ESTIMATING THE UPPER LEVEL SUBSTITUTION BIAS IN THE AUSTRALIAN CPI
5.1 Consumers’ purchasing patterns react to price change over time, where goods and services with high inflation are typically substituted with low inflation alternatives. Like most CPIs, the Australian CPI uses a fixed–base Laspeyres–type formula (also known as the Lowe index formula), which 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. This overstates the price change of the basket as it is not able to take account of the substitution consumers make in response to relative price change and changes in preferences, resulting in substitution bias.
5.2 With each release of the new CPI weights, the ABS constructs a retrospective superlative–type index which more closely reflects true inflation. This enables an estimate of the upper level substitution bias in the Australian CPI to be derived. This superlative index takes the weights from both the earlier and later periods into consideration, thereby accounting for substitution across goods and services (in this case expenditure classes).
5.3 In the past, the ABS has used the following methodology to derive an estimate of the substitution bias:
 Construct Laspeyres–type (Lowe), Paasche–type and superlative Fisher–type indexes at the All groups CPI level, using the published CPI weights. These weights have been price updated from the period of the HES survey (199899, 200304 and 200910) to the link period, which is the quarter prior to the implementation of the weights (June quarter 2000, June quarter 2005 and June quarter 2011).
 For the Paasche–type index, which requires current period weights, a linear model is applied between re–weighting periods to obtain quarterly weights.
 An estimate of the upper level substitution bias is then obtained as the difference between the Fisher–type index (the geometric mean of the Laspeyres and Paasche) and the Laspeyres–type index, which represents the CPI.
5.4 As part of the 17th series review, the ABS conducted an investigation into the methodology used to estimate substitution bias. This has resulted in changes to the previous methodology, enabling more accurate estimates to be calculated.
5.5 The methodology applied in the 17th series is as follows:
 Calculate financial year Laspeyres and Paasche–type indexes, instead of quarterly, using the original HES weights for each series of the CPI and financial year estimates of price change. Under this approach, the Laspeyres index is a true Laspeyres, and not a Lowe index as was previously the case.
 For the Paasche index, the weights for each financial year in between re–weighting periods are interpolated using a linear model.
 The geometric mean of the Laspeyres and Paasche approximates the Fisher.
 The Fisher is compared to the Laspeyres index to estimate the level of substitution bias, consistent with international practice.
5.6 This approach results in a more accurate estimate of true inflation, due to the original financial year weights being used, and the period of the indexes and weights now aligning.
5.7 Using this methodology, the ABS has produced an upper level substitution bias estimate for the 199899 to 201516 period. The results reveal that the amount of bias in the Australian CPI is on average 0.22 of a percentage point per year between 199899 and 201516, due to the inability to take account of the upper level item substitution effect. This is lower than previously estimated (+0.24 of a percentage point between June 2000 and June 2011), predominantly due to the low inflationary environment over recent years.
5.8 The results also show that the average annual substitution bias increases at a faster rate the longer the period between re–weights. Table 5.1 illustrates that the average annual bias is 0.11 one year after a re–weight, increasing to 0.20 in the sixth year.
TABLE 5.1 AVERAGE ANNUAL ITEM SUBSTITUTION BIAS (a) 

Time since re–weight  Bias (Laspeyres – Fisher) 

1 year  0.11 
2 years  0.17 
3 years  0.17 
4 years  0.18 
5 years  0.21 
6 years (b)  0.20 

(a) This takes the average of the annual substitution bias for the 199899 to 200304, 200304 to 200910 and 200910 to 201516 periods.
(b) The six year average annual substitution bias is only based on the 200304 to 200910 and 200910 to 201516 periods. 
5.9 With the move to annual re–weighting, the ABS will continue to review the methodology for producing estimates of substitution bias. While the weights will be updated more frequently in future, there are other challenges such as differing data sources that need to be addressed. The ABS will conduct these investigations and provide an update of intentions in due course.
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