic Modelling, Elsevier, vol. 99(C).
    • Handle: RePEc:eee:ecmode:v:99:y:2021:i:c:s0264999321000468
    DOI: 10.1016/j.econmod.2021.02.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0264999321000468
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econmod.2021.02.012?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. Grant, James H & Hamermesh, Daniel S, 1981. "Labor Market Competition among Youths, White Women and Others," The Review of Economics and Statistics, MIT Press, vol. 63(3), pages 354-360, August.
    2. 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.
    3. Rolf Färe & Daniel Primont, 2012. "Dual allocative efficiency parameters," Journal of Productivity Analysis, Springer, vol. 37(3), pages 233-238, June.
    4. Kumbhakar, Subal C. & Wang, Hung-Jen, 2006. "Estimation of technical and allocative inefficiency: A primal system approach," Journal of Econometrics, Elsevier, vol. 134(2), pages 419-440, October.
    5. Tsionas, Mike G. & Mallick, Sushanta K., 2019. "A Bayesian semiparametric approach to stochastic frontiers and productivity," European Journal of Operational Research, Elsevier, vol. 274(1), pages 391-402.
    6. Kumbhakar, Subal C., 2012. "Specification and estimation of primal production models," European Journal of Operational Research, Elsevier, vol. 217(3), pages 509-518.
    7. Raymond J. Kopp, 1981. "The Measurement of Productive Efficiency: A Reconsideration," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 96(3), pages 477-503.
    8. Chan, M W Luke & Mountain, Dean C, 1983. "Economies of Scale and the Tornqvist Discrete Measure of Productivity Growth," The Review of Economics and Statistics, MIT Press, vol. 65(4), pages 663-667, November.
    9. Kumbhakar, Subal C. & Tsionas, Mike G., 2020. "On the estimation of technical and allocative efficiency in a panel stochastic production frontier system model: Some new formulations and generalizations," European Journal of Operational Research, Elsevier, vol. 287(2), pages 762-775.
    10. Greene, William H., 1980. "On the estimation of a flexible frontier production model," Journal of Econometrics, Elsevier, vol. 13(1), pages 101-115, May.
    11. Schmidt, Peter & Knox Lovell, C. A., 1979. "Estimating technical and allocative inefficiency relative to stochastic production and cost frontiers," Journal of Econometrics, Elsevier, vol. 9(3), pages 343-366, February.
    12. Kim, H Youn, 1992. "The Translog Production Function and Variable Returns to Scale," The Review of Economics and Statistics, MIT Press, vol. 74(3), pages 546-552, August.
    13. Kumbhakar, Subal C. & Parmeter, Christopher F. & Tsionas, Efthymios G., 2013. "A zero inefficiency stochastic frontier model," Journal of Econometrics, Elsevier, vol. 172(1), pages 66-76.
    14. Burgess, David F., 1975. "Duality theory and pitfalls in the specification of technologies," Journal of Econometrics, Elsevier, vol. 3(2), pages 105-121, May.
    15. 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.
    16. Li, Kui-Wai & Liu, Tung, 2011. "Economic and productivity growth decomposition: An application to post-reform China," Economic Modelling, Elsevier, vol. 28(1), pages 366-373.
    17. Kumbhakar, Subal C., 1997. "Modeling allocative inefficiency in a translog cost function and cost share equations: An exact relationship," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 351-356.
    18. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "The Joint Measurement of Technical and Allocative Inefficiencies: An Application of Bayesian Inference in Nonlinear Random-Effects Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 736-747, September.
    19. Lai, Hung-pin & Kumbhakar, Subal C., 2019. "Technical and allocative efficiency in a panel stochastic production frontier system model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 255-265.
    20. 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.
    21. Lau, Lawrence J & Yotopoulos, Pan A, 1971. "A Test for Relative Efficiency and Application to Indian Agriculture," American Economic Review, American Economic Association, vol. 61(1), pages 94-109, March.
    22. Berndt, Ernst R & Christensen, Laurits R, 1974. "Testing for the Existence of a Consistent Aggregate Index of Labor Inputs," American Economic Review, American Economic Association, vol. 64(3), pages 391-404, June.
    23. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 126(2), pages 355-384, June.
    24. Battese, George E. & Coelli, Tim J., 1988. "Prediction of firm-level technical efficiencies with a generalized frontier production function and panel data," Journal of Econometrics, Elsevier, vol. 38(3), pages 387-399, July.
    25. Atkinson, Scott E. & Primont, Daniel, 2002. "Stochastic estimation of firm technology, inefficiency, and productivity growth using shadow cost and distance functions," Journal of Econometrics, Elsevier, vol. 108(2), pages 203-225, June.
    26. Subal C. Kumbhakar, Orjan Mydland, Andrew Musau, and Gudbrand Lien, 2020. "Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation: The Case of Norwegian Electricity Distribution Firms," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 143-160.
    27. Appelbaum, Elie, 1978. "Testing neoclassical production theory," Journal of Econometrics, Elsevier, vol. 7(1), pages 87-102, February.
    28. Schmidt, Peter, 1988. "Estimation of a fixed-effect Cobb-Douglas system using panel data," Journal of Econometrics, Elsevier, vol. 37(3), pages 361-380, March.
    29. Timothy J. Coelli & D.S. Prasada Rao & Christopher J. O’Donnell & George E. Battese, 2005. "An Introduction to Efficiency and Productivity Analysis," Springer Books, Springer, edition 0, number 978-0-387-25895-9, November.
    30. Hanoch, Giora, 1975. "The Elasticity of Scale and the Shape of Average Costs," American Economic Review, American Economic Association, vol. 65(3), pages 492-497, June.
    31. Berndt, Ernst R. & Christensen, Laurits R., 1973. "The translog function and the substitution of equipment, structures, and labor in U.S. manufacturing 1929-68," Journal of Econometrics, Elsevier, vol. 1(1), pages 81-113, March.
    32. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    33. Bauer, Paul W., 1990. "Recent developments in the econometric estimation of frontiers," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 39-56.
    34. Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
    35. Kumbhakar, Subal C. & Wang, Hung-Jen, 2006. "Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis," Journal of Econometrics, Elsevier, vol. 134(2), pages 317-340, October.
    36. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    37. Kopp, Raymond J. & Diewert, W. Erwin, 1982. "The decomposition of frontier cost function deviations into measures of technical and allocative efficiency," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 319-331, August.
    Full references (including those not matched with items on IDEAS)

