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Handling estimated proportions in public sector data envelopment analysis

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Periodically data envelopment analysis (DEA) is conducted on values that include estimated proportions, such as defect, satisfaction, mortality, or adverse event rates computed from samples. This occurs frequently in healthcare and public sector analysis where proportions frequently are estimated from partial samples. These estimates can produce statistically biased and variable estimates of DEA results, even as sample sizes become fairly large. This paper discusses several approaches to these problems, including Monte Carlo (MC), bootstrapping, chance constrained, and optimistic/pessimistic DEA methods. The performance of each method was compared using previously published data for fourteen Florida juvenile delinquency programs whose two of three inputs and one output were proportions. The impact of sample size and number of estimated rates also were investigated. In most cases, no statistically significant differences were found between the true DEA scores and the midpoints of optimistic/pessimistic, MC, and bootstrap intervals, the latter two after bias correction. True DEA results are strongly correlated with those produced by the MC (r=0.9865, p>0.001), chance constraint (r=0.9536,p>0.001), bootstrapping (r=0.9368,p>0.001), and optimistic/pessimistic (r=0.6799,p>0.001) approaches. While all methods perform fairly well, the MC approach tends to produce slightly better results and be fairly easy to implement. Copyright Springer Science+Business Media, LLC 2014

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  • Mehmet Ceyhan & James Benneyan, 2014. "Handling estimated proportions in public sector data envelopment analysis," Annals of Operations Research, Springer, vol. 221(1), pages 107-132, October.
    • Handle: RePEc:spr:annopr:v:221:y:2014:i:1:p:107-132:10.1007/s10479-011-1007-z
    DOI: 10.1007/s10479-011-1007-z
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    Cited by:

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    2. Panagiotis Mitropoulos & Ioannis Mitropoulos, 2020. "Performance evaluation of retail banking services: Is there a trade‐off between production and quality?," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 41(7), pages 1237-1250, October.
    3. Sandiford, P. & Vivas Consuelo, D. & Rouse, P. & Bramley, D., 2018. "The trade-off between equity and efficiency in population health gain: Making it real," Social Science & Medicine, Elsevier, vol. 212(C), pages 136-144.
    4. 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.
    5. Polcyn, Jan, 2017. "Edukacja jako dobro publiczne - próba kwantyfikacji [Education as a public good – an attempt at quantification]," MPRA Paper 76606, University Library of Munich, Germany, revised 2017.

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