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CHAPTER 7 WEIGHTS AND THEIR SOURCES


INTRODUCTION

7.1 Price indexes use weights to dictate the relative importance of items in the aggregate measure of price movement.

7.2 In HPI compilation, the price relatives of the median prices of the clusters are multiplied by the weights of each cluster to derive a weighted average index number. Therefore, the contribution of a particular cluster's price movement to the movement of the capital city index will be determined by its relative importance in the construction of that index.

7.3 Weights in this instance are value weights: the value of the stock of houses in each cluster. The stock of houses used in the value weights are a fixed quantity: they are held constant from period to period.


HOUSE PRICE INDEX COMPARED TO OTHER INDEXES

7.4 Price indexes such as the Consumer Price Index (CPI) and Producer Price Index (PPI) use a variety of weighting practices. At the lowest level of the index (referred to in CPI and PPI as the "elementary aggregate" level) a sample of individual price observations for particular items are combined each period to enable a period to period measure of price change for the item. This measure of elementary aggregate price movement can be calculated as a ratio of average prices, as an unweighted geometric mean of price relatives, or as a weighted arithmetic mean of price relatives. Choice of method is dependent on assumptions relating to the behaviour of the consumer or producer, and other factors such as availability of weighting information. For more information refer to the CPI and PPI Concepts, Sources and Methods publications (cat. nos. 6461.0 and 6429.0 respectively).

7.5 These lower level price movements are subsequently weighted up the index structure. Weightings are derived to take into account whether the index is an input index (expenditure on goods and services being consumed or used) or output index (revenue from goods or services being produced), and reflect the importance of the good or service in the market covered by the index.

7.6 Weights are usually fixed at the published level of the index, and are reviewed periodically. Below the published level of the index weights can be varied at any time, and often are.

7.7 Compared to the CPI and PPI, the structure of the HPI is quite simple. The lowest level of the index, the elementary aggregate level, corresponds to the clusters which constitute each capital city. For each cluster there is only one price observation each quarter used to calculate its quarterly movement: this is the median price of all transactions observed in that cluster. As it is not possible to price the same house each quarter, a sample of observed house prices are used to measure the price change, and from this sample, a single median price is calculated to represent price of houses in this homogenous grouping of houses (cluster).

7.8 The elementary aggregate (cluster) level of the index is not published. The next level of aggregation is the capital city, and then the eight capital city weighted average.

7.9 Within each capital city, the housing stock has been allocated to particular clusters according to the stratification methodology which maximises the homogeneity of the cluster as well as the number of transactions observed each period. Some clusters will have greater weights than other clusters, reflecting the distribution of housing with particular characteristics across the city. For example, a cluster which groups houses which are large, of high quality, and close to the water will have a small weight if these types of houses make up a small proportion of the total value of housing stock in a city. Suburbs are the building blocks of the clusters, and all suburbs in a city at the weight reference period (see below) are allocated to clusters.

7.10 After a review of the stratification method in 2007 the number of clusters changed (as did the suburbs allocated to them). A new set of weights was introduced into the HPI in December quarter 2008 to reflect the new clusters and an updated stock of houses.


SOURCES OF DATA FOR WEIGHTS

7.11 The HPI is compiled using weights calculated as the value of the stock of established houses. The quantities (stock) of houses used in this calculation are derived from the count of separate houses recorded in the Census of Population and Housing. The HPI series commencing in March quarter 2002 used house counts from the 2001 Census, and house counts from the 2006 Census were used in the new set of weights introduced after the 2007 review.

7.12 An initial value of the established housing stock in each cluster is estimated by aggregating suburb counts of detached houses to the cluster level and valuing them at base period or link period prices. In other words, the quantity of houses in each cluster is multiplied by a measure of the average price of houses in the cluster at the base period or link period. Refer to Chapters 10 and 11 for further information on this process in practice.

7.13 As discussed earlier in Chapter 4, the approach used in HPI is that is that of the Laspeyres index. Therefore, 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 index. What is held constant is the number of houses underpinning these values. The price relatives of the median prices of the clusters for the current and previous quarters are used to price update (inflate or deflate) these stock values for each cluster in each city. Algebraically, this produces the same outcome as weighting together prices for each cluster in each quarter using quantities as the weights but it is much easier to implement operationally.

7.14 The weighting patterns of the clusters in each capital city (below the published level of the index) are not released to users.


WEIGHTED EIGHT CAPITAL CITY INDEX

7.15 The weighted average of the eight capital city indexes represents the aggregated movement of the capital cities, according to their relative importance.

7.16 Just as cluster value weights are aggregated to derive the value for each city, these city value weights are then aggregated to the eight capital city level of the index. The weighted eight capital city index is derived as the sum of the price updated values of each capital city divided by the sum of the base period or link period values of each capital city, multiplied by the base period or link period index number.

7.17 Appendix 1 details the weighting pattern of the eight capital cities index.


WEIGHT REFERENCE PERIOD

7.18 The weight reference period is the time period to which the weights relate. For reasons of stability and representativity, the weight reference period is frequently a year or even longer period.

7.19 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 is selected because:

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