IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v281y2020i2p439-448.html
   My bibliography  Save this article

A coherent approach to Bayesian Data Envelopment Analysis

Author

Listed:
  • Tsionas, Mike G.

Abstract

Mitropoulos et al. (2015) suggested the use of a Bayesian approach in Data Envelopment Analysis (DEA) which can be used to obtain posterior distributions of efficiency scores. In this paper, we avoid their assumption that alternative data sets are simulated from the predictive distribution obtained from their simple data generating process of a normal distribution for the data. The new approach has two significant advantages. First, the posterior proposed in this paper is coherent or principled in the sense that it is consistent with the DEA formulation. Second, and perhaps surprisingly, it is not necessary to solve linear programming problems for each observation in the sample. Bayesian inference is organized around Markov Chain Monte Carlo techniques that can be implemented quite easily. We conduct extensive Monte Carlo experiments to investigate the finite-sample properties of the new approach. We also provide an application to a large U.S banking data set. The sample is an unbalanced panel of US banks with 2,397 bank–year observations for 285 banks. The main purpose of the analysis is to compare distributions of efficiency scores. Relative to DEA, Bayes DEA provides different efficiency scores and their sample distribution has significantly less probability concentration around unity. The comparison with bootstrap-DEA shows that results from Bayes DEA are in broad agreement.

Suggested Citation

  • Tsionas, Mike G., 2020. "A coherent approach to Bayesian Data Envelopment Analysis," European Journal of Operational Research, Elsevier, vol. 281(2), pages 439-448.
  • Handle: RePEc:eee:ejores:v:281:y:2020:i:2:p:439-448
    DOI: 10.1016/j.ejor.2019.08.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037722171930709X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Leopold Simar & Paul Wilson, 2000. "A general methodology for bootstrapping in non-parametric frontier models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(6), pages 779-802.
    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. Tsionas, Efthymios G. & Papadakis, Emmanuel N., 2010. "A Bayesian approach to statistical inference in stochastic DEA," Omega, Elsevier, vol. 38(5), pages 309-314, October.
    4. Mitropoulos, Panagiotis & Talias, Μichael A. & Mitropoulos, Ioannis, 2015. "Combining stochastic DEA with Bayesian analysis to obtain statistical properties of the efficiency scores: An application to Greek public hospitals," European Journal of Operational Research, Elsevier, vol. 243(1), pages 302-311.
    5. Gondzio, Jacek, 1995. "HOPDM (version 2.12) -- A fast LP solver based on a primal-dual interior point method," European Journal of Operational Research, Elsevier, vol. 85(1), pages 221-225, August.
    6. Robert L. Smith, 1984. "Efficient Monte Carlo Procedures for Generating Points Uniformly Distributed over Bounded Regions," Operations Research, INFORMS, vol. 32(6), pages 1296-1308, December.
    7. Tsionas, Efthymios G., 2003. "Combining DEA and stochastic frontier models: An empirical Bayes approach," European Journal of Operational Research, Elsevier, vol. 147(3), pages 499-510, June.
    8. Emir Malikov & Subal C. Kumbhakar & Mike G. Tsionas, 2016. "A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1407-1429, November.
    9. Claude J. P. Bélisle & H. Edwin Romeijn & Robert L. Smith, 1993. "Hit-and-Run Algorithms for Generating Multivariate Distributions," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 255-266, May.
    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. Martin Pincus, 1970. "Letter to the Editor—A Monte Carlo Method for the Approximate Solution of Certain Types of Constrained Optimization Problems," Operations Research, INFORMS, vol. 18(6), pages 1225-1228, December.
    12. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
    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. & 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.

