An illustration of dynamic network DEA in commercial banking including robustness tests

• Benchmarking sixteen foreign banks against thirty-two domestic banks after reforms in China.
• Divisional and between-period interactions are reflected in efficiency estimates.
• Interest-bearing operations and non-interest operations are linked by number of referrals.
• Undesirable outputs are treated as carry-overs that impact efficiency of following periods.
• Robustness examines dimensionality, stability and sensitivity to weights and returns-to-scale.

The main motivation of this article is to illustrate dynamic network data envelopment analysis (DN-DEA) in commercial banking with emphasis on testing robustness. To this end, sixteen foreign banks in China are benchmarked against thirty-two domestic banks for the post-2007 period that follows major reforms. When network and dynamic dimensions are brought together, a more comprehensive analysis of the period 2008–2010 is enabled where divisional and between-period interactions are reflected in efficiency estimates. Weighted, variable returns-to-scale, non-oriented dynamic network slacks-based measure is used within the framework of the intermediation approach to bank behavior. A bank network (i.e., a decision-making unit, DMU) is conceptualized as comprised of two divisions or sub-DMUs, namely, interest-bearing operations and non-interest operations linked by number of referrals. Undesirable outputs from sub-DMUs 1 and 2 (non-performing loans, and proportion of fruitless referrals, respectively) are treated as carry-overs that impact the efficiency of the following periods. Under robustness testing, the illustrative application discusses discrimination by efficiency estimates, dimensionality of the performance model, stability of estimates through re-sampling (leave-one-out method), and sensitivity of results to divisional weights and returns-to-scale assumptions. The results based on Chinese commercial banks are illustrative in nature because of simulated data used on two of the variables.