Why price index number formulae differ: economic theory and evidence on price dispersion

The results from different index number formulae can differ and can do so substantially. The main criteria for explaining such differences, and governing choice between them, are their ability to satisfy desirable test properties - the axiomatic approach - and their correspondence with plausible substitution behavior as predicted from economic theory. Yet the numerical differences between such formulae has been shown to be related to the extent of, and changes in, the dispersion of prices. However, within the index number literature there is, to the author's knowledge, no formal attempt to explain differences between the results from individual formulae in terms of theories and evidence on price dispersion. Explaining differences between formulae in terms of changes in the dispersion of prices benefits from the existence of economic theoretical frameworks to explain such dispersion, and thus improve our understanding of why differences from formulae occur. Such frameworks include search cost and menu cost theories and signal extraction models. This paper outlines the nature of the relationships between formulae in term of price dispersion, then considers economic theories of price dispersion and uses them to model price variation both within months and over time using an extensive scanner data set on television sets amounting to over 70,000 observations over 51 months. It concludes by considering the implications for index number construction