The Theory of Exact and Superlative Index Numbers Revisited

This paper proposes to clarify some important questions that are still open in the field of index number theory. The main results are the following: (i) the so-called Quadratic Identity on which the superlative index numbers are based can be applied in more general cases than those traditionally considered; (ii) it is not only the Toernqvist index number that does not rely on separability restrictions, but also some other indicators of absolute or relative changes are not based on such restrictions; (iii) in practice, however, all the index numbers or indicators that are considered to be superlative in Diewert's (1976) sense generally fail by construction to be really superlative; (iv) these hybrid index numbers may be far from providing the expected second-order approximation to the true index and may be found beyond the Laspeyres-Paasche interval even in the homothetic case. In conclusion, it would be more appropriate to construct a range of alternative index numbers (including even those that are not superlative) rather than follow the common practice of searching for only one optimal formula