    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. Tung Liu, 2020. "Measuring Technical, Allocative inefficiency, and Cost Inefficiency by Applying Duality Theory," Working Papers 202001, Ball State University, Department of Economics, revised Jun 2020.
    2. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    3. Kumbhakar, Subal C. & Wang, Hung-Jen, 2006. "Estimation of technical and allocative inefficiency: A primal system approach," Journal of Econometrics, Elsevier, vol. 134(2), pages 419-440, October.
    4. Atkinson, Scott E. & Dorfman, Jeffrey H., 2006. "Chasing Absolute Cost and Profit Savings in a World of Relative Inefficiency," 2006 Annual meeting, July 23-26, Long Beach, CA 21058, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    5. Tsionas, Efthymios & Kumbhakar, Subal, 2006. "Estimation of Technical and Allocative Inefficiencies in a Cost System: An Exact Maximum Likelihood Approach," MPRA Paper 20173, University Library of Munich, Germany.
    6. Wang, Hung-Jen, 2006. "Stochastic frontier models," MPRA Paper 31079, University Library of Munich, Germany.
    7. 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.
    8. Brissimis, Sophocles N. & Delis, Manthos D. & Tsionas, Efthymios G., 2010. "Technical and allocative efficiency in European banking," European Journal of Operational Research, Elsevier, vol. 204(1), pages 153-163, July.
    9. Gian Carlo Scarsi, 1999. "Local Electricity Distribution in Italy: Comparative Efficiency Analysis and Methodological Cross-Checking," Working Papers 1999.16, Fondazione Eni Enrico Mattei.
    10. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 126(2), pages 355-384, June.
    11. Lai, Hung-pin & Kumbhakar, Subal C., 2019. "Technical and allocative efficiency in a panel stochastic production frontier system model," European Journal of Operational Research, Elsevier, vol. 278(1), pages 255-265.
    12. Resti, Andrea, 1997. "Evaluating the cost-efficiency of the Italian Banking System: What can be learned from the joint application of parametric and non-parametric techniques," Journal of Banking & Finance, Elsevier, vol. 21(2), pages 221-250, February.
    13. Giannis Karagiannis & Stelios Katranidis & Vangelis Tzouvelekas, 1999. "Measuring Productive Efficiency of Seabass and Seabream Farms in Greece," Working Papers 9911, University of Crete, Department of Economics.
    14. Kumbhakar, Subal C. & Tsionas, Mike G., 2020. "On the estimation of technical and allocative efficiency in a panel stochastic production frontier system model: Some new formulations and generalizations," European Journal of Operational Research, Elsevier, vol. 287(2), pages 762-775.
    15. Lundgren, Tommy & Marklund, Per-Olov & Zhang, Shanshan, 2016. "Industrial energy demand and energy efficiency – Evidence from Sweden," Resource and Energy Economics, Elsevier, vol. 43(C), pages 130-152.
    16. Karagiannis, Giannis & Tzouvelekas, Vangelis, 2001. "Self-Dual Stochastic Production Frontiers and Decomposition of Output Growth: The Case of Olive-Growing Farms in Greece," Agricultural and Resource Economics Review, Cambridge University Press, vol. 30(2), pages 168-178, October.
    17. William C. Horrace & Yulong Wang, 2022. "Nonparametric tests of tail behavior in stochastic frontier models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 537-562, April.
    18. Juan Aparicio & José L. Zofío, 2017. "Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach," Journal of Productivity Analysis, Springer, vol. 48(2), pages 133-146, December.
    19. Amsler, Christine & Prokhorov, Artem & Schmidt, Peter, 2016. "Endogeneity in stochastic frontier models," Journal of Econometrics, Elsevier, vol. 190(2), pages 280-288.
    20. Martin, Juan Carlos & Voltes-Dorta, Augusto, 2007. "Marginal Cost Estimations In Airports. Multiproductive Cost Functions And Stochastic Frontiers: An International Airports Case Study," 48th Annual Transportation Research Forum, Boston, Massachusetts, March 15-17, 2007 207931, Transportation Research Forum.

    More about this item

    Keywords

    Cost inefficiency; Technical inefficiency; Allocative inefficiency; Duality theory;
    All these keywords.

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

    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:ecmode:v:99:y:2021:i:c:s0264999321000468. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/30411 .

    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.