A note on decomposing the Malmquist productivity index by means of subvector homotheticity

This paper introduces a decomposition of the Malmquist productivity index into component indexes. The motivation is to derive an analogue of the decomposition of the Törnqvist index into productivity and quality change provided by Fixler and Zieschang (1992) to the Malmquist index. Since we employ no second order approximations, this decomposition requires additional structure, namely a generalized version of Shephard's (1970) inverse homotheticity, which we dub subvector homotheticity. We show that subvector homotheticity is necessary and sufficient for our decomposition.