The Hicks–Moorsteen Productivity Index Satisfies the Determinateness Axiom

Abstract:     
In the literature, two types of factor productivity indices are defined as a function of a primal notion of technology. The Malmquist and the Hicks–Moorsteen productivity indices take a ratio‐based approach, whereas the Luenberger and the Luenberger–Hicks–Moorsteen productivity indices follow a difference‐based approach. The purpose of this note is to establish that the Hicks–Moorsteen type of productivity index, contrary to the Malmquist type of index, is well defined and satisfies the determinateness property under weak conditions on technology. This conclusion results from the fact that the underlying distance functions are always based on a feasible direction.

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