APPENDIX 7 IMPACT OF FREQUENCY OF WEIGHT UPDATES
INTRODUCTION
1. This appendix describes upper level item substitution in the CPI, provides the results of ABS and Statistics New Zealand's analyses and outlines future ABS work.
ITEM SUBSTITUTION, INDEX FORMULAE AND THE FREQUENCY OF CPI WEIGHT UPDATES
2. As consumer expenditure patterns change over time, a fixed set of weights used in the CPI runs the risk of becoming unrepresentative, and can lead to potential item substitution bias. Item substitution occurs when households react to changes in relative prices by choosing to reduce purchases of goods and services showing higher relative price change, and instead buy more of those showing lower relative price change.
3. Under such circumstances, a fixedbase Laspeyres index will overstate the price change of the whole basket as it is unable to take account of changes in the substitutions that consumers make in response to relative price changes. For example, were the price of beef to increase more than the price of chicken, one would expect consumers to purchase more chicken and less beef than before. As a fixedbase index would continue to price the original quantities of beef and chicken, the actual price change faced by consumers would be overstated.
4. Item substitution bias is due to changes in the pattern of household consumption which takes place over time as a result of both demand and supply changes. The longer the period between weight revision periods, the more time there is for consumers to substitute towards or away from goods and services in reaction to relative price changes, and as a result of changes in income. Similarly, supply conditions (and therefore the availability, or otherwise, of certain goods and services) can change substantially over the period in which the weights are fixed.
5. Like most CPIs, the Australian CPI is calculated using a baseweighted modified Laspeyres index formula which keeps quantities fixed between major revisions but allows prices to vary. A Laspeyres (or in most cases a Laspeyrestype) index measures the change in the cost of purchasing the same basket of goods and services in the current period as was purchased in a specified base period. The weights reflect expenditures from an historical period, the base period.
6. Laspeyres indexes are practical and easy to interpret, however they do not capture the substitution that occurs towards relatively cheaper items.
7. Superlative indexes make use of both beginningofperiod and endofperiod information on both prices and quantities (expenditures), thereby accounting for substitution across items. However, in order to construct a superlative index both price and quantity (expenditure) data are required for both periods under consideration. Given that current period expenditure data are not available on a sufficiently timely basis, a superlative formula cannot be used in the routine production of the CPI, which is why statistical agencies tend to rely on fixed baskets. Most, if not all, statistical agencies use a Laspeyrestype index (the requirement for endofperiod information in real time is the reason this type of index is an impractical option for statistical offices for the compilation of the CPI).
8. Superlative CPIs can be produced retrospectively once the required weighting data is available.
CONSTRUCTION
9. The ABS has constructed a superlative index, retrospectively, to provide an estimation of potential item (upper level) substitution bias in the fixedweight Australian CPI, as is done by Statistics New Zealand (SNZ) following each CPI reweight of the NZ CPI (see Statistics New Zealand, 2008).
10. Superlative indexes allow for substitution as they make use of weights for both the earlier and later periods under consideration (basically averaging across historical and current expenditures to derive a ‘representative’ set of weights for the period) whereas the Laspeyres index uses only base period weights. Given that current period weights are not available on a sufficiently timely basis, a superlative index cannot be used in the routine production of the CPI. However, superlative CPIs can be produced retrospectively, once the required weighting data is available.
11. Numerical estimates of item substitution bias have been made at relatively high levels of aggregation. The analysis is limited to expenditure class data as this is the lowest level for which reliable weighting information (from the HES) is available and this is the level at which the underlying quantity weights remain fixed between CPI reviews. Thus, the analysis captures substitution from one expenditure class to another, e.g. from Beef and veal to Poultry, but not within a given expenditure class, e.g. from beef to veal.
12. A superlative index has been constructed between the June quarter 2000 (start of the 14th series) and June quarter 2005 (start of the 15th series) reweighting periods, based on national (weighted average of eight capital cities) price indexes and expenditure weights for 88 of the 90 expenditure classes. The Financial services subgroup (comprising the Deposit and loan facilities and Other financial services expenditure classes) has been excluded from the analysis as it was introduced into the CPI in 2003, between the two periods under consideration (i.e. wasn't in the 14th series). To obtain an identical basket for comparison, the 15th series weighting pattern was recalculated excluding Financial services.
13. Using the expenditure class data, i) direct Laspeyrestype, ii) direct Paasche, and iii) direct Fisher indexes have been calculated at the All groups level. The indexes have all been calculated with the base period June quarter 2000 = 100.0. For the Paasche index, to estimate current period weights each quarter, the ABS applied a linear model between the June 2000 and June 2005 weighting patterns. Index numbers and percentage changes are presented to one decimal place, in line with the standard CPI rounding procedures.
