Stochastic copula-DEA model based on the dependence structure of stochastic variables: An application to twenty bank branches

The DEA is a nonparametric method of assessing the efficiency of decision-making units using mathematical programming. The classic DEA model assumes that input and output variables are deterministic. However, there are many applications where the variables are of a stochastic nature. Based on the consideration of input and output levels as random variables, the Stochastic Data Envelopment Analysis (SDEA) was developed. Statistical distributions therefore play a major role in this regard. By considering the dependency between input and output variables, and also their simultaneous dependencies in this study, we have introduced three copula-SCCR models. We used three copulas of Gaussian, Clayton, and Gumbel to estimate the dependence between the random variables with normal distribution. We evaluated the proposed models using real data from 20 bank branches. The results showed that considering stochastic dependency between the inputs or outputs causes different results. A comparison between the Copula-SCCR models and the SCCR models revealed that the efficiency of the DMUs using the Copula-SCCR models differed from the SCCR model by a significant margin of at least 20%.