Cross Efficiency Malmquist Index to Investigate the Productivity Change in DEA

In traditional data envelopment analysis (DEA), the efficiency and productivity changes computations are based on an optimistic perspective and an efficient unit may perform rather poorly when the realist weights are assigned to inputs and outputs. Hence, the results of productivity change of decision making units (DMUS) between two time periods may change from progress to regress or vice versa when the weights are modified. Because of the cross efficiency merits, we use it to obtain a common set of weights so called common set of cross weights. On the other hand, we need a base for comparing the productivity change of DMUs. To this end, the common set of cross weights are used to approximate the cross efficient frontier as a base for determining cross Malmquist (CM) index for evaluating the productivity change. This leads to introduce a new efficiency, weight efficiency, and the decomposition of the cross efficiency. Some DEA and cross efficiency models are modified to find the value of the proposed CM index and its components. An empirical example is used to compare the proposed method and the technical Malmquist index.