**CHAPTER 10** RE-REFERENCING AND LINKING PRICE INDEXES

**INTRODUCTION**

**10.1** It is important that price indexes produced by the ABS are reviewed regularly to ensure the indexes are contemporary and that index results accurately represent price movements in the market.

**10.2** The HPI has been subject to two reviews in its history, the first of which significantly changed the methodology, and the second of which provided some further refinements.

**10.3** The changes to methodology which were implemented as a result of the first review produced a 'break' in the index series. This means that the conceptual and structural framework of the indexes were so different that the measurement of the changes in house prices over time were not able to be compared. This is reflected in the different index reference periods.

**10.4** The most recent review did not result in further methodological changes, but ensured that the HPI reflected the contemporary nature of the housing market. Therefore, the current series could be linked to the previous series, without a break.

**10.5** This chapter explains the concept of an index reference period and describes how to re-reference and link price indexes.

**INDEX REFERENCE PERIOD**

**10.6** The reference period of an index series (also commonly labelled base or reference base) is that period for which the value of the index is set to 100.0. Prices in other periods are expressed as percentages of the price in the reference period. For example, if the HPI had increased 15% since the reference period the index number would be 115.0; similarly, if it had fallen by 15% the index would be 85.0. In the case of the HPI, the index reference period is the 2003-04 financial year (i.e. 2003-04 = 100.0).

**10.7** The index reference period of the series compiled under the previous methodology is 1989-90 = 100.0.

**10.8** The index reference period should not be confused with the price reference period and the weight reference period. As described in Chapters 4 and 7 respectively, the price reference period is the period whose prices are compared with the prices in the current period, and the weight reference period is the period of the data used to calculate the value weights.

**RE-REFERENCING INDEXES**

**10.9** The derivation of the reference period index number is the arithmetic average of the index numbers for the financial year. That is, September, December, March and June quarters. To re-reference an index series to a particular reference period, the arithmetic average of the index numbers in the period is calculated and divided by 100, and all index numbers in the series are subsequently adjusted by this factor. The arithmetic average of the four quarters in the reference period will now be 100.0. The percentage change between any two periods will be maintained in the re-referenced series.

**10.10** When using a number of different price indexes to compare price changes, the user should ensure that the index reference period of each series is the same, re-referencing where necessary.

**CHAIN LINKING**

**10.11** When an index is reviewed to ensure the weights and structure are contemporary, the process of incorporating the new weights and structures into an existing price index is known as chain linking.

**10.12** Three steps are involved in the linking process: choosing the link period; price updating the value data; and chaining the new index to the existing index.

**Link period**

**10.13** The link period is the quarter in which the index is calculated on both the old weights and structure and the new weights and structure. The choice of link period is determined by a number of factors, but the aim is to avoid any periods where economic behaviour may be influenced by an abnormal event, such as regulatory changes.

**10.14** The international trade price indexes, for example, are linked every year through the June quarter.

**10.15** The latest review of the HPI was implemented in December quarter 2008; however, due to the two stage approach to HPI compilation (described in chapter 11.23), the link period which was used was March quarter 2008. This means that indexes for June quarter 2008 (benchmark), September quarter 2008 (P2, second estimate) and December quarter 2008 (P1, first estimate) were calculated from the index for March quarter 2008, but with revised structures and weighting patterns.

**Price updating value data**

**10.16** When linking price indexes to implement a review or re-weight, 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 chapter 7). Therefore it is necessary to price update (revalue) the values from the weight reference period to the price levels of the link period.

**10.17** The method for calculating price updated link period values for each cluster in the HPI differs to that of other ABS price indexes due to the fact that for HPI actual quantities for the weight reference period are available. In other indexes a measure of price change between the link period and the weight reference period is derived, and this is multiplied by the value or expenditure weights from the weight reference period. The updated value aggregates are aggregated to determine the upper level value aggregates.

**10.18 **In the HPI, the updated value of the housing stock is determined by multiplying the house counts obtained from Census data by a measure of average price for the link period (the 'mean-adjusted median') for each cluster. Although the HPI method is different to that employed by other indexes described above, it delivers a mathematically equivalent result. For more information on this process refer to Chapter 11.

**10.19** The resulting link period value aggregate is then expressed in terms of prices from the link period and quantities from the weight reference period.

**Chain linking through a link period**

**10.20** Prior to any reviews or re-weights, a price index in the current period is constructed as a multiple of the index in the base period and the ratio of the current value aggregate and the base period value aggregate.

**10.21** Subsequent to a review or re-weight, comparisons will be made with the link period rather than the base period. That is, the index will be constructed as a multiple of the index in the link period and the ratio of the current value aggregate and the link period value aggregate (both with the new weighting pattern).

**10.22** It should be noted that the index reference period remains the same - while the weights and structure have been updated, the index series is not broken and price movements relative to the base period may still be determined.

This page last updated 11 December 2009