IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v251y2016i1p2-21.html
   My bibliography  Save this article

Stochastic Data Envelopment Analysis—A review

Author

Listed:
  • Olesen, Ole B.
  • Petersen, Niels Christian

Abstract

This paper provides a review of stochastic Data Envelopment Analysis (DEA). We discuss extensions of deterministic DEA in three directions: (i) deviations from the deterministic frontier are modeled as stochastic variables, (ii) random noise in terms of measurement errors, sample noise, and specification errors is made an integral part of the model, and (iii) the frontier is stochastic as is the underlying Production Possibility Set (PPS).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:251:y:2016:i:1:p:2-21
    DOI: 10.1016/j.ejor.2015.07.058
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715007134
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.07.058?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. Gong, Byeong-Ho & Sickles, Robin C., 1992. "Finite sample evidence on the performance of stochastic frontiers and data envelopment analysis using panel data," Journal of Econometrics, Elsevier, vol. 51(1-2), pages 259-284.
    2. John Ruggiero, 2004. "Data envelopment analysis with stochastic data," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(9), pages 1008-1012, September.
    3. Timo Kuosmanen & Andrew Johnson & Antti Saastamoinen, 2015. "Stochastic Nonparametric Approach to Efficiency Analysis: A Unified Framework," International Series in Operations Research & Management Science, in: Joe Zhu (ed.), Data Envelopment Analysis, edition 127, chapter 7, pages 191-244, Springer.
    4. Bădin, Luiza & Daraio, Cinzia & Simar, Léopold, 2012. "How to measure the impact of environmental factors in a nonparametric production model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 818-833.
    5. 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).
    6. W. Cooper & C. Lovell, 2011. "History lessons," Journal of Productivity Analysis, Springer, vol. 36(2), pages 193-200, October.
    7. Subhash C. Ray & Subal C. Kumbhakar & Pami Dua (ed.), 2015. "Benchmarking for Performance Evaluation," Springer Books, Springer, edition 127, number 978-81-322-2253-8, November.
    8. William Cooper & Zhimin Huang & Vedran Lelas & Susan Li & Ole Olesen, 1998. "Chance Constrained Programming Formulations for Stochastic Characterizations of Efficiency and Dominance in DEA," Journal of Productivity Analysis, Springer, vol. 9(1), pages 53-79, January.
    9. Léopold Simar, 2007. "How to improve the performances of DEA/FDH estimators in the presence of noise?," Journal of Productivity Analysis, Springer, vol. 28(3), pages 183-201, December.
    10. Kuosmanen, Timo & Saastamoinen, Antti & Sipiläinen, Timo, 2013. "What is the best practice for benchmark regulation of electricity distribution? Comparison of DEA, SFA and StoNED methods," Energy Policy, Elsevier, vol. 61(C), pages 740-750.
    11. Charnes, A. & Cooper, W. W. & Huang, Z. M. & Sun, D. B., 1990. "Polyhedral Cone-Ratio DEA Models with an illustrative application to large commercial banks," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 73-91.
    12. 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.
    13. R D Banker & K Kotarac & L Neralić, 2015. "Sensitivity and stability in stochastic data envelopment analysis," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 134-147, January.
    14. Hall P. & Simar L., 2002. "Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 523-534, June.
    15. Wei, Guiwu & Chen, Jian & Wang, Jiamin, 2014. "Stochastic efficiency analysis with a reliability consideration," Omega, Elsevier, vol. 48(C), pages 1-9.
    16. Bharat Sarath & Ajay Maindiratta, 1997. "On the Consistency of Maximum Likelihood Estimation of Monotone and Concave Production Frontiers," Journal of Productivity Analysis, Springer, vol. 8(3), pages 239-246, August.
    17. Hatami-Marbini, Adel & Emrouznejad, Ali & Tavana, Madjid, 2011. "A taxonomy and review of the fuzzy data envelopment analysis literature: Two decades in the making," European Journal of Operational Research, Elsevier, vol. 214(3), pages 457-472, November.
