What is price-index theory?

There are three broad approaches for motivating the price-index formulas that get used in practice by statistical agencies—the axiomatic approach, the economic approach, and the stochastic approach. Each approach is useful in its own right, and all three give different perspectives and understandings for the various index-number formulas that are used to construct price indices. Taken together, these different approaches constitute a theory of price indices.

Each of the three approaches can be thought of as answering a different question about how to construct a price index. The axiomatic approach attempts to answer the question “How can information for a collection of prices and quantities be combined to satisfy certain properties?” This is essentially a set theoretic approach for how to best construct an index number. By contrast, the economic approach attempts to answer the question “What should a price index measure?” The goal with the economic approach is to use the machinery of microeconomic theory to define a price index so as to measure the experience of a change in prices for consumers and producers. The stochastic approach is more pragmatic in its scope, and attempts to answer the question “How can information on prices be used to best predict a change in price for a good or service?” This is essentially a question about how to best inflate and deflate prices over time.

This part of the course gives a practical introduction to each of the three approaches, focusing on how they can be used to motivate the way price indices are constructed in practice. Despite having a more practical focus, however, this material is still concerned with theory that can be quite technical. Rather than focusing on the technical details (of which there are many), this part of the course gives enough of a glimpse into the technical machinery to show what is going on, while providing the economic intuition and overarching ideas from the theory. Selvanathan and Rao (1994, chap. 2) gives an excellent overview of these approaches without too much technical apparatus.