Minimum distance efficiency measure in bank production: A directional slack inefficiency approach

Abstract

In the non-radial efficiency measurement literature, it is common to estimate technical (in)efficiency by maximising weighted slacks primarily from the computational viewpoint. This means that efficiency measures and targets are obtained based on farthest distance projections. However, when the decision making units (DMUs) operate at less than the efficient scale, such modelling approach can be very restrictive. This paper proposes a minimum distance Data Envelopment Analysis (DEA) model in order to evaluate the efficiency of Japanese banking sector over the period 2013–2019. The proposed model is based on Koopmans notion of strong efficiency. When comparing our findings from the minimum distance slack inefficiency model with those against the traditional slack inefficiency model, we find significant differences. These differences are primarily based on the way the benchmark targets have been set in the two methodological frameworks. Finally our finding brings forward the importance and the implications on bank efficiency measurement, when non-feasible targets are set during the bank efficiency evaluation.

Keywords:

• Data envelopment analysis
• minimum/shortest/least distance inefficiency
• slack inefficiency
• banks
• benchmarking

Acknowledgements

We would like to thank the Editor Said Salhi, the Associate Editor and the reviewers for their constructive comments on an earlier version of our manuscript. Any remaining errors are solely the authors’ responsibility.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 It must be noted the minimum distance models are difficult to solve using linear programs.

2 See Remark 1 for the justification and the origin of the “slack” term.

3 Aparicio et al.’s (2018) additive model includes the input-output constraints, $$x_n^{}={\sum }_{j\in \partial (J)}^{}{x}_{nj}^{}{\lambda }_j^{}(n\in N),$$ $$y_m^{}={\sum }_{j\in \partial (J)}^{}{y}_{mj}^{}{\lambda }_j^{}(m\in M).$$ But Eq. (4) does not include these constraints, because these are not necessary due to their redundancy. At the optimum, the convex combinations represent the points on the efficient frontier.

4 The slack inefficiency measure can also be thought of as a generalization of the additive model and the range-adjusted measure.

5 Aparicio et al. (2007) and Zhu et al. (2018) use the minimum distance versions of unweighted additive measure and range-adjusted measure, respectively. The current study utilizes the minimum distance directional slack inefficiency (mdDSI) measure (5). See Appendix for comparisons.

6 A face $F$ is said to be maximal if $F\subseteq E$ and a face $F^{\prime }$ with $F^{\prime }\cap F\ne \varnothing$ and $F^{\prime }\subseteq E$ implies $F^{\prime }\subseteq F.$ See Fukuyama and Sekitani (2012).

7 While Zhu et al. (2018) do not provide how to estimate $\eta ,$ we provide a way to obtain it using the duality theory and the concept of face.

8 Note that “$\circ$” is the Hadamard product.

9 The analytical findings are available upon request.

10 For a critique on range adjusted models see Steinmann and Zweifel (2001).

11 For the purpose of our analysis we use efficiencies rather than inefficiency estimates.

12 The analytical findings of Phillips and Sul’s (2007) approach are available upon request.