Exploring the source of metafrontier inefficiency for various bank types in the two-stage network system with undesirable output

•A new approach developed to decompose metafrontier inefficiency in a two-stage network system with undesirable output.•The foreign banks in Taiwan do not have efficiency as high as we expected in developed country.•The metafrontier operational inefficiency of domestic banks originated from managerial inefficiency during 2004–2009.•The metafrontier operational inefficiency of domestic banks attributed to the technical gap during 2010–2012.

This paper integrates the production and intermediation approaches to define the inputs, intermediates, desirable and undesirable outputs of banks and to develop a new approach to decompose metafrontier inefficiency in a two-stage network system. This approach can help explore the sources of metafrontier inefficiency for managers of various banks. The empirical results demonstrate that foreign banks do not have efficiency as high as we expected in developed countries. These results also indicate that domestic banks enjoy a strong competitive advantage in the first stage; however, in the second stage, domestic banks' operational performances are worse than those of foreign banks when the meta-technology set is used as the evaluation basis for the 2004–2009 period. However, the production and operational performances of foreign banks outperform those of domestic banks when the meta-technology set is used as the evaluation basis for the 2010–2012 period. The production and operational inefficiencies of the metafrontier are derived from the managerial inefficiency of domestic and foreign banks from 2004 to 2009; however, the operational inefficiency of the metafrontier stems from the technical gap between the metafrontier and group frontiers in the second stage in domestic banks from 2010 to 2012.