In this paper we show that in order to aggregate individual efficiency scores into a group (e.g., industry) efficiency score in such a way that the multiplicative structure of further decompositions is preserved with equal weights across components, the weighted geometric mean is required. We...

Inada (1963) provided properties of the production function that are useful in the study of economic growth. Shephard (1970a) provided an axiomatic approach to the study of production theory. He applied these axioms to give a formal statement of the law of diminishing returns [(Shephard,...