More on stochastic index numbers

There are three major approaches used to estimate index numbers. The first is Fisher's test approach whereby indexes are judged on their ability to satisfy certain criteria. The economic theory of index numbers is the second approach and this deals with their foundations in utility theory. The third approach is a less well-known methodology, but one which is now attracting considerable attention, the stochastic approach which is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. While providing a point estimate for the index number like the other two approaches, the stochastic approach additionally provides the SE of the point estimate. This article enhances understanding of stochastic index numbers by showing that they are formally equivalent to the familiar optimal combination of forecasts with the individual prices playing the role of n forecasts of the overall rate of inflation. This leads to new analytical results on the impact of adding additional information within the stochastic approach framework. We provide two concrete examples of the sources of such additional information: (i) the quantity theory of money; and (ii) the use of quantity data in addition to price data. We also illustrate some of these theoretical results using real data.