IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v121y2009i1p203-211.html
   My bibliography  Save this article

A DEA estimation of a lower bound for firms' allocative efficiency without information on price data

Author

Listed:
  • Leleu, Hervé
  • Briec, Walter

Abstract

In this paper, we estimate a lower bound for the sum of firms' allocative efficiencies in the absence of information on prices. For this purpose, we only estimate technical efficiency at both the firm and the industry level using a directional distance function and choosing a relevant direction. Our result relies on the decomposition of overall inefficiency into technical and allocative inefficiency at both the firm and the industry level. The convexity of a technology induces a transfer from both total technical inefficiency and part of allocative inefficiency at the firm level to technical inefficiency solely at the industry level. The remaining firms' allocative inefficiency could be counted at the industry level. Hence, the difference between technical inefficiencies at both levels can be interpreted as a lower bound for the sum of allocative inefficiency in the industry. We show how to implement this bound in a DEA framework.

Suggested Citation

  • Leleu, Hervé & Briec, Walter, 2009. "A DEA estimation of a lower bound for firms' allocative efficiency without information on price data," International Journal of Production Economics, Elsevier, vol. 121(1), pages 203-211, September.
    • Handle: RePEc:eee:proeco:v:121:y:2009:i:1:p:203-211
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925-5273(09)00158-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. repec:bla:scandj:v:94:y:1992:i:4:p:599-608 is not listed on IDEAS
    2. Cherchye, Laurens & Kuosmanen, Timo & Post, Thierry, 2002. "Non-parametric production analysis in non-competitive environments," International Journal of Production Economics, Elsevier, vol. 80(3), pages 279-294, December.
    3. Walter Briec & Benoit Dervaux & Hervé Leleu, 2003. "Aggregation of Directional Distance Functions and Industrial Efficiency," Journal of Economics, Springer, vol. 79(3), pages 237-261, July.
    4. Ray, Subhash C. & Chen, Lei & Mukherjee, Kankana, 2008. "Input price variation across locations and a generalized measure of cost efficiency," International Journal of Production Economics, Elsevier, vol. 116(2), pages 208-218, December.
    5. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
    6. Rodriguez-Alvarez, Ana & Fernandez-Blanco, Victor & Lovell, C. A. Knox, 2004. "Allocative inefficiency and its cost:: The case of Spanish public hospitals," International Journal of Production Economics, Elsevier, vol. 92(2), pages 99-111, November.
    7. Briec, Walter & Comes, Christine & Kerstens, Kristiaan, 2006. "Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results," International Journal of Production Economics, Elsevier, vol. 103(1), pages 48-63, September.
    8. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    9. Briec, W. & Lemaire, B., 1999. "Technical efficiency and distance to a reverse convex set," European Journal of Operational Research, Elsevier, vol. 114(1), pages 178-187, April.
    10. Rodriguez-Alvarez, Ana & Tovar, Beatriz & Trujillo, Lourdes, 2007. "Firm and time varying technical and allocative efficiency: An application to port cargo handling firms," International Journal of Production Economics, Elsevier, vol. 109(1-2), pages 149-161, September.
    11. Ylvinger, Svante, 2000. "Industry performance and structural efficiency measures: Solutions to problems in firm models," European Journal of Operational Research, Elsevier, vol. 121(1), pages 164-174, February.
    12. W. Briec, 1997. "A Graph-Type Extension of Farrell Technical Efficiency Measure," Journal of Productivity Analysis, Springer, vol. 8(1), pages 95-110, March.
    13. 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.
    14. Halme, Merja & Joro, Tarja & Koivu, Matti, 2002. "Dealing with interval scale data in data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 137(1), pages 22-27, February.
    15. Chambers, Robert G. & Chung, Yangho & Fare, Rolf, 1996. "Benefit and Distance Functions," Journal of Economic Theory, Elsevier, vol. 70(2), pages 407-419, August.
    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. Aparicio, Juan & Pastor, Jesus T. & Ray, Subhash C., 2013. "An overall measure of technical inefficiency at the firm and at the industry level: The ‘lost profit on outlay’," European Journal of Operational Research, Elsevier, vol. 226(1), pages 154-162.
    2. Arnaud Abad & Rabaozafy Louisa Andriamasy & Walter Briec, 2018. "Surplus measures and luenberger Hicks–Moorsteen productivity indicator," Journal of Economics, Springer, vol. 125(3), pages 279-308, November.
    3. Fang, Lei & Li, Hecheng, 2013. "A comment on “solving the puzzles of structural efficiency”," European Journal of Operational Research, Elsevier, vol. 230(2), pages 444-446.
    4. Färe, Rolf & Grosskopf, Shawna & Karagiannis, Giannis, 2018. "On technical inefficiency indicators at the industry level," International Journal of Production Economics, Elsevier, vol. 196(C), pages 333-334.
    5. Francesco Sandulli & José Fernández-Menéndez & Antonio Rodríguez-Duarte & José López-Sánchez, 2012. "The productivity payoff of information technology in multimarket SMEs," Small Business Economics, Springer, vol. 39(1), pages 99-117, July.
    6. Wang, Ying-Ming & Chin, Kwai-Sang, 2010. "Some alternative models for DEA cross-efficiency evaluation," International Journal of Production Economics, Elsevier, vol. 128(1), pages 332-338, November.
    7. Juan Aparicio & Jesus T. Pastor & Subhash Ray, 2012. "An Overall Measure of Technical Inefficiency at the Firm and at the Industrial Level: The 'Lost Return on the Dollar' Revisited," Working papers 2012-02, University of Connecticut, Department of Economics.
    8. Rolf Färe & Giannis Karagiannis, 2022. "Aggregation and decomposition of Farrell efficiencies," Operational Research, Springer, vol. 22(5), pages 5675-5683, November.
    9. Mahlberg, Bernhard & Sahoo, Biresh K., 2011. "Radial and non-radial decompositions of Luenberger productivity indicator with an illustrative application," International Journal of Production Economics, Elsevier, vol. 131(2), pages 721-726, June.
    10. Walheer, Barnabe & Hudik, Marek, 2019. "Reallocation of resources in multidivisional firms: A nonparametric approach," International Journal of Production Economics, Elsevier, vol. 214(C), pages 196-205.

