Stochastic efficiency measures for production units with correlated data

Abstract

While the real world is stochastic in nature, in many cases deterministic data envelopment analysis (DEA) models are used to measure the relative efficiency of a set of production units for simplicity. However, deterministic DEA models are not able to differentiate efficient units. More seriously, the decision maker will be over-confident with the presumably uncertain and probably misleading results. By applying a standard normal transformation, this paper develops a stochastic DEA model which is able to take the correlation between the input/output factors of each production unit to be evaluated into account to obtain the distribution of the stochastic efficiency. The efficiency distribution is more discriminative and informative than the single-valued efficiency, in that the probability that the stochastic efficiency of a unit is greater than that of another unit can be calculated. The case of twenty-five Taiwanese commercial banks discussed in a previous study that assumed the input/output factors to be independent is used to illustrate the characteristics of different models. The data is shown to be correlated, and the results confirm that ignoring the correlations between the input/output factors in measuring efficiency obtains misleading rankings.