Abstract
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 alsoat 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.
Zusammenfassung
Dieser Artikel zeigt, daß die Grenz-Produktionsfunktion (“frontier production function”, FPF) von Aigner und Chu bestenfalls ein Spezialfall der Farrell-Methode ist. Die FPF-Methode erzeugt nämlich implizit eine hypothetische Entscheidungseinheit (“decision making unit”, DMU) aus den Originaldaten und verwendet die Grenze, die diese hypothetische DMU bewertet, zur Bewertung aller DMUs, was die geschätzte Grenze, die Effizienzzahlen und das Ranking der DMUs unidentifizierbar machen kann. Das Paper zeigt auch, daß eine von Senguptas “minimax”-Methoden bestenfalls ein Spezialfall der Farrell-Methode ist (denn sie verwendet die Grenze, die die ineffizienteste DMU bewertet, zur Bewertung aller DMUs) und daß die anderen “minimax”-Methoden von Sengupta keine sinnvollen Effizienzzahlen und Produktionsgrenzen erzeugen können. Zusammenfassend ist die Farrell-Methode, die die gesamte stückweise-lineare Grenze zur Bewertung der DMUs verwendet, besser als die FPF-Methode und Senguptas “minimax”-Methoden.
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The author wishes to thank Professor C.A. Knox Lovell and an anonymous referee for helpful advice and comments. The usual disclaimer applies.
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Chang, KP. Using the frontier production function and minimax approaches in measuring productive efficiency: Critical remarks. OR Spektrum 20, 91–95 (1998). https://doi.org/10.1007/BF01539858
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DOI: https://doi.org/10.1007/BF01539858