    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. Panagiotis Mitropoulos & Panagiotis D. Zervopoulos & Ioannis Mitropoulos, 0. "Measuring performance in the presence of noisy data with targeted desirable levels: evidence from healthcare units," Annals of Operations Research, Springer, vol. 0, pages 1-30.
    2. Wijesiri, Mahinda & Yaron, Jacob & Meoli, Michele, 2017. "Assessing the financial and outreach efficiency of microfinance institutions: Do age and size matter?," Journal of Multinational Financial Management, Elsevier, vol. 40(C), pages 63-76.
    3. 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.
    4. Zaiwu Gong & Xiaoqing Chen, 2017. "Analysis of Interval Data Envelopment Efficiency Model Considering Different Distribution Characteristics—Based on Environmental Performance Evaluation of the Manufacturing Industry," Sustainability, MDPI, Open Access Journal, vol. 9(12), pages 1-25, November.
    5. Paradi, Joseph C. & Rouatt, Stephen & Zhu, Haiyan, 2011. "Two-stage evaluation of bank branch efficiency using data envelopment analysis," Omega, Elsevier, vol. 39(1), pages 99-109, January.
    6. Casu, Barbara & Girardone, Claudia, 2010. "Integration and efficiency convergence in EU banking markets," Omega, Elsevier, vol. 38(5), pages 260-267, October.
    7. Sebastian Kohl & Jan Schoenfelder & Andreas Fügener & Jens O. Brunner, 2019. "The use of Data Envelopment Analysis (DEA) in healthcare with a focus on hospitals," Health Care Management Science, Springer, vol. 22(2), pages 245-286, June.
    8. Halkos, George & Tzeremes, Nickolaos, 2007. "Examining the relationship between firm internationalization and firm performance: A nonparametric analysis," MPRA Paper 32082, University Library of Munich, Germany.
    9. Halkos, George & Tzeremes, Nickolaos, 2010. "Measuring the effect of virtual mergers on banks’ efficiency levels:A non parametric analysis," MPRA Paper 23696, University Library of Munich, Germany.
    10. Halkos, George E. & Tzeremes, Nickolaos G., 2013. "Estimating the degree of operating efficiency gains from a potential bank merger and acquisition: A DEA bootstrapped approach," Journal of Banking & Finance, Elsevier, vol. 37(5), pages 1658-1668.
    11. Karl-Hans Hartwig & Raimund Scheffler, 2009. "Größenvorteile im deutschen ÖSPV – Eine empirische Analyse," Working Papers 13, Institute of Transport Economics, University of Muenster.
    12. Hung-Tso Lin & Tsung-Yu Chou & Yen-Ting Chen & Yin-Chi Huang, 2014. "Profitability analysis using IDEA–DA framework," Annals of Operations Research, Springer, vol. 223(1), pages 291-308, December.
    13. 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.
    14. Merkert, Rico & Hensher, David A., 2011. "The impact of strategic management and fleet planning on airline efficiency - A random effects Tobit model based on DEA efficiency scores," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(7), pages 686-695, August.
    15. Bernardino Benito & José Solana & María-Rocío Moreno, 2014. "Explaining efficiency in municipal services providers," Journal of Productivity Analysis, Springer, vol. 42(3), pages 225-239, December.
    16. Wijesiri, Mahinda & Yaron, Jacob & Meoli, Michele, 2015. "Performance of microfinance institutions in achieving the poverty outreach and financial sustainability: When age and size matter?," MPRA Paper 69821, University Library of Munich, Germany.
    17. Panagiotis Mitropoulos & Panagiotis D. Zervopoulos & Ioannis Mitropoulos, 2020. "Measuring performance in the presence of noisy data with targeted desirable levels: evidence from healthcare units," Annals of Operations Research, Springer, vol. 294(1), pages 537-566, November.
    18. Franz R. Hahn, 2007. "Determinants of Bank Efficiency in Europe. Assessing Bank Performance Across Markets," WIFO Studies, WIFO, number 31499.
    19. Büschken, Joachim, 2009. "When does data envelopment analysis outperform a naïve efficiency measurement model?," European Journal of Operational Research, Elsevier, vol. 192(2), pages 647-657, January.
    20. 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.

    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:281:y:2020:i:2:p:439-448. 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: (Nithya Sathishkumar). 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 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.

    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.