The Choice of Index Number: Part I, Valuation and Evaluation

Abstract:     
This paper defines and discusses the choices that are implicit in alternative approaches to constructing index numbers. The central theoretical result is the exogeneity theorem, which states that an index number system possesses certain generally desirable properties, associated with meaningfulness, relevance and consistency if and only if it admits of a welfare interpretation that is invariant to the data to which it is applied. An index number system that does not permit a fixed welfare interpretation of this kind will fail to possess these properties. Moreover, it will not be possible to undertake meaningful multilateral comparisons between all possible units of comparison to which the index number system may be applied without adopting a meta-evaluative criterion that expresses welfare judgments concerning the relation between distinct evaluative standards. Therefore, explicit or implicit normative judgments are inescapable in the construction and use of index numbers intended to permit meaningful comparisons over an unrestricted domain.

We identify a set of bounds on the index numbers that an index number system produces (the generalized within bounds requirement) which define necessary and sufficient conditions for them to be rationalizable (i.e. to possess a welfare interpretation). However, multilateral index number systems that are widely in use violate this and other requirements of the exogeneity theorem. As a result, the index numbers they produce do not admit of a welfare interpretation which is invariant to the data to which they are applied, and indeed may not admit of any welfare interpretation at all. The exogeneity theorem establishes that the rationale for exact index number systems is much less compelling than widely believed.

A fixed welfare interpretation is also a necessary and sufficient condition for the path-independence of the Divisia index. The theorem therefore establishes a three-way equivalence between desirable properties of continuous index number systems, desirable properties of discrete index number systems and the existence of a fixed welfare interpretation.

Number of Pages in PDF File: 59

Keywords: Index Numbers, Rationalizability, Welfare Interpretation

JEL Classification: A13, C43, D60, D63, E31

working papers series