Applying Path-Based Models to Negative Data with a Focus on Super-Efficiency

Negative data are encountered in various applications, such as insurance, accounting, or finance. Although Data Envelopment Analysis (DEA) models have been originally designed for non-negative data, the path-based models (such as the input or output radial models, the directional distance function models or the hyperbolic distance function model) can be modified to handle negative data. We analyse the extension of these models for the super-efficiency measurement and demonstrate the results on a numerical example.