CONSUMER PRICE INDEX - WEIGHTED MEDIAN AND TRIMMED MEAN Introduction The ABS has received a number of requests to consider publishing the weighted median and trimmed mean consumer price measures in Consumer Price Index, Australia (6401.0). The purpose of this paper is to provide some background on the issues surrounding measures of this type. Weighted Median The weighted median inflation rate, as defined by the Reserve Bank of Australia (RBA), is the inflation rate for that item or group of items which is in the middle of the total distribution - that is, half the weighted price changes are on one side of the 1 median, and half on the other . It is calculated by ranking price movements for CPI expenditure classes by their size in percentage change terms, and then attaching corresponding weights to allow the median value to be identified. The data are obtained from table 7 of Consumer Price Index, Australia (6401.0). Prices Branch have calculated the weighted median from December quarter 2000 to December quarter 2002 using the RBA’s methodology but with data at two different levels of aggregation. The first is for the 89 expenditure classes at the “total Australia” level (referred to as the “8 capital cities”). This is consistent with the level of aggregation used by the RBA but the ABS has used unpublished data which enables the calculations to be made with a higher degree of precision. The second is also at the expenditure class level but the weighted median is based on taking each expenditure class for each individual city into account. Weighted Median Comparison Tabulated below is a comparison between each of the three measures of the weighted median and the CPI. The first measure, labelled “RBA”, is the series as published by the RBA (using the methodology described above). The second measure, labelled “ABS (8 caps)” is based on the percentage change in the 89 expenditure classes for the 8 capital cities (89 items) while the third measure, labelled “ABS (by city)”, uses the percentage change in the 89 expenditure classes for the individual capital cities (712 items). The comparison indicates there are differences over time between the published RBA measure and the two other measures calculated by the ABS. The largest difference is 0.2 percentage points in June quarter 2001.
1 Source : Reserve Bank of Australia Bulletin, August 1994
CPI vs Weighted Medians CPI % change Dec-00 0.3 Mar-01 1.1 Jun-01 0.8 Sep-01 0.3 Dec-01 0.9 Mar-02 0.9 Jun-02 0.7 Sep-02 0.7 Dec-02 0.7
RBA % change 0.4 0.9 0.9 0.7 0.7 0.5 0.6 0.8 0.6
ABS (8 caps) % change 0.4 0.9 1.0 0.7 0.7 0.5 0.6 0.8 0.6
ABS (by city) % change 0.3 0.8 0.7 0.6 0.6 0.5 0.5 0.7 0.6
The following two tables help explain why there are differences between ABS (8 caps) and ABS (by city). The first table shows, for each quarter, the number of 8 capital city expenditure classes which increased, the number that decreased, and the number which were unchanged. The second table provides the information when expenditure classes for the individual capital cities are used.
Eight Capital Cities - change in expenditure classes Decrease % No change % Dec-00 33 37.1 4 4.5 Mar-01 16 18.0 1 1.1 Jun-01 13 14.6 9 10.1 Sep-01 23 25.8 4 4.5 Dec-01 21 23.6 4 4.5 Mar-02 30 33.7 1 1.1 Jun-02 22 24.7 5 5.6 Sep-02 29 32.6 2 2.2 Dec-02 27 30.3 4 4.5
Increase 52 72 67 62 64 58 62 58 58
% 58.4 80.9 75.3 69.7 71.9 65.2 69.7 65.2 65.2
Total 89 89 89 89 89 89 89 89 89
Capital City - change in expenditure classes Decrease % No Change Dec-00 262 36.8 68 Mar-01 172 24.1 41 Jun-01 151 21.2 90 Sep-01 212 29.8 44 Dec-01 172 24.2 60 Mar-02 243 34.1 51 Jun-02 215 30.2 75 Sep-02 242 34.0 34 Dec-02 213 29.9 74
% 9.5 5.8 12.6 6.2 8.4 7.2 10.5 4.8 10.4
Increase 382 499 471 456 480 418 422 436 425
% 53.7 70.1 66.2 64.0 67.4 58.7 59.3 61.2 59.7
Total 712 712 712 712 712 712 712 712 712
Trimmed Mean The trimmed mean inflation rate involves calculating the weighted mean of price movements in the central core of the quarterly data. Effectively the upper and lower tails of the data are cut off. The size of the central core can be varied but, in the examples presented in this paper, the central 70 per cent has been chosen. The comparison of the trimmed mean (refer to table below) showed only minor variations between the Reserve Bank results using published expenditure class data and measures calculated by the ABS. These were based on the 89 expenditure classes for the 8 capital cities combined (referred to as “ABS (8 caps)”) and using data from the 89 expenditure classes for each of the individual capital cities (referred to as “ABS (by city)”). A key area of concern with the trimmed mean approach is that the choice of the cutoff is subjective. CPI vs Trimmed Means CPI % change Dec-00 0.3 Mar-01 1.1 Jun-01 0.8 Sep-01 0.3 Dec-01 0.9 Mar-02 0.9 Jun-02 0.7 Sep-02 0.7 Dec-02 0.7
RBA % change 0.4 0.9 0.9 0.7 0.7 0.6 0.5 0.6 0.7
ABS (8 caps) % change 0.4 0.9 0.9 0.7 0.7 0.6 0.5 0.6 0.6
ABS (by city) % change 0.4 0.9 0.9 0.6 0.7 0.6 0.5 0.6 0.6
Where to from here? The ABS has considered whether to publish either or both of the measures. In doing so, issues taken into account were: (a) the statistical validity of the measure and (b) the purpose of the measure - ie, the particular aspect of inflation that the measure is seeking to inform users about. In respect of (a), the ABS has reservations about the trimmed mean in particular, because of the subjective nature of the cutoff. In respect of (b), there is demand for a measure that users feel provides a systematic means of assessing the trend of the CPI, which they often refer to as a measure of “underlying inflation”. The ABS would be concerned about publishing measures that could be viewed as ‘competing’ with the ‘headline CPI’ measure. The CPI is probably the ABS’s best known and widely used statistic, and as such the ABS has a responsibility to ensure that the broad user community is not confused by the presence of an ‘alternative’ CPI.
However, the ABS does publish in tables 9 & 10 of the CPI publication a range of analytical measures to assist sophisticated users in understanding the drivers of household sector inflation, so if it was decided to introduce a new measure or measures then this could be a place to present them. The ABS is mindful that neither of the two measures is mentioned in the international standards or manuals for CPI statistics and we are not aware of any other country that publishes such measures as part of their CPI, but this by itself is not a reason for the ABS not to publish the measures.
Prices Branch Australian Bureau of Statistics April 2003