    18. Timo Kuosmanen, 2008. "Representation theorem for convex nonparametric least squares," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 308-325, July.
    19. 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.
    20. SIMAR , Léopold, 1995. "Aspects of Statistical Analysis in DEA-Type Frontier Models," LIDAM Discussion Papers CORE 1995061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    21. 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.
    22. O. Olesen, 2006. "Comparing and Combining Two Approaches for Chance Constrained DEA," Journal of Productivity Analysis, Springer, vol. 26(2), pages 103-119, October.
    23. Meeusen, Wim & van den Broeck, Julien, 1977. "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(2), pages 435-444, June.
    24. Xiaohong Chen & Norman R. Swanson (ed.), 2013. "Recent Advances and Future Directions in Causality, Prediction, and Specification Analysis," Springer Books, Springer, edition 127, number 978-1-4614-1653-1, November.
    25. Léopold Simar & Paul Wilson, 2011. "Two-stage DEA: caveat emptor," Journal of Productivity Analysis, Springer, vol. 36(2), pages 205-218, October.
    26. Simar, Leopold & Wilson, Paul W., 1999. "Estimating and bootstrapping Malmquist indices," European Journal of Operational Research, Elsevier, vol. 115(3), pages 459-471, June.
    27. Banker, Rajiv D. & Gadh, Vandana M. & Gorr, Wilpen L., 1993. "A Monte Carlo comparison of two production frontier estimation methods: Corrected ordinary least squares and data envelopment analysis," European Journal of Operational Research, Elsevier, vol. 67(3), pages 332-343, June.
    28. Ondrich, Jan & Ruggiero, John, 2001. "Efficiency measurement in the stochastic frontier model," European Journal of Operational Research, Elsevier, vol. 129(2), pages 434-442, March.
    29. Léopold Simar & Paul W. Wilson, 1998. "Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models," Management Science, INFORMS, vol. 44(1), pages 49-61, January.
    30. H. David Sherman & Joe Zhu, 2006. "Service Productivity Management," Springer Books, Springer, number 978-0-387-33231-4, November.
    31. Leopold Simar & Paul Wilson, 2010. "Inferences from Cross-Sectional, Stochastic Frontier Models," Econometric Reviews, Taylor & Francis Journals, vol. 29(1), pages 62-98.
    32. Sueyoshi, Toshiyuki, 2000. "Stochastic DEA for restructure strategy: an application to a Japanese petroleum company," Omega, Elsevier, vol. 28(4), pages 385-398, August.
    33. Korostelev, A. P. & Simar, L. & Tsybakov, A. B., 1995. "Estimation of monotone boundaries," LIDAM Reprints CORE 1178, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    34. Simar, Leopold & Wilson, Paul W., 2002. "Non-parametric tests of returns to scale," European Journal of Operational Research, Elsevier, vol. 139(1), pages 115-132, May.
    35. Andrew L. Johnson & Timo Kuosmanen, 2015. "An Introduction to CNLS and StoNED Methods for Efficiency Analysis: Economic Insights and Computational Aspects," Springer Books, in: Subhash C. Ray & Subal C. Kumbhakar & Pami Dua (ed.), Benchmarking for Performance Evaluation, edition 127, chapter 0, pages 117-186, Springer.
    36. Wang, Yongqiao & Wang, Shouyang & Dang, Chuangyin & Ge, Wenxiu, 2014. "Nonparametric quantile frontier estimation under shape restriction," European Journal of Operational Research, Elsevier, vol. 232(3), pages 671-678.
    37. O. B. Olesen & N. C. Petersen, 1995. "Chance Constrained Efficiency Evaluation," Management Science, INFORMS, vol. 41(3), pages 442-457, March.
    38. Rajiv D. Banker & Srikant M. Datar & Chris F. Kemerer, 1991. "A Model to Evaluate Variables Impacting the Productivity of Software Maintenance Projects," Management Science, INFORMS, vol. 37(1), pages 1-18, January.
    39. R. D. Banker & A. Charnes & W. W. Cooper, 1984. "Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis," Management Science, INFORMS, vol. 30(9), pages 1078-1092, September.
    40. Thompson, Russell G. & Langemeier, Larry N. & Lee, Chih-Tah & Lee, Euntaik & Thrall, Robert M., 1990. "The role of multiplier bounds in efficiency analysis with application to Kansas farming," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 93-108.
