A new cross-efficiency meta-frontier analysis method with good ability to identify technology gaps

Cross-efficiency evaluation and meta-frontier analysis (MFA) have been widely used to measure performance in many areas. However, cross-efficiency MFA (CMFA) has rarely been studied due to its potential violation of the basic MFA property, that is, the efficiency relative to the group frontier is not less than that relative to the meta-frontier. In this paper, we deduce the conditions under which the cross-efficiency score generated by the current CMFA method relative to the group frontier is smaller than that relative to the meta-frontier, and the conditions under which the current CMFA method is unable to identify the technical gaps between the group frontiers and the meta-frontier. To guarantee the basic property and identify technical gaps, we introduce a new CMFA method, where the efficiencies relative to the group frontiers are first cross-evaluated by the traditional cross-evaluation approach and then those relative to the meta-frontier are cross-evaluated by using modified data envelopment analysis models. Compared with the existing CMFA method, our approach has the following advantages: it can successfully ensure that the cross-efficiencies and cross-efficiency scores relative to the group frontiers are not less than those relative to the meta-frontier; it has a good identification of technology gaps and provides more detailed information about the inefficiency; all the mathematical programming models involved in our CMFA method are feasible. Theoretical analyses and numerical examples support the practicality and superiority of our method.