The curse of dimensionality of decision-making units: A simple approach to increase the discriminatory power of data envelopment analysis

Data envelopment analysis (DEA) is a technique for identifying the best practices of a given set of decision-making units (DMUs) whose performance is categorized by multiple performance metrics that are classified as inputs and outputs. Although DEA is regarded as non-parametric, the sample size can be an issue of great importance in determining the efficiency scores for the evaluated units, empirically, when the use of too many inputs and outputs may result in a significant number of DMUs being rated as efficient. In the DEA literature, empirical rules have been established to avoid too many DMUs being rated as efficient. These empirical thresholds relate the number of variables with the number of observations. When the number of DMUs is below the empirical threshold levels, the discriminatory power among the DMUs may weaken, which leads to the data set not being suitable to apply traditional DEA models. In the literature, the lack of discrimination is often referred to as the “curse of dimensionality”. To overcome this drawback, we provide a simple approach to increase the discriminatory power between efficient and inefficient DMUs using the well-known pure DEA model, which considers either inputs only or outputs only. Three real cases, namely printed circuit boards, Greek banks, and quality of life in Fortune's best cities, have been discussed to illustrate the proposed approach.