3.6 Linking old indices

Index base periods, weights and the range of commodities included in the index are updated from time to time, usually at one-year or five-year intervals. Once updated, the index is calculated using only the new weights and the new commodity basket. Index scores published for older base periods are continued by coefficients, i.e. they are linked to the new index.

Old index scores are needed for purposes of various agreements that are tied to indices with an earlier base-year than in the new index. The long series of indices that are created in this way are also easier to use when compiling time series and studying longer time periods.

There are no international guidelines for linking procedures, nor does there exist any single mathematically superior linking method. Some of the methods commonly used are described below.

A. The index is updated each year

In some countries the base period, weights and range of commodities included in the consumer price index and the producer price index are renewed each year.

Price indices that are renewed annually and produced monthly will be chained in December. The new index figure in December is always 100,00. The old index is not chained to the previous year's index, but for example to an EU index with the most recent base-year. The price indices that are currently updated each year are chained to an index anchored to the base-year of 2000. The procedure is as follows:

In December 2003 the current, official index was anchored to December 2002 (2002:12=100). In January 2004 the base period for the official index was December 2003.

In January 2004 index scores were calculated both for the current, official index and for 2000=100 as well as older indices still in use. The linking coefficient between the indices 2000=100 and 2003:12=100 is the quotient of the scores of the old and new December 2003 index, i.e. 104.47 / 100.00 = 1.0447. The latest index score for January 2004 is multiplied by the coefficient to obtain the January score for the index whose base-year is 2000.

B. The index is updated less often than once a year, usually once every five years

The same procedure is followed in linking indices that are updated less often than once a year. The old and new index are usually chained at their last overlapping month or quarter. It is also possible to use the base-year of the new index as the linking point. The example below shows how the consumer prices indices 1995=1000 and 2000=1000 are chained.

The coefficients are virtually the same regardless of whether they are calculated from December 2001 or the average for 2000. The official coefficient is 1.079602 (110.94 / 102.76 = 1.079602), calculated on the basis of the December 2001 index score.

The coefficients for indices with older base periods (e.g. the cost-of-living index 19051:10=100) are calculated accordingly:

Next lesson: Using indices to perform calculations and to express change