    41. Eskelinen, Juha & Kuosmanen, Timo, 2013. "Intertemporal efficiency analysis of sales teams of a bank: Stochastic semi-nonparametric approach," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5163-5175.
    42. 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.
    43. Rajiv D. Banker, 1993. "Maximum Likelihood, Consistency and Data Envelopment Analysis: A Statistical Foundation," Management Science, INFORMS, vol. 39(10), pages 1265-1273, October.
    44. Timo Kuosmanen & Mika Kortelainen, 2012. "Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints," Journal of Productivity Analysis, Springer, vol. 38(1), pages 11-28, 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. 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.
    2. Quaranta, Anna Grazia & Raffoni, Anna & Visani, Franco, 2018. "A multidimensional approach to measuring bank branch efficiency," European Journal of Operational Research, Elsevier, vol. 266(2), pages 746-760.
    3. 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.
    4. 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.
    5. 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.
    6. Julia Schaefer & Marcel Clermont, 2018. "Stochastic non-smooth envelopment of data for multi-dimensional output," Journal of Productivity Analysis, Springer, vol. 50(3), pages 139-154, December.
    7. Christopher F. Parmeter & Valentin Zelenyuk, 2019. "Combining the Virtues of Stochastic Frontier and Data Envelopment Analysis," Operations Research, INFORMS, vol. 67(6), pages 1628-1658, November.
    8. Amir Moradi-Motlagh & Ali Emrouznejad, 2022. "The origins and development of statistical approaches in non-parametric frontier models: a survey of the first two decades of scholarly literature (1998–2020)," Annals of Operations Research, Springer, vol. 318(1), pages 713-741, November.
    9. 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.
    10. Kuosmanen, Timo & Johnson, Andrew, 2017. "Modeling joint production of multiple outputs in StoNED: Directional distance function approach," European Journal of Operational Research, Elsevier, vol. 262(2), pages 792-801.
    11. Banker, Rajiv & Natarajan, Ram & Zhang, Daqun, 2019. "Two-stage estimation of the impact of contextual variables in stochastic frontier production function models using Data Envelopment Analysis: Second stage OLS versus bootstrap approaches," European Journal of Operational Research, Elsevier, vol. 278(2), pages 368-384.
    12. Emrouznejad, Ali & De Witte, Kristof, 2010. "COOPER-framework: A unified process for non-parametric projects," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1573-1586, December.
    13. Luis R. Murillo‐Zamorano, 2004. "Economic Efficiency and Frontier Techniques," Journal of Economic Surveys, Wiley Blackwell, vol. 18(1), pages 33-77, February.
    14. Vincent Charles & Ioannis E. Tsolas & Tatiana Gherman, 2018. "Satisficing data envelopment analysis: a Bayesian approach for peer mining in the banking sector," Annals of Operations Research, Springer, vol. 269(1), pages 81-102, October.
    15. Thanh Ngo & Kan Wai Hong Tsui, 2022. "Estimating the confidence intervals for DEA efficiency scores of Asia-Pacific airlines," Operational Research, Springer, vol. 22(4), pages 3411-3434, September.
    16. 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.
    17. Mark Andor & Frederik Hesse, 2014. "The StoNED age: the departure into a new era of efficiency analysis? A monte carlo comparison of StoNED and the “oldies” (SFA and DEA)," Journal of Productivity Analysis, Springer, vol. 41(1), pages 85-109, February.
    18. 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.
    19. Liu, John S. & Lu, Louis Y.Y. & Lu, Wen-Min, 2016. "Research fronts in data envelopment analysis," Omega, Elsevier, vol. 58(C), pages 33-45.
    20. Kittelsen,S.A.C., 1999. "Monte Carlo simulations of DEA efficiency measures and hypothesis tests," Memorandum 09/1999, Oslo University, Department of Economics.

    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:251:y:2016:i:1:p:2-21. 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/eor .

    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.