IDEAS home Printed from https://ideas.repec.org/p/wsu/wpaper/friesner-1.html
   My bibliography  Save this paper

Inferring the Latent Incidence of Inefficiency from DEA Estimates and Bayesian Priors

Author

Listed:
  • Daniel Friesner
  • Ron Mittelhammer
  • Robert Rosenman

    (School of Economic Sciences, Washington State University)

Abstract

Data envelopment analysis (DEA) is among the most popular empirical tools for measuring cost and productive efficiency. Because DEA is a linear programming technique, establishing formal statistical properties for outcomes is difficult. We show that the incidence of inefficiency within a population of Decision Making Units (DMUs) is a latent variable, with DEA outcomes providing only noisy sample-based categorizations of inefficiency. We then use a Bayesian approach to infer an appropriate posterior distribution for the incidence of inefficient DMUs based on a random sample of DEA outcomes and a prior distribution on the incidence of inefficiency. The methodology applies to both finite and infinite populations, and to sampling DMUs with and without replacement, and accounts for the noise in the DEA characterization of inefficiency within a coherent Bayesian approach to the problem. The result is an appropriately up-scaled, noise-adjusted inference regarding the incidence of inefficiency in a population of DMUs.

Suggested Citation

  • Daniel Friesner & Ron Mittelhammer & Robert Rosenman, 2006. "Inferring the Latent Incidence of Inefficiency from DEA Estimates and Bayesian Priors," Working Papers 2006-8, School of Economic Sciences, Washington State University.
  • Handle: RePEc:wsu:wpaper:friesner-1
    as

