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A Superlative Index Number Formula for the Hicks-Moorsteen Productivity Index

Hideyuki Mizobuchi
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Hideyuki Mizobuchi: Faculty of Economics, Ryukoku University

No WP032016, CEPA Working Papers Series from University of Queensland, School of Economics

Abstract: The Malmquist and Hicks-Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth. Since these productivity indexes are defined by unknown distance functions, it is necessary to estimate the distance functions to compute them in principle. On the other hand, the Törnqvist productivity index is an empirical index number formula that is directly computable from the prices and quantities of the inputs and outputs alone. Caves, Christensen, and Diewert (1982) (CCD) imply that the Malmquist index coincides with the Törnqvist index, under profit maximising behaviour and constant returns to scale technology. The purpose of the present paper is to point out that the Hicks-Moorsteen productivity index coincides with the Törnqvist productivity index under the same condition. We emphasize that the condition of constant returns to scale is indispensable for deriving the equivalence between two indexes. Moreover, even when this condition is relaxed to the 𠛼 returns to scale, the equivalence between the Hicks-Moorsteen and Törnqvist productivity indexes is shown to hold true.

Keywords: Törnqvist productivity index; Hicks-Moorsteen productivity index; Malmquist productivity index; Translog functional form; Superlative index number (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-eff
Date: 2016-03
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