CHAPTER 11 HOUSE PRICE INDEX CALCULATION IN PRACTICE


INTRODUCTION

11.1 This chapter will collate and expand on the information provided in previous chapters to describe how the HPI is calculated in practice.


SUBURBS AS BUILDING BLOCKS

11.2 As outlined in the previous chapters, the approach adopted by the ABS to control for compositional effects in measuring price movements is the stratification method. The allocation of suburbs (the building blocks of the indexes) to clusters in each city is determined by the type of stratification implemented.


CLUSTERING

After the 2004 HPI Review

11.3 The 2004 HPI review developed a stratification based on attributes that can be broadly defined as the structural, locational and 'neighbourhood' characteristics of suburbs. An analysis determined that four structural variables, four locational variables and one neighbourhood variable were the most relevant in determining the similarity of suburbs for stratification purposes.

11.4 The structural variables were determined from 2001 Census of Population and Housing data and described the percentage of dwellings in a suburb with particular characteristics, such as number of bedrooms. The locational variables were determined from geographic data and described average distance to facilities, such as the nearest shops, by suburb. The neighbourhood variable was represented by the ABS Socio-Economic Index for Areas (SEIFA(footnote 1) ), which is a measure, derived from Census data, summarising different aspects of the socio-economic conditions of people living in an area.

11.5 The number of non-SEIFA variables were reduced into two principal components, one each for the structural variables and the locational variables. A process of cluster analysis was then undertaken using these two principal components and SEIFA as variables to select the optimal number of clusters. As there was an aim at the time to publish the HPI at lower levels than the city, this analysis was applied with a constraint to ensure that only suburbs within the same statistical subdivision(footnote 2) (SSD) could be grouped together and clusters could not cross SSD boundaries. A detailed description of the changes to the index resulting from the 2004 review is provided in Information Paper: Renovating the Established House Price Index (cat. no. 6417.0).

11.6 The HPI was compiled using this clustering methodology from September quarter 2005 to September quarter 2008 (and backcast to March quarter 2002). The index over this period is referred to as Series 1. During this period, further assessments of the capacity of the stratification methodology to control for compositional change were undertaken. Practical considerations became apparent, such as the large number of clusters in some cities. This resulted in median price volatility in some clusters due to the low number of transactions observed during a quarter. Also, investigations by the Reserve Bank of Australia (RBA) published in 2006 suggested that long-term prices of suburbs were a suitable characteristic on which to determine clusters of similar suburbs (Prasad and Richards, 2006).


Improvements to the stratification

11.7 As outlined in the ABS Methodology Advisory Committee (MAC) paper Refining the Stratification for the Established House Price Index (cat. no. 1352.0.55.093), published in 2008, four areas for improvement to the stratification were identified:

• remove the constraint of clustering suburbs within statistical subdivision (SSD) boundaries, allowing suburbs in geographically diverse areas within a capital city to be clustered together;
• include long-term median price and socio-economic characteristics of suburbs as stratification variables;
• simplify the stratification methodology; and
• utilise updated datasets from the most recent Census (2006) to form the basis of stratification.

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):

1 Number of clusters
	Series 1 (from March quarter 2002)	Series 2 (from March quarter 2008)
Sydney	55	22
Melbourne	39	20
Brisbane	51	20
Adelaide	27	11
Perth	14	10
Hobart	8	5
Darwin	5	6
Canberra	14	7

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.


CALCULATING WEIGHTS

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 I_LP is the index number for the link period (March quarter 2008 for the HPI Series 2), and V_CP and V_LP 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.

2 Calculating index numbers: price relatives
	Previous period (pt-1)	Current period (pt)	Price relative (pt/pt-1)
	$	$	no.
Cluster 1	1 500 000	1 260 000	0.840
Cluster 2	800 000	800 000	1.000
Cluster 3	500 000	505 000	1.010
Cluster 4	400 000	412 000	1.030
Cluster 5	300 000	315 000	1.050

3 Calculating index numbers
	Link period	Previous period	Current period	% change
	no.	no.	no.	%
Value aggregates ($'000)
Cluster 1	600 000	650 000	546 000	-16.0
Cluster 2	8 000 000	7 500 000	7 500 000	-
Cluster 3	15 000 000	16 000 000	16 160 000	1.0
Cluster 4	15 000 000	17 500 000	18 025 000	3.0
Cluster 5	2 000 000	3 200 000	3 360 000	5.0
City A	40 600 000	44 850 000	45 591 000	1.7
Index numbers
Cluster 1	105.0	113.8	95.6	-16.0
Cluster 2	105.0	98.4	98.4	-
Cluster 3	94.0	100.3	101.3	1.0
Cluster 4	91.0	106.2	109.4	3.0
Cluster 5	96.0	153.6	161.3	5.0
City A	93.0	102.7	104.4	1.7
- nil or rounded to zero (including null cells)

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.


REVISIONS

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.


ROUNDING CONVENTIONS

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.


FORMULAE

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 (q_i0) 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