    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. Briec, Walter & Dumas, Audrey & Kerstens, Kristiaan & Stenger, Agathe, 2022. "Generalised commensurability properties of efficiency measures: Implications for productivity indicators," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1481-1492.
    2. Timo Kuosmanen & Mika Kortelainen & Timo Sipiläinen & Laurens Cherchye, 2005. "Firm and Industry Level Profit Efficiency Analysis Under Incomplete Price Data: A Nonparametric Approach based on Absolute and Uniform Shadow Prices," Microeconomics 0509011, University Library of Munich, Germany.
    3. Carlos Pestana Barros & Guglielmo Maria Caporale & Luis A. Gil-Alana, 2007. "Identification of Segments of European Banks with a Latent Class Frontier Model," CESifo Working Paper Series 2110, CESifo.
    4. Briec, Walter & Fukuyama, Hirofumi & Ravelojaona, Paola, 2021. "Exponential distance function and duality theory," European Journal of Operational Research, Elsevier, vol. 293(3), pages 1002-1014.
    5. Juan Aparicio & José L. Zofío & Jesús T. Pastor, 2023. "Decomposing Economic Efficiency into Technical and Allocative Components: An Essential Property," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 98-129, April.
    6. Kuosmanen, Timo & Kortelainen, Mika & Sipiläinen, Timo & Cherchye, Laurens, 2010. "Firm and industry level profit efficiency analysis using absolute and uniform shadow prices," European Journal of Operational Research, Elsevier, vol. 202(2), pages 584-594, April.
    7. Bogetoft, Peter & Leth Hougaard, Jens, 2004. "Super efficiency evaluations based on potential slack," European Journal of Operational Research, Elsevier, vol. 152(1), pages 14-21, January.
    8. Ravelojaona, Paola, 2019. "On constant elasticity of substitution – Constant elasticity of transformation Directional Distance Functions," European Journal of Operational Research, Elsevier, vol. 272(2), pages 780-791.
    9. Tovar, Beatriz & Wall, Alan, 2015. "Can ports increase traffic while reducing inputs? Technical efficiency of Spanish Port Authorities using a directional distance function approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 71(C), pages 128-140.
    10. Briec, Walter & Mussard, Stéphane, 2014. "Efficient firm groups: Allocative efficiency in cooperative games," European Journal of Operational Research, Elsevier, vol. 239(1), pages 286-296.
    11. Briec, Walter & Mussard, Stéphane, 2020. "Improvement of technical efficiency of firm groups," European Journal of Operational Research, Elsevier, vol. 283(3), pages 991-1001.
    12. W. Briec & K. Kerstens, 2009. "Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 55-73, April.
    13. Jean‐Philippe Boussemart & Walter Briec & Kristiaan Kerstens & Jean‐Christophe Poutineau, 2003. "Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration," Bulletin of Economic Research, Wiley Blackwell, vol. 55(4), pages 391-405, October.
    14. Guironnet, J.-P. & Peypoch, N., 2007. "Human capital allocation and overeducation: A measure of French productivity (1987, 1999)," Economic Modelling, Elsevier, vol. 24(3), pages 398-410, May.
    15. Briec, Walter & Comes, Christine & Kerstens, Kristiaan, 2006. "Temporal technical and profit efficiency measurement: Definitions, duality and aggregation results," International Journal of Production Economics, Elsevier, vol. 103(1), pages 48-63, September.
    16. Beatriz Tovar & Alan Wall, 2017. "Dynamic Cost Efficiency in Port Infrastructure Using a Directional Distance Function: Accounting for the Adjustment of Quasi-Fixed Inputs Over Time," Transportation Science, INFORMS, vol. 51(1), pages 296-304, February.
    17. Hien Thu Pham & Antonio Peyrache, 2015. "Industry Inefficiency Measures: A Unifying Approximation Proposition," CEPA Working Papers Series WP102015, School of Economics, University of Queensland, Australia.
    18. Tsionas, Mike & Parmeter, Christopher F. & Zelenyuk, Valentin, 2023. "Bayesian Artificial Neural Networks for frontier efficiency analysis," Journal of Econometrics, Elsevier, vol. 236(2).
    19. Jesus Pastor & C. Lovell & Juan Aparicio, 2012. "Families of linear efficiency programs based on Debreu’s loss function," Journal of Productivity Analysis, Springer, vol. 38(2), pages 109-120, October.
    20. Mondelaers, Koen & Kuosmanen, Timo & Van Passel, Steven & Buysse, Jeroen & Lauwers, Ludwig H. & Van Huylenbroeck, Guido, 2011. "Sustainable Efficiency Of Firms When New Sustainability Targets Are Introduced," 2011 International Congress, August 30-September 2, 2011, Zurich, Switzerland 114633, European Association of Agricultural Economists.

    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:proeco:v:121:y:2009:i:1:p:203-211. 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/ijpe .

    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.