Price and quantity relatives

In §1.7 we noted that many of the series used in quantitative analysis of historical trends and fluctuations take the form of index numbers of the changes in either prices or quantities, and gave a few examples of controversies in which they have figured prominently. The aim of the present appendix is to outline the main principles involved in the construction of index numbers. Slightly more formal presentation of the principal concepts and definitions is also given in panels B.1 and B.2 for those comfortable with the algebra.

It may help to clarify the nature of a proper index number if we refer first to price and quantity relatives. These are not index numbers, although they look exactly like them because they also have one item in the series shown as 100. However these relatives are merely series that have been converted from an absolute to a relative basis. All that this involves is choosing some particular year for which the value of the series is taken as 100, and then expressing all the other items in the series as a ratio to the value in the chosen year. The advantage of doing this is that it makes it easier to see the relationship between values; fewer digits are required and the comparative dimension is more readily grasped.