Chain Index Numbers

The runs of index numbers of Chapter 4 are subject to the limitation that each is simply a sequence of binary comparisons between the current year t and the base year 0. There is no reference whatever to the course of prices/quantities in between. Something better than this must be sought, something more in line with economic common sense and making more efficient use of all the data. The suggestion which now comes up for consideration is that, in the practical job of calculating and publishing an index year by year, use can be made of all the price/quantity information from the base year up to and including the current year. Such an index provides a rolling comparison of year t back to year 0 using all the data as cumulated to the current year. This concept leads to the Divisia Integral Index in theory and to the chain index as its practical realisation. It is not to be confused with the more extreme exercise, to be pursued in Chapter 7, of estimating all index numbers in a given period from all the data of the period. The present job is to make the current index depend on back data; the wider problem has an index dependent both on back data and on data to come within the overall period.