Cross efficiency Malmquist index to investigate the productivity change in DEA

Ghasem Tohidi, Shabnam Razavyan, Simin Tohidnia



In traditional data envelopment analysis (DEA) the efficiency and productivitychange computations are based on an optimistic perspective and an efficient unit mayperform rather poorly when the realist weight are assigned to inputs and outputs.Hence, the productivity change results of decision making units (DMU) between twotime periods may be changed from progress to regress or vice versa when the weightsare modified. Based on the merits of the cross efficiency this paper uses it to obtain acommon set of weights so called common set of cross weights.On the other hand we need a base to compare the productivity change of DMUs.To this end, the common set of cross weights are used to approximate the cross efficientfrontier as a base to determine cross Malmquist (CM) index for determining theproductivity change. This leads to introduce a new efficiency, weight efficiency, andthe decomposition of the cross efficiency. Some DEA and cross efficiency models aremodified to find the value of the proposed CM index and its components. An empiricalexample is used to compare the proposed method and the technical Malmquist index.


Data Envelopment Analysis (DEA), Cross Efficiency, Malmquist index, Productivity.

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