Underlying Inflation Measures: Explaining the Trimmed Mean and Weighted Median
By staff from the Consumer Price Index section of the ABS
Purpose of underlying inflation measures
The Australian Bureau of Statistics (ABS) produces two key measures of underlying inflation – the Trimmed mean and the Weighted median. These measures, also known as ‘core’ inflation, provide an indication of the medium-term trajectory of inflation. Tracking medium-term inflation is important as it assists in inflation-targeting and assessing the health of the Australian economy. In short, the underlying inflation measures produced by the ABS are calculated by reducing the impact of irregular or temporary price changes in the Consumer Price Index (CPI).
A brief history of Australia’s underlying inflation measures
Various measures of underlying inflation have been produced by the ABS and other organisations over the years. The Australian Treasury initially produced ‘exclusion-based’ measures, which were estimated back to 1971. These measures used data from the CPI and removed certain products with volatile price change, such as fruit and vegetables, meat and seafood, and automotive fuel. The ABS has since taken responsibility of producing the exclusion-based measures, the number and type of which have grown and changed to meet the needs of users.
Since 1993, the Reserve Bank of Australia (RBA) has targeted inflation of between 2 and 3 per cent, on average, over the course of the business cycle. (Roberts, 2005) Inflation-targeting resulted in an increased need to measure the medium-term inflationary trend. It was around this time that the RBA began using underlying inflation measures in its analysis of the Australian economy1. This included exclusion-based measures, such as those produced by the Treasury and the ABS, as well as developing other measures derived from the CPI data, such as the Trimmed mean and Weighted median.
In 2007, the ABS assumed responsibility for the calculation and publication of the Trimmed mean and Weighted median series’ developed by the RBA. These measures, and the exclusion-based measures, can be found in table 8 of the CPI publication (cat. no. 6401.0).
In 2010, the ABS conducted a major review of the Australian CPI. The review recommended a number of changes. One of these changes was the calculation of seasonally adjusted CPI estimates, which are a key input into the calculation of underlying inflation measures. From September 2011, the number of seasonally adjusted Expenditure Classes2 increased from around 20 per cent of the weight of the CPI, to a little over 60 per cent. The CPI review, and subsequent changes, enhanced the quality of the seasonally adjusted data, which in turn enhanced the Trimmed mean and Weighted median measures.
To produce the Trimmed mean and Weighted median, seasonally adjusted quarterly movements of the CPI are used. Without the use of seasonally adjusted movements, some Expenditure Classes may always be excluded from the underlying measure due to the volatile nature of their price change. This may include Expenditure Classes that:
- i. are highly seasonal (e.g. fruit); or
ii. have once-a-year price changes (e.g. education fees).
This approach more closely aligns the underlying measures with the rate of inflation experienced by Australian households, as measured by the CPI.
For both underlying measures, all 87 of the CPI Expenditure Classes (ECs) are sorted from lowest to highest in terms of seasonally adjusted quarterly percentage change. The quarterly movements, combined with each Expenditure Class’s respective weight, are used to create a distribution of cumulative weights by Expenditure Class.
The Trimmed mean is calculated using a weighted average of percentage change from the middle 70 per cent of the distribution. That is, Expenditure Classes with a cumulative total below 15 per cent and above 85 per cent are excluded (trimmed) from the calculation. Expenditure Classes which cross the 15 per cent and 85 per cent thresholds are partially included, using the component of their weight which falls within the 70 per cent trim.
The Weighted median is simply the seasonally adjusted quarterly percentage change of the Expenditure Class at (or immediately over) the 50th percentile of the distribution. This can also be thought of as a 50 per cent Trimmed mean.
Chart 1 and 2: Trimmed mean and Weighted median illustration
A more detailed explanation of the calculations behind these measures can be found in Appendix 3: Calculation of Underlying Trend Inflation measures using published CPI data.
CPI compared to the Trimmed mean and Weighted median
Chart 3 illustrates the relative smoothness of the Trimmed mean and Weighted median compared to the CPI, largely due to the removal of temporary or one-off impacts. One such example is the 400 per cent rise in banana prices that occurred in mid-2006 due to supply disruptions caused by Cyclone Larry. This was followed by a sharp fall in banana prices as they returned to normal price levels in 2007. A similar event occurred again in 2011, with banana prices rising as a result of Cyclone Yasi, and later falling to normal price levels. Chart 3 shows that while the CPI was significantly affected by these events, the Trimmed mean and Weighted median were largely unaffected, giving a better picture of the trend of inflation over this period, without the impact of temporary shocks. Another instance where the CPI was affected by a one-off event is the introduction of the childcare rebate in 2007, which saw childcare costs for households fall 33 per cent.
Economic shocks can also have a significant and temporary impact on the CPI, such as the fall in the price of financial services in 2008-09 following the onset of the Global Financial Crisis; and changes in world oil prices, such as those in 2014-15, which resulted in a fall in automotive fuel prices of 22 per cent.
Chart 3: CPI compared to underlying inflation, annual percentage change
Since the changes implemented in 2011, the average annual CPI movement has been 2.0 per cent. In comparison, the average annual movements in the Trimmed mean and Weighted median are 2.1 per cent and 2.2 per cent respectively. The difference between the CPI and these two measures is largely attributable to the fall in automotive fuel prices in 2014-15, which was trimmed from the underlying inflation measures.
Chart 3 shows that the Trimmed mean and Weighted median measures provide a useful compliment to the CPI, which provide an insight into the medium-term inflationary trend. These measures are useful for analysis purposes to assess the health of the Australian economy for important users of the CPI such as the RBA, researchers and economists.
- From 1993 to 1998 the target inflation rate was a measure of underlying inflation which excluded a fixed set of items from the CPI. Since 1998, the target measure of inflation has been the CPI. (Roberts, 2005)
- Expenditure Classes are a grouping of similar goods or services. Examples include Bread; Garments for women; Electricity; and Domestic holiday and travel.
Australian Bureau of Statistics (ABS) 2010, Outcome of the 16th Series Australian Consumer Price Index Review, Dec 2010, cat. no. 6469.0.
ABS 2011, Seasonal Adjustment of Consumer Price Indexes, Sep 2011, cat. no. 6401.0.55.003.
Parliament of Australia 1997, Treasury's Underlying Rate of Inflation, Monthly Statistical Bulletin Feature Articles, November 1997.
Roberts, I. 2005, Underlying Inflation: Concepts, Measurement and Performance, Research Discussion Paper 2005-05, Reserve Bank of Australia.