Using the frontier production function and minimax approaches in measuring productive efficiency: Critical remarks

This paper shows that Aigner and Chu's frontier production function (FPF) method is, at best, a special case of the Farrell method. That is, the FPF method implicitly creates a hypothetical decision-making-unit (DMU) from the original data and uses the frontier evaluating the hypothetical DMU to evaluate all the DMUs, which may make the estimated frontier, efficiency scores and the ranking of DMUs unidentifiable. The paper also shows that one of Sengupta's minimax methods is also at best a special case of the Farrell method (i.e., it uses the frontier evaluating the most inefficient DMU to evaluate all the DMUs), and Sengupta's other minimax method cannot produce meaningful efficiency scores and production frontiers. The Farrell method, which uses the whole piecewise linear frontier to evaluate DMUs, is concluded to be better than both the FPF and Sengupta's methods.