Australian Bureau of Statistics
6464.0 - House Price Indexes: Concepts, Sources and Methods, Australia, 2009
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 14/12/2009
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CHAPTER 11 HOUSE PRICE INDEX CALCULATION IN PRACTICE
11.8 Analyses of various clustering options were undertaken (refer to above MAC paper). An optimal stratification was defined as one which maximised the homogeneity of the suburbs in a cluster, while also maximising the number of price observations each quarter. That is, reducing the number of clusters in a city would be expected to increase the number of price observations in most clusters, producing more robust cluster medians from which to derive price relatives, however, it could also have the effect of creating less homogenous clusters.
11.9 The recommendations of the methodological analyses were implemented in the December quarter 2008 publication of the HPI. The series were linked in the 'benchmark' quarter, March quarter 2008. The time series period of the HPI which is calculated using the new clusters is referred to as Series 2.
11.10 The resultant stratification was simplified to cluster suburbs according to long-term median price (mean-adjusted median) and SEIFA. Suburbs in a cluster therefore share common characteristics regardless of whether they fall within the same SSD. The number of clusters in each city were reduced (apart from Darwin), which has also contributed to improvements in analysis and editing processes.
11.11 The following table shows the number of clusters currently used for each city (Series 2), compared to the previous series (Series 1):
11.12 Data from the 2006 Census were used to update the coverage of the capital cities. This meant that transactions which had previously been excluded from cluster median calculations now contribute to index compilation if the suburb in which they are located was recorded in the 2006 Census. The opportunity was also taken to review the various permutations of locality nomenclature to ensure all in-scope transactions are included.
11.13 The 2006 Census data also contributed to the updated weighting of the HPIs, as described in Chapter 7.
11.14 When calculating new weights after a review, the link period is usually different from the period for which the new value weights have been calculated (for more information on the weight reference period refer to chapters 7 and 10). Therefore it is necessary to price update (revalue) the values from the weight reference period to the price levels of the link period.
11.15 As described in chapter 10, the methodology for price updating the value data for each cluster in the HPI differs to that of other ABS price indexes. In other indexes a measure of price change between the link period and the weight reference period is derived for the index component, and this is multiplied by the values from the weight reference period.
11.16 In the HPI, the updated value of the housing stock is determined by multiplying quantities from the weight reference period by prices from the link period for each cluster. Cluster quantities are house counts obtained from 2006 Census data. Cluster prices are derived as the 'mean-adjusted median' for the link period (March quarter 2008). This measure is calculated by finding the ratio of the mean and median for the four consecutive quarters up to and including the link period, and then averaging these ratios. This average ratio is applied to the link period median with the intention of deriving a more robust 'mean' price for the cluster than is possible by calculating a mean price for one quarter (which is influenced by any unusual transactions).
11.17 The resulting link period value aggregate is then expressed in terms of prices from the link period and quantities from the weight reference period.
CALCULATING INDEX NUMBERS
11.18 Chapter 7 also referred to the HPI methodology of deriving price relatives. Other ABS indexes derive price relatives by comparing the prices of items in the current period with the prices in the base period (or price reference period), and then calculating an average of these price relatives for the product grouping. A percentage change for the group (or 'elementary aggregate') is then determined from current and previous average price relatives.
11.19 In the HPI, the median price of a cluster in the current period is compared with the median price of the cluster in the previous period. As described in Chapter 7, the clusters are the lowest level, or elementary aggregate of the HPI index structure. The price relative derived then is used to revalue the value of housing stock in the previous period to produce a current period value for the cluster. The updated value provides an estimate of the value of the base period stock of houses in the current period.
11.20 The price updated values for the clusters are then summed to derive the current value of the total housing stock. Index numbers are calculated from the value aggregates at every level of the index.
11.21 When a price index has not been linked, indexes for any component can be calculated simply by dividing the current period value aggregate by its value aggregate in the index reference period and multiplying by 100 (when the index is set to 100.0). However, the HPI has been linked once since its reference period (2003-04) and the index numbers must be calculated from
where ILP is the index number for the link period (March quarter 2008 for the HPI Series 2), and VCP and VLP are the value aggregates in the current periods and link periods respectively.
11.22 The process can be illustrated by the example in Tables 2 and 3 which show the index calculation for a city which is made up of five clusters. In this example, the first step is to calculate the price movement for each cluster via a price relative. The next step is to produce a current period value for each cluster by using the price relative to inflate or deflate the previous period value. The cluster values can be aggregated to produce values for the city. The final step is to produce a current period price index by dividing the current period value by the link period value and then multiplying this by the link period index number. This example demonstrates that the movement in the aggregate index is determined not just by the price movements, but also by the weights. Cluster 1 shows a very large price fall, however its impact on the overall index movement reflects its relatively low weight.
THE TWO STAGE APPROACH
The benchmark series
11.23 Though a complete coverage of property sales data can eventually be obtained from the VGs, this data is not available on a timely basis for the most recent quarters. As a result, the ABS has adopted a two-stage approach to produce the HPI. The first stage is to compile a benchmark series based on the complete, or near complete, VGs dataset for each quarter. In practice, the data underlying the benchmark series for any quarter is not sufficiently complete until two more quarters of data has been received. For example, the benchmark HPI for March quarter each year will not be available until it is released with the September quarter issue of the HPI publication. Thus, in the March quarter issue, the index is preliminary; the index is subsequently revised in the June quarter issue, but it is still preliminary until it is revised for the final time in the September quarter issue. See below for a further explanation of revisions.
