Assessing efficiency profiles of UK commercial banks: a DEA analysis with regression-based feedback

Data envelopment analysis (DEA) has witnessed increasing popularity in banking studies since 1985. In this paper, we propose a new DEA-based analysis framework with a regression-based feedback mechanism, where regression analysis provides DEA with feedback that informs about the relevance of the inputs and the outputs chosen by the analyst. Unlike previous studies, the DEA models used within the proposed framework could use both inputs and outputs, only inputs, or only outputs. So far, the UK banking sector remains relatively under researched despite its crucial importance to the UK economy. We use the proposed framework to address several research questions related to both the efficiency of the UK commercial banking sector and DEA analyses with and without regression-based feedback. Empirical results suggest that, on average, the commercial banks operating in the UK-whether domestic or foreign-are yet to achieve acceptable levels of overall technical efficiency, pure technical efficiency, and scale efficiency. On the other hand, DEA analyses with and without a linear regression-based feedback mechanism seem to provide consistent findings; however, in general DEA analyses without feedback tend to over- or under-estimate efficiency scores depending on the orientation of the analyses. Furthermore, in general, a linear regression-based feedback mechanism proves effective at improving discrimination in DEA analyses unless the initial choice of inputs and outputs is well informed.