6440.0 - Information Paper: A Guide to the Consumer Price Index, 1998
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 15/02/1999
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Once price movements are calculated for each elementary aggregate, the expenditure aggregates can be moved forward and then summed to derive the current cost of the basket. It is from the expenditure aggregates that index numbers are calculated at any level of the index. The stylised example above is continued, to show the process for the Bread expenditure class.
The expenditure aggregates are revalued to period 2 prices by applying the movements between period 1 and period 2. The expenditure aggregate for the expenditure class Bread is the sum of the expenditure aggregates for the elementary aggregates comprising the expenditure class. Summing the elementary aggregates says that in period 2 it would cost $8.160m to buy the volume of Bread in period 1 that cost $8m. The price change for Bread between period 1 and 2 is simply the ratio of these expenditure aggregates, that is, a price increase of 2.0% (8.160/8). Thus if the price index for bread was 100.0 in period 1, it would be 102.0 in period 2. The derivation of the expenditure class movement as shown above is mathematically equivalent to a weighted average of the price movements for the individual elementary aggregates, that is, a weighted version of the mean of price relatives formula discussed above. In this case period 1 expenditure aggregates are the weights. The same formula is used at higher levels of the index. Similar procedures are used to derive price movements at higher levels of the CPI. For example, the current period cost of purchasing items in the Cereal products subgroup of the CPI is obtained by summing the current period expenditure aggregates of the expenditure classes Bread, Cakes and biscuits, Breakfast cereals and Other cereal products. The ratio of the current and previous period expenditure aggregates for the Cereal products subgroup gives the price movement for the subgroup. Points contributions (see 'Analysing the CPI', Chapter 3) are also calculated using the expenditure aggregates. The current period points contribution of a CPI component, for example the expenditure class Bread, is the current period expenditure aggregate for Bread relative to the expenditure aggregate for the All groups CPI multiplied by the current period All groups index number. The CPI publication does not show the expenditure aggregates, but rather the index numbers derived from the expenditure aggregates. Expenditure aggregates vary considerably in size and would make the publication difficult to read and interpret. The published index numbers and points contributions are a convenient presentation of the information.
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