The axiomatic approach

A price index combines information about prices and quantities at two points in time in order to produce a ratio of prices between these points in time. Unless there is only one price at each point in time, however, there is no unique way to combine prices over time—there are an infinity of possible index-number formulas that can be used to calculate a price index. This embarrassment of riches is undesirable, as it introduces considerable choice into how a price change should be measured. The axiomatic approach attempts to solve this problem by considering a general class of price indices, and finding which members of this class satisfy certain intuitive, or reasonable, properties that a price index ought to satisfy. This is equivalent to making a normative statement about how a price index should behave—what are the fundamental axioms that define a price index? The idea is to start with a very broad class of possible index-number formulas, and define axioms to whittle away index-number formulas that don’t behave as a price index should.

The ideal outcome from the axiomatic approach is a single, unique index-number formula that satisfies a minimal set of uncontroversial conditions that a price index ought satisfy. This would mean that there is only one index-number formula that should be used to make a price index. The reality, however, is that compromises must be made, and keeping certain conditions requires ignoring others. Consequently, a distinction is made between axioms—fundamental statements that any reasonable price index should satisfy—and tests, which are properties that are desirable but not as fundamental as axioms. A small set of key axioms are always maintained, whereas tests can be mutually inconsistent, and choices need to be made about which tests an index should satisfy depending on its purpose. Axioms can be seen as the first sieve to remove any unreasonable index-number formulas, with tests acting as a second sieve to further refine what is left over.

This section of the course starts the journey into price index theory by giving a brief outline of the axiomatic approach to price index theory. This has been an area of considerable study, and consequently there is a lot of interesting material that is not covered in this course. The interested reader can consult either ILO et al. (2004a, chap. 16) or ILO et al. (2004b, chap. 16) for more detail, or Balk (2008).

📖 Balk (1995), skip section 4 and appendix.

📖 PPI Manual: Chapter 1, section C.