A Note on Different Approaches to Index Number Theory

摘要

The central question in a recent paper by J. Peter Neary (2004) concerning real incomes and the Penn World Tables is: what exactly do the numbers mean? This question is important, because these data are widely used in empirical research. More generally, index number data, including indicators of inflation and economic growth, are used so extensively in research throughout the profession that it indeed seems helpful to understand what they actually indicate.rnIn the literature, two approaches to index numbers are distinguished: the axiomatic approach and the economic approach. In this note we would like to discuss the way in which these two approaches differ and how that affects what the numbers mean. In Neary's paper the difference is described as one between an approach that does and an approach that does not assume that quantities arise from optimizing behavior. This is in line with a tradition in index number theory that can be traced back to Ragnar Frisch (1936). We will argue that a more accurate description is that the difference lies in whether or not optimizing agents, or representative consumers, are assumed to optimize the same utility function. It is exactly this distinction that sets the (different) limitations of both approaches for constructing a meaningful indicator of real income. Those limitations will be described in some detail, and being aware of them is helpful for assessing the value of results from both the axiomatic and the economic approach. They also suggest ways in which the two approaches may be complementary for constructing meaningful index numbers. Introducing the Geary-Allen International Accounts (GAIA) system, Neary combines taking the economic approach with judging the resulting indices in view of some axioms. We think that this makes his paper a suitable point of departure for the discussion of how the two approaches handle differences in relative prices on the one hand, and differences in preferences on the other.