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A coherent approach to Bayesian Data Envelopment Analysis


  • Tsionas, Mike G.


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

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    References listed on IDEAS

    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.
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    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.
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