12. Robust Efficiency via Average Correlation: The Case of Academic Departments

Many types of efficiency methods for decision-making units (DMUs) have been suggested in the literature. Often in the same application, several efficiency methods are given, making it hard for decision makers to choose which efficiency method to use. This chapter provides a simple method to choose a robust efficiency, by calculating the average correlations of each method with all other methods. This robust method is applied to the case of 21 academic departments within a university, taken from the literature, with two inputs and three outputs. A variety of data envelopment analysis (DEA) methods for measuring DMUs’ efficiencies are considered here: constant return to scale (CRS), variable return to scale (VRS), super efficiency (SE), and cross-efficiency (CE). A few multivariate statistical efficiency methods in the DEA context are also used: discriminant analysis, canonical correlation, and regression analysis. For this case study, the robust continuous efficiency scale method turned out to be the CE-CRS method. For validating the results, we also used rankings of the efficiencies, and applied nonparametric statistical tests. Since the two inputs used in the case study had monetary values, we also created a one-input model using the sum of the two inputs. Thus, we were able to use, in addition to the above-mentioned efficiency methods, a version of stochastic frontier analysis via multiple linear regression. Even in this case, CE-CRS turned out to be the robust efficiency method, including for the ranks of efficiencies.