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Malmquist-type indices in the presence of negative data: An application to bank branches

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  • Portela, Maria C.A.S.
  • Thanassoulis, Emmanuel

Abstract

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

Suggested Citation

  • Portela, Maria C.A.S. & Thanassoulis, Emmanuel, 2010. "Malmquist-type indices in the presence of negative data: An application to bank branches," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1472-1483, July.
  • Handle: RePEc:eee:jbfina:v:34:y:2010:i:7:p:1472-1483
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    3. Aparicio, Juan & Pastor, Jesus T. & Vidal, Fernando, 2016. "The directional distance function and the translation invariance property," Omega, Elsevier, vol. 58(C), pages 1-3.
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    9. Sahoo, Biresh K. & Mehdiloozad, Mahmood & Tone, Kaoru, 2014. "Cost, revenue and profit efficiency measurement in DEA: A directional distance function approach," European Journal of Operational Research, Elsevier, vol. 237(3), pages 921-931.
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    18. Giraleas, Dimitris & Emrouznejad, Ali & Thanassoulis, Emmanuel, 2012. "Selecting between different productivity measurement approaches: An application using EU KLEMS data," MPRA Paper 37965, University Library of Munich, Germany.
    19. George Assaf, A. & Barros, Carlos P. & Matousek, Roman, 2011. "Productivity and efficiency analysis of Shinkin banks: Evidence from bootstrap and Bayesian approaches," Journal of Banking & Finance, Elsevier, vol. 35(2), pages 331-342, February.
    20. Alexakis, Christos & Izzeldin, Marwan & Johnes, Jill & Pappas, Vasileios, 2019. "Performance and productivity in Islamic and conventional banks: Evidence from the global financial crisis," Economic Modelling, Elsevier, vol. 79(C), pages 1-14.
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    22. Paradi, Joseph C. & Zhu, Haiyan, 2013. "A survey on bank branch efficiency and performance research with data envelopment analysis," Omega, Elsevier, vol. 41(1), pages 61-79.
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    24. Walheer, Barnabé, 2019. "Malmquist productivity index for multi-output producers: An application to electricity generation plants," Socio-Economic Planning Sciences, Elsevier, vol. 65(C), pages 76-88.
    25. Jia-Ching Juo & Yu-Hui Lin & Tsai-Chia Chen, 2015. "Productivity change of Taiwanese farmers’ credit unions: a nonparametric metafrontier Malmquist–Luenberger productivity indicator," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(1), pages 125-147, March.

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