Comparison of the Dependence Structures of Stochastic Copula-DEA Model

The stochastic data envelopment analysis (SDEA) is based on treating input values and output values as random variables. Typically, in research related to stochastic data envelopment analysis, variables are assumed to be independent of one another. It is likely that there will be a dependency structure between variables. We investigated the dependence structure between input variables and between output variables. To estimate this dependence structure, we used the Copula approach. Therefore, we have proposed a stochastic DEA model with a dependence structure called Copula-SDEA in this study and evaluated this model using both input-oriented and output-oriented models. We evaluated the proposed models using real data from 10 car companies. The implementation of the proposed model showed that, different results can be drawn when taking into account the dependence structure between stochastic inputs and (or) outputs. Additionally, a comparison of Copula-SDEA models with the SDEA model revealed that the evaluation of the efficiency of DMUs with Copula-SDEA models differed significantly from the SDEA model. Moreover, the results indicate that in both input- and output-oriented models, considering the dependence structure between inputs is more important than considering the dependence structure between outputs.