14. Using these indexes, an estimate of potential item substitution bias in the CPI is obtained by subtracting the Fisher index from the Laspeyres index. The Fisher index is regarded as the best practical approximation of a 'true' (or 'ideal') price index, being the geometric average of the Laspeyres and Paasche indexes.
RESULTS
Table 1  Alternative CPI indexes, June quarters 20002005
 Quarter(a)  Change (%) 
Index type  Jun2000  Jun2001  Jun2002  Jun2003  Jun2004  Jun2005  Jun2000 to Jun2005 

Laspeyres  100.0  106.0  109.0  112.0  114.7  117.6  17.6 
Paasche  100.0  105.8  108.7  111.2  113.2  115.2  15.2 
Fisher  100.0  105.9  108.9  111.6  114.0  116.4  16.4 
Laspeyres minus Fisher (potential bias)  0.0  0.1  0.1  0.4  0.7  1.2  1.2 

(a) Index number base: June quarter 2000 = 100.0 
15. The analysis found that the All groups CPI was upwardly biased (as measured by the difference between the Laspeyres index and the Fisher index) by 1.2 percentage points at the end of the five year period due to the inability of the fixedbase index to take account of the item substitution effect. The All groups index calculated using a fixedweight direct Laspeyrestype formula increased by a total of 17.6% over the fiveyear period from June quarter 2000 to June quarter 2005. The retrospective superlative index, calculated using the Fisher formula, rose by 16.4% over the same period.
16. On an annual basis this equates to an average difference of 0.2 of a percentage point per year. Thus, it can be said that the CPI for the period June quarter 2000 to June quarter 2005 is potentially upwardly biased by 0.2 of a percentage point per year due to the inability to take account of the upper level item substitution effect.
17. These results are consistent with studies by other national statistical agencies.
Graph 1  Potential upper level item substitution bias in the All groups CPI (indicated by the difference between the Laspeyres and Fisher indexes)
18. The results show that the longer the period between reweights, the larger the potential upper level item substitution bias effect on the index. Table 1 and Graph 1 above illustrate the cumulative nature of the potential bias.
19. The ABS analysis estimates the annual potential item substitution bias following the second year (i.e. holding the basket constant for two years) to be 0.1 of a percentage point, whereas the period between the fourth and fifth years (i.e. holding the basket constant for five years) has an estimated potential annual bias of 0.5 of a percentage point. This finding is consistent with the SNZ analysis which shows that item substitution bias is considerably greater when NZ CPI weights are updated at sixyearly rather than threeyearly intervals (see below).
20. While there are five main sources of bias in CPIs, this analysis focuses on one type only  upper level item substitution bias  and therefore the results in the analysis should not be taken to equate to the total bias in the CPI, which will be the net sum of all sources of bias. It should also be noted that a new tax system was introduced in Australia during the analysis period, principally the inclusion of the goods and services tax (GST). It is not known whether this has impacted upon the results of the analysis.
SNZ ANALYSES
21. SNZ compiled Laspeyres and retrospective superlative index time series for four scenariosbetween June quarter 2002, June quarter 2006 and June quarter 2008that cover different combinations of the frequency of weight updates and the level in the hierarchical CPI structure of weight updates. Generally, the results show that item substitution bias in the fixedbase New Zealand CPI grows over time during the period in which weights are fixed, and that the lower the level at which the weights are fixed (i.e. if lowerlevel weights are not updated between revision periods), the larger the bias.
22. Of particular interest, given that the Australian CPI is currently reweighted every six years, SNZ demonstrated how the New Zealand CPI might have tracked had a scheduled (2006) reweight not occurred (by holding the 2002 weights fixed at the class level for the period June quarter 2002 to June quarter 2008). The analyses show that employing fixed weights for six years would have resulted in an annual average increase of 3.2% in the New Zealand All groups CPI for the period June quarter 2006 to June quarter 2008, compared with an annual average increase of 3.0% for the same period under the current SNZ practice of threeyearly weight updates.
FUTURE WORK
23. The ABS will finalise the 16th series weighting pattern in October 2011. The ABS will then be in a position to extend its analyses and construct a retrospective superlative index for the period June 2005 to June 2011, providing an estimate of the bias in the CPI due to the current sixyearly weight update cycle, and producing a retrospective superlative index time series from June 2000 to June 2011.
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