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

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 eff...

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Bibliographic Details
Published in:Journal of banking & finance 2010-07, Vol.34 (7), p.1472-1483
Main Authors: Portela, Maria C.A.S., Thanassoulis, Emmanuel
Format: Article
Language:English
Subjects:
Bank branches
Bank management
Bank operations
Banks
Branch banking
Comparative analysis
DEA
Directional distance functions
Directional distance functions Negative data in DEA Malmquist indices Luenberger indicators Meta-frontier Bank branches DEA
Efficiency
Financial economics
Indexes
Luenberger indicators
Malmquist indices
Meta-frontier
Negative data in DEA
Performers
Productivity
Productivity measurement
Studies
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Summary: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.
ISSN:0378-4266
1872-6372
DOI:10.1016/j.jbankfin.2010.01.004