**WEIGHTS AND THEIR SOURCES**

**INTRODUCTION**

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**6.1 ** This section describes the role of weights in the indexes as well as their sources.

**6.2** Price indexes use weights to represent the relative importance of products or components in the aggregate measure of price change. For example, in the HPI and ADPI, each stratum has a weight which reflects its relative importance to the capital city indexes. For the RPPI, the weight of established houses compared to the weight of attached dwellings reflect their importance in each capital city.

**6.3 ** Weights in this instance are value shares: the value of the stock of dwellings. The stock of dwellings used to underpin the value shares (as value is a combination of prices and quantities) are a fixed quantity: they are held constant from period to period.

**THE ROLE OF WEIGHTS**

**6.4** In the HPI and ADPI each stratum represents the lowest level of the index (footnote 10). In the indexes, the median price change of each stratum is used to measure price change for the entire capital city. Without explicit weights, price changes for all strata would be given equal weight in calculating the price change for the whole capital city. This may not be a true reflection of the relative importance of each stratum in terms of its share of the value of the stock of dwellings.

**6.5 ** Indexes at the strata level are not published. The next level of aggregation is the capital city, and then the eight capital city weighted average. To arrive at the aggregate weighted average of eight capital cities index, the price relatives of the lower level indexes are multiplied by their relative weights to derive the respective aggregate index (footnote 11).The RPPI is calculated by multiplying the HPI and ADPI in the same way.

**6.6 ** Within each capital city, the value of the dwelling stock in each suburb has been allocated to particular strata according to the stratification methodology which maximises the homogeneity of the stratum as well as the number of transactions observed each period (footnote 12).Some strata will have greater weights than other strata reflecting the distribution of dwellings with particular characteristics across the city. For example, a stratum which groups dwellings which are large and exclusive will have a small weight if these types of dwellings make up a small proportion of the total value of dwelling stock in a city.

**SOURCE OF DATA FOR WEIGHTS**

**6.7 ** The indexes are compiled using weights derived from the value of the stock of dwellings in scope of the index. The quantities (stock) of dwellings used in this calculation are taken from the count of in scope dwellings recorded in the ABS Census of Population and Housing.

**6.8** An initial value of the dwelling stock in each stratum is estimated by aggregating suburb counts of dwellings to the stratum level and valuing them at price reference period prices. In other words, the quantity of dwellings in each stratum is multiplied by a measure of the average price of dwellings in the stratum at the price reference period. In the current series this means 2011 Census counts multiplied by March quarter 2013 prices. Refer to **Calculation in Practice** and **Linking and Re-referencing **for further information on this process in practice.

**6.9 **As discussed earlier in **Residential Property Price Index Theory**, the approach used in the indexes is the Lowe index. It is important to understand that it is not the stock values that are held constant from period to period in the compilation of the indexes. What is held constant is the quantity of dwellings underpinning these values. The price relatives of the median prices of the strata for the current and previous quarters are used to price update (inflate or deflate) these stock values for each stratum in each city. Algebraically, this is the same as weighting together prices for each stratum in each quarter using quantities as the weights and calculating the ratio of the two quarters but it is easier to implement operationally.

**WEIGHT REFERENCE PERIOD**

**6.10 **The weight reference period is the time period to which the weights refer. For reasons of stability and representivity, the weight reference period is frequently a year or an even longer period.

**6.11 **The accuracy and reliability of a price index are determined, in large part, by the weighting structure. For this reason, the choice of the period covered by the weights is crucial. The period chosen to be the weight reference period should generally meet the following criteria:

- the economic activity over the period is reasonably normal/stable and representative of likely future activity;
- it is not too distant from the price reference period (the period where the weights are introduced to the index series); and
- the required data are available.

**6.12 **The weight reference period and the price reference period used in a price index formula are rarely the same period in practice. New weights are introduced during a specific quarter, known as the link period (which in the case of the property price indexes becomes the new price reference period for the index). For this reason, weights are price updated to account for price changes between the weight reference period and the price reference period.

**6.13 **The weight reference period for the current series of the indexes is 2011 and the price reference period (and link period) is March quarter 2013.

**UPDATING WEIGHTS**
**6.14 **The current weights, based on the 2011 Census, will be updated once data becomes available from the 2016 Census. At that time, the ABS will also re-examine the existing strata to determine whether they need to be updated for any of the capital cities.

**6.15 ****Linking and Re-referencing** outlines the processes involved in re-linking indexes following changes in the underlying weights.

10

Sometimes referred to as the ‘elementary aggregate’ level, for example in the CPI and PPI.

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11

**Appendix 2** details the weighting pattern of the weighted average of the eight capital cities and the RPPI.

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12

See

**Calculation in Practice**, for more details.

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