The quarterly change in the All groups CPI represents the weighted average price change of all the items included in the CPI. While publication of index numbers and percentage changes for components of the CPI are useful in their own right, these data are often not sufficient to enable important contributors to overall price change to be reliably identified. What is required is some measure that encapsulates both an item's price change and its relative importance in the index.
Points contribution and points contribution change
If the All groups index number is thought of as being derived as the weighted average of indexes for all its component items, then the index number for a component multiplied by its weight to the All groups index results in what is called its ‘points contribution’. It follows that the change in a component item’s points contribution from one period to the next provides a direct measure of the change in the All groups index resulting from a change in that component’s price.
Information on points contribution and points contribution change, is of immense value when analysing sources of price change and for answering ‘what if’ type questions. Consider the following data extracted from the September quarter 1998 CPI publication.
 |
| |
| | Index numbers
| Per
cent
change | | Points contribution
|
Points
change
| |
|
| June qtr | Sept. qtr | | June qtr | Sept. qtr | |
|
| |
|
| 121.0 | 121.3 | 0.2 | | 121.0 | 121.3 | 0.3 | |
|
| 103.3 | 110.2 | 6.7 | | 1.50 | 1.60 | 0.10 | |
|
| |
Using points contributions
Armed only with knowledge of the index numbers, the most that can be said is that between the June and September quarters 1998, prices of fresh vegetables increased by more than the CPI on average (by 6.7% compared with an increase in the All groups of 0.2%). The additional information on points contribution and points change can be used to:
(a) Calculate the effective weight for fresh vegetables in the June and September quarters (given by the points contribution for Fresh vegetables divided by the All groups index). For June, the weight is calculated as 1.50/121.0x100 = 1.24% and for September as 1.60/121.3x100 = 1.32%. Although the underlying quantities are held fixed, the effective weight in expenditure terms has increased due to the fact that prices of fresh vegetables have increased by more than the prices of all other items in the basket (on average).
(b) Calculate the relative contribution of the change in fresh vegetable prices to the change in the All groups index (given by the points change for Fresh vegetables divided by the points change in the All groups index). In September quarter 1998 this is calculated as 0.10/0.3x100 = 33.3%. In other words, the 6.7% increase in fresh vegetable prices accounted for one third of the increase in the All groups index. Note: Calculations of this type are not always meaningful, for example when the total points change is small or when the change in the component is of a different sign to the change in the total.
(c) Calculate the percentage increase that would have been observed in the CPI if all prices other than those for fresh vegetables had remained unchanged (given by the points change for Fresh vegetables divided by the All groups index number in the previous period). For September quarter 1998 this is calculated as 0.10/121.0x100 = 0.1%. In other words, a 6.7% increase in fresh vegetable prices in September quarter 1998 resulted in an increase in the overall CPI of 0.1%.
(d) Calculate the average percentage change in all other items excluding fresh vegetables (given by subtracting the points contribution for Fresh vegetables from the All groups index in both quarters and then calculating the percentage change between the resulting numbers—which represent the points contribution of the ‘other’ items). For the above example, the numbers for All groups excluding Fresh vegetables are: June, 121.0–1.50 = 119.5; September, 121.3–1.60 = 119.7; and the percentage change, (119.7–119.5)/119.5x100 = 0.2%. In other words, prices of all items other than fresh vegetables increased by 0.2% on average between the June and September quarters 1998.
(e) Estimate the effect on the All groups CPI of a forecast change in the prices of one of the items (given by applying the forecast percentage change to the item's points contribution and expressing the result as a percentage of the All groups index number). For example, if prices of fresh vegetables were forecast to increase by 25% in December quarter 1998, then the points change for Fresh vegetables would be 1.60x0.25 = 0.4, which would deliver an increase in the All groups index of 0.4/121.3x100 = 0.3%. In other words, a 25% increase in fresh vegetable prices in December quarter 1998 would have the effect of increasing the CPI by 0.3%.
ABS rounding conventions
To ensure consistency in application of data produced from the CPI, it is necessary for the ABS to adopt a set of consistent rounding conventions or rules for the calculation and presentation of data. The conventions strike a balance between maximising the usefulness of the data for analytical purposes and retaining a sense of the underlying precision of the estimates. These conventions need to be taken into account when using CPI data for analytical or other special purposes.
Index numbers are always published to a base of 100.0. Index numbers and percentage changes are always published to one decimal place, with the percentage changes being calculated from the rounded index numbers. Points contributions are published to two decimal places, with points contributions change being calculated from the rounded points contributions. Index numbers for periods longer than a single quarter (e.g. for financial years) are calculated as the simple arithmetic average of the relevant rounded quarterly index numbers.
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