Radii of Classification Preservation in Data Envelopment Analysis: a Case Study of ‘Program Follow-Through’

Abstract

Sensitivity and robustness of efficiency classifications for the additive model and its geometric equivalents in Data Envelopment Analysis (DEA) are addressed. The minimum distance (measured by a Tchebycheff norm) separating an organization from reclassification is computed via linear programming formulations and shown to constitute a generalized ‘residual’ for each organization. Without this sensitivity information, findings can be distorted when marginally efficient or inefficient units are distinguished solely on the basis of their classification. Analysis of these residuals from an earlier (inconclusive) DEA study further reveals how substantive differences in a sample's underlying groups can be detected. Properties of group efficiency and group proximity to the efficient frontier are investigated using these new indicators.