Axiomatic Foundations of Inefficiency Measurement on < input, output > Space

We provide an axiomatic foundation for efficiency measurement in the full space, referred to as “graph efficiency” measurement by Färe, Grosskopf, and Lovell [1985]. We posit four types of axioms: indication, monotonicity, independence of units of measurement, and continuity. We analyze six well-known inefficiency indexes from the operations-research and economics literature and discuss several other related indexes. We present two impossibility results demonstrating that no index can satisfy all of the axioms on a general class of (well-behaved) technologies. Specifically, no inefficiency index can satisfy both indication and continuity (in either quantities or technologies), and no inefficiency index can satisfy both monotonicity and unit independence. We present a full evaluation of the trade-offs involved in selecting among the indexes.