Underrestimation of Inefficiency in Social Efficiency Benchmarking with Non-Parametric Methodsof Production Technology Identification: A Note

In the conventional social productive efficiency measurement, a DEA-based non-parametric method is typically employed to identify the piece-wise-linear production possibility frontier. Applying the directional distance-function approach a-la Luenberger (1992) to the production possibility frontier obtained in this fashion can, however, lead to an underestimation of inefficiency for a DMU with relatively large undesirable outputs. This underestimation becomes more acute if the sample size is small or data are clustered. This paper reveals the mechanism behind this underestimation bias, and then quantifies the degree of underestimation using nine-year panel data of rail and aviation sectors in Japan. Through a comparative analysis between parametric and non-parametric methods, we find, among others, that the underestimation of the aviation sector's productive inefficiency is as large as 80%, which the non-parametric method failed to detect.