11.24 The benchmark series index numbers for a city are calculated, in the manner described above, using price relatives for each cluster which have been calculated from price observations sourced from the VGs. The weighted average index for eight capital cities is compiled in the same way as the benchmark series (i.e. aggregating the revalued value of housing stock in each city, dividing that aggregate by the link period aggregate value for the eight capital cities, and then multiplying this ratio by the link period index number for the eight capital cities).
Compiling the 'leading indicator' series
11.25 The second stage, referred to as the 'leading indicator' series, involves compiling price indexes for the two most recent quarters (e.g. in the September quarter issue, the June and September quarters) based on a combination of mortgage lenders’ data and the VGs data available at that point in time. The weighting of the leading indicator series are determined by the weights as they are inflated or deflated each quarter in the benchmark series. That is, when the benchmark quarter is compiled, the resultant value aggregates of each cluster are used in the subsequent leading indicator series, to be revalued by the price relatives produced in that series.
11.26 The process of compiling the leading indicator series is presented algebraically below.
11.27 In merging the VGs and mortgage lenders’ datasets for the leading indicator series, any property transactions appearing in both are removed from the mortgage lenders’ data.
11.28 Chapter 8 describes the method of calculating price relatives which is used to address the changing composition of VGs and mortgage lenders' data in the sets of prices collected for each quarter.
11.29 As the VGs based benchmark indexes become available, they are used to progressively replace the leading indicator series. As a result, the most recent two quarters’ estimates of the HPI are preliminary, and subject to revision. The expectation is that the second preliminary estimate published for a quarter will be closer to the final estimate than was the first preliminary estimate published.
11.30 The latest quarterly observation (labelled with a ‘p’) in the HPI tables is the first preliminary estimate based on a combination of the available VGs data and mortgage lenders’ data. The second latest observation (also labelled with a ‘p’) will be the revised estimate from the previous quarter’s publication. It will be the second preliminary estimate based on available VGs data (more than were available for the first estimate) and mortgage lenders’ data. The third latest observation (labelled with an ‘r’ if it has been revised since the previous quarter’s estimate) is the first publication of the benchmark series compiled from a comprehensive set of VGs data only.
11.31 The ABS' aim is to develop a single optimal model for producing a final price movement in a more timely manner than is currently possible. While continuing investigations and analysis are underway, the HPI publication also includes a table stating the size of the revisions applied to these series over time. The first, second and final estimates of the index numbers for any particular quarter are collated (with this information dating back to June quarter 2005, when the first leading indicators were available). The size of the revision between the final index number and the two preliminary estimates is also published. This information eliminates the need to reference previous publications to determine what index number was initially published for a quarter, and also provides an indication of the accuracy of the leading indicator series.
11.32 The revisions to the indexes for each of the eight capital cities and for the weighted average of the eight capital cities are published as a time series spreadsheet in Table 9 of 6416.0 on the ABS website.
11.33 A summary of the preliminary and final index numbers, quarterly and annual percentage change, and the magnitude of the revisions to the percentage change is also published in Table 9.
11.34 To ensure consistency in the application of data produced from ABS price indexes, it is necessary for the ABS to adopt a set of consistent rounding conventions or rules for the calculation and presentation of data. The conventions strike a balance between maximising the usefulness of the data for analytical purposes and retaining a sense of the underlying precision of the estimates. These conventions need to be taken into account when using price index data for analytical or other special purposes.
11.35 Index numbers are always published to a base of 100.0. Index numbers and percentage changes are always published to one decimal place, with the percentage changes being calculated from the rounded index numbers. Index numbers for periods longer than a single quarter (e.g. for financial years) are calculated as the simple arithmetic average of the relevant rounded quarterly index numbers. Percentage changes between these periods are calculated from the rounded average index numbers.
11.36 A summary of the concepts described above is described algebraically below. As discussed in Chapter 4, Laspeyres price index formula (where quantities in the base period (qi0) are fixed) can be expressed as follows:
11.37 That is, the index in the current period, t, for the sum of i clusters, is calculated by dividing the sum of current values by the sum of base period values, or alternatively multiplying the ratio of the median price in the current period to the median price in the base period (the price relative as described in Chapter 4) by the value weight of the cluster in the base period, and then calculating the index by summing these component indexes.
The HPI in practice
11.38 In practice, the counts of houses (quantity) in the base period are fixed, and the value of the housing stock is updated each quarter. Median prices in the current and previous periods are compared, rather than in the current and base period.
11.39 As the value weight of each cluster is inflated or deflated each quarter by the price relative of the current quarter median to the previous quarter median, the formula can be expressed in the form:
The leading indicator series
11.40 Further, value weights of the clusters in the most recent quarters, P1 and P2, are derived from the weights of the clusters in the benchmark (BM) quarter. Hence equation (11.3) becomes:
1 The ABS' Socio-Economic Index for Areas (SEIFA) ranks geographic areas according to their social and economic conditions. For further information, refer to Information paper: An Introduction to Socio-Economic Indexes for Areas (SEIFA), 2006 (cat. no. 2039.0). <back
2 The Australian Standard Geographic Classification (ASGC) is a set of hierarchical geographic structures. The main structure consists of spatial units in each of the following hierarchical levels: Australia; States/Territories; Statistical Divisions (SDs); Statistical Subdivisions (SSDs); Statistical Local Areas and Census Collection Districts. The HPI weights and structure have been updated most recently using the 2006 edition of the ASGC (which was used in the 2006 Census of Population and Housing). For more information on the ASGC refer to Australian Standard Geographical Classification (ASGC) (cat. no. 1216.0). <back
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This page last updated 11 December 2009