    Download full text from publisher

    File URL: http://faculty.ses.wsu.edu/WorkingPapers/WP_2006-8-Friesner.pdf
    File Function: First version, 2006
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. GIJBELS, Irène & MAMMEN, Enno & PARK, Byeong U. & SIMAR, Léopold, 1997. "On estimation of monotone and concave frontier functions," LIDAM Discussion Papers CORE 1997031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Per Andersen & Niels Christian Petersen, 1993. "A Procedure for Ranking Efficient Units in Data Envelopment Analysis," Management Science, INFORMS, vol. 39(10), pages 1261-1264, October.
    3. S Y Sohn & H Choi, 2006. "Random effects logistic regression model for data envelopment analysis with correlated decision making units," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(5), pages 552-560, May.
    4. S Y Sohn, 2006. "Random effects logistic regression model for ranking efficiency in data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(11), pages 1289-1299, November.
    5. Subhash C. Ray, 1991. "Resource-Use Efficiency in Public Schools: A Study of Connecticut Data," Management Science, INFORMS, vol. 37(12), pages 1620-1628, December.
    6. Stanton, Kenneth R., 2002. "Trends in relationship lending and factors affecting relationship lending efficiency," Journal of Banking & Finance, Elsevier, vol. 26(1), pages 127-152, January.
    7. Kneip, Alois & Park, Byeong U. & Simar, Léopold, 1998. "A Note On The Convergence Of Nonparametric Dea Estimators For Production Efficiency Scores," Econometric Theory, Cambridge University Press, vol. 14(6), pages 783-793, December.
    8. Robert Rosenman & Daniel Friesner, 2004. "Scope and scale inefficiencies in physician practices," Health Economics, John Wiley & Sons, Ltd., vol. 13(11), pages 1091-1116, November.
    9. Léopold Simar & Paul Wilson, 1999. "Some Problems with the Ferrier/Hirschberg Bootstrap Idea," Journal of Productivity Analysis, Springer, vol. 11(1), pages 67-80, February.
    10. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    11. Chirikos, Thomas N. & Sear, Alan M., 1994. "Technical efficiency and the competitive behavior of hospitals," Socio-Economic Planning Sciences, Elsevier, vol. 28(4), pages 219-227, December.
    12. C A K Lovell & A P B Rouse, 2003. "Equivalent standard DEA models to provide super-efficiency scores," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(1), pages 101-108, January.
    13. Jeong, Seok-Oh & Park, Byeong U., 2004. "Limit Distribution of Convex-Hull Estimators of Boundaries," Papers 2004,39, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    14. Jati Sengupta, 1998. "The efficiency distribution in a production cost model," Applied Economics, Taylor & Francis Journals, vol. 30(1), pages 125-132.
    15. Chilingerian, Jon A., 1995. "Evaluating physician efficiency in hospitals: A multivariate analysis of best practices," European Journal of Operational Research, Elsevier, vol. 80(3), pages 548-574, February.
    16. Juang, Muh-Guey & Anderson, Gary, 2004. "A Bayesian method on adaptive preventive maintenance problem," European Journal of Operational Research, Elsevier, vol. 155(2), pages 455-473, June.
    17. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
    18. Mickael Lothgren & Magnus Tambour, 1999. "Testing scale efficiency in DEA models: a bootstrapping approach," Applied Economics, Taylor & Francis Journals, vol. 31(10), pages 1231-1237.
    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. Friesner, Daniel & Mittelhammer, Ron & Rosenman, Robert, 2013. "Inferring the incidence of industry inefficiency from DEA estimates," European Journal of Operational Research, Elsevier, vol. 224(2), pages 414-424.
    2. Simar, Leopold & Wilson, Paul W., 2007. "Estimation and inference in two-stage, semi-parametric models of production processes," Journal of Econometrics, Elsevier, vol. 136(1), pages 31-64, January.
    3. R. Amy Puenpatom & Robert Rosenman, 2006. "Efficiency of Thai provincial public hospitals after the introduction of National Health Insurance Program," Working Papers 2006-2, School of Economic Sciences, Washington State University.
    4. Reuben Elan & Verma Bharat Bhushan & Bhat Ramesh, 2001. "Hospital Efficiency: An Empirical Analysis of District and Grant-in-Aid Hospitals in Gujarat," IIMA Working Papers WP2001-07-05, Indian Institute of Management Ahmedabad, Research and Publication Department.
    5. Davtalab-Olyaie, Mostafa & Asgharian, Masoud & Nia, Vahid Partovi, 2019. "Stochastic ranking and dominance in DEA," International Journal of Production Economics, Elsevier, vol. 214(C), pages 125-138.
    6. Alois Kneip & Léopold Simar & Paul Wilson, 2011. "A Computationally Efficient, Consistent Bootstrap for Inference with Non-parametric DEA Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 38(4), pages 483-515, November.
    7. Zervopoulos, Panagiotis & Emrouznejad, Ali & Sklavos, Sokratis, 2019. "A Bayesian approach for correcting bias of data envelopment analysis estimators," MPRA Paper 91886, University Library of Munich, Germany.
    8. Sickles, Robin C. & Song, Wonho & Zelenyuk, Valentin, 2018. "Econometric Analysis of Productivity: Theory and Implementation in R," Working Papers 18-008, Rice University, Department of Economics.
    9. Léopold Simar & Paul W. Wilson, 2015. "Statistical Approaches for Non-parametric Frontier Models: A Guided Tour," International Statistical Review, International Statistical Institute, vol. 83(1), pages 77-110, April.
    10. Chiang Kao & Shiang-Tai Liu, 2022. "Stochastic efficiencies of network production systems with correlated stochastic data: the case of Taiwanese commercial banks," Annals of Operations Research, Springer, vol. 315(2), pages 1151-1174, August.
    11. Kao, Chiang & Liu, Shiang-Tai, 2009. "Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks," European Journal of Operational Research, Elsevier, vol. 196(1), pages 312-322, July.
    12. Andrea Guerrini & Giulia Romano & Bettina Campedelli, 2013. "Economies of Scale, Scope, and Density in the Italian Water Sector: A Two-Stage Data Envelopment Analysis Approach," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(13), pages 4559-4578, October.
    13. Olesen, Ole B. & Petersen, Niels Christian, 2016. "Stochastic Data Envelopment Analysis—A review," European Journal of Operational Research, Elsevier, vol. 251(1), pages 2-21.
    14. Valentin Zelenyuk, 2019. "Data Envelopment Analysis and Business Analytics: The Big Data Challenges and Some Solutions," CEPA Working Papers Series WP072019, School of Economics, University of Queensland, Australia.
    15. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    16. Puig-Junoy, Jaume, 2000. "Partitioning input cost efficiency into its allocative and technical components: an empirical DEA application to hospitals," Socio-Economic Planning Sciences, Elsevier, vol. 34(3), pages 199-218, September.
    17. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    18. Léopold Simar & Paul Wilson, 2011. "Inference by the m out of n bootstrap in nonparametric frontier models," Journal of Productivity Analysis, Springer, vol. 36(1), pages 33-53, August.
    19. Lampe, Hannes W. & Hilgers, Dennis, 2015. "Trajectories of efficiency measurement: A bibliometric analysis of DEA and SFA," European Journal of Operational Research, Elsevier, vol. 240(1), pages 1-21.
    20. Michali, Maria & Emrouznejad, Ali & Dehnokhalaji, Akram & Clegg, Ben, 2023. "Subsampling bootstrap in network DEA," European Journal of Operational Research, Elsevier, vol. 305(2), pages 766-780.

    More about this item

    Keywords

    Data Envelopment Analysis; latent inefficiency; Bayesian inference; Beta priors; posterior incidence of inefficiency;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wsu:wpaper:friesner-1. 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: Danielle Engelhardt (email available below). General contact details of provider: https://edirc.repec.org/data/ecwsuus.html .

    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.