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The authors provide an axiomatic foundation for efficiency measurement in the full (input, output) space, referred to as "Graph efficiency" measurement by Fare, Grosskopf, and Lovell . They posit four types of axioms: indication, monotonicity, independence of units of measurement, and continuity. They analyze six well-known inefficiency indexes from the operations-research and economics literature and discuss several other related indexes. They present two impossibility results demonstrating that no index can satisfy all of the axioms on a general class of (well-behaved) technologies.
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