Further Results on Stochastic Index Numbers

The stochastic approach is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. Rather than just providing a single number for the rate of inflation, the stochastic approach provides the whole probability distribution of inflation. This paper 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 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) money market equilibrium, or the quantity theory equation of exchange, and (ii) the use of quantity data in addition to price data. Some related approaches are also reviewed.