Monthly Weighted Median CPI YoY

The Monthly Weighted Median CPI (Consumer Price Index, a basket tracking household prices) YoY tracks underlying inflation for Australia. Underlying inflation means the broad trend without one-off spikes and drops, and YoY means change versus the same month a year earlier. The Australian Bureau of Statistics builds it for metropolitan households in 8 capital cities from 87 expenditure classes, groupings of similar items, in 11 groups. It is not headline inflation (All groups CPI, the full basket total), and the quarterly CPI stays the principal measure.

Prices are collected at regular intervals each month, with food and fuel weekly, about half the basket monthly, and other items quarterly or annually. The index is released about 4 weeks after the reference month at 11:30am Sydney time, with November data in January for holidays. Each release shows the All groups index, 11 groups and selected classes with time series spreadsheets, plus the Trimmed mean and Weighted median. Headline data stays unrevised except in exceptional cases, while adjusted medians revise routinely, so compare with a year earlier or 3 months prior.

Broad centre moves matter more than one-off spikes because the median sits at the middle of ranked price changes.

• Food, alcohol and tobacco: household food and drink purchases, alcoholic drinks and tobacco products.
• Clothing and household furnishings: garments and shoes, home furnishings, appliances and household services.
• Housing: dwelling construction excluding land, rents and related costs excluding mortgage interest.
• Health, education and insurance: health goods and services, education fees set yearly, and insurance and financial service costs.
• Transport and communication: private motoring including automotive fuel plus other transport, and communication goods and services.
• Recreation and culture: holiday travel and accommodation plus recreational and cultural goods and services.

The June 2020 quarter (press release July 29, 2020) shows the filter, with headline CPI down 1.9%, the largest fall in 72 years. Free child care fell 95.0%, automotive fuel fell 19.3% and pre-school and primary education fell 16.2%, while the index without those three rose 0.1%. Annual inflation was negative 0.3%, yet Trimmed mean fell 0.1% and Weighted median rose 0.1%, both described as relatively flat. The median stayed positive because it took the centre price change and left the huge one-off falls at the bottom.

1. Seasonally adjusted inputs: Start from adjusted monthly changes for 87 classes, removing calendar effects so fruit or education fees do not always drop out.
2. Rank from lowest to highest: Rank classes by monthly change and attach each class weight from its previous month contribution.
3. Cumulate weights: Cumulate weights along the sorted order to 100, forming the distribution of price changes by spending share. Weights update yearly from household spending surveys and national accounts data between surveys.
4. Median pick: Take the first class reaching cumulative weight 50 as the monthly median movement. The Trimmed mean is the weighted average of classes between 15 and 85. For illustration, five toy changes of negative 0.4%, 0.2%, 1.0%, 3.0% and 5.0% carry weights 20, 10, 25, 15 and 30. Cumulative weights reach 20, 30, 55, 70 and 100, so domestic holiday and travel at 55 gives median positive 1.0%.
5. Chain to YoY: Chain the median move into its index and compute YoY as (Index now minus Index then) divided by Index then times 100. In the publisher example the All groups index rose from 113.5 to 114.2 for a 0.6% monthly move. It rose from 106.7 to 114.2 for a 7.0% annual move, and the national index averages 8 capitals.
6. Carry-forward: Items with no new price in a month carry forward with zero movement. The month measures only newly priced items and completes the rest by carry-forward.