Chapter 11 - Re-referencing and linking price indexes
Introduction
11.1 This chapter explains the reference periods used in the WPI and the chain linking process.
Reference periods
11.2 The following reference periods are discussed in this chapter:
- Price reference period is the period for which prices are used as denominators in the index calculation.
- Index reference period is the period for which the index is set to 100.0.
Re-referencing
11.3 The ABS changes the index reference period (a process known as re-referencing) of the WPI from time to time, but not frequently. This is because frequently changing the index reference period is inconvenient for users, and may result in the loss of some detailed historic data, especially for long series. When the WPI first commenced, the index reference period was the September quarter 1997 = 100.0. This was the first quarter for which data was available. Since the September quarter 2004, the Labour Price Index (as it was then known) used an index reference period of 2003–04 = 100.0. With the introduction of the 2006 edition of the Australian and New Zealand Standard Industrial Classification (ANZSIC), all indexes are now presented on an index reference period of 2008–09 = 100.0.
11.4 The conversion of an index series from one index reference period to another involves calculating a conversion factor using the ratio between the two series of index numbers. For example, for the total hourly rates of pay excluding bonuses index for Australia the conversion factor is calculated as follows:
The index number for 2008–09 (using an index reference period of 2003–04 = 100.0) is 121.755
The index number for 2008-09 (using an index reference period of 2008–09 = 100.0) is 100.0
Conversion factor = (100.0/121.755) = 0.8212
11.5 The conversion factors were applied to the "old" series to produce the "new" series. Table 11.1 shows the indexes on the old and new index reference periods.
| Index reference period(a) | ||
|---|---|---|
| Period | 2003–04=100.0 | 2008–09=100.0 |
| Mar qtr 2008 | 117.6 | 96.6 |
| Jun qtr 2008 | 118.7 | 97.5 |
| Sep qtr 2008 | 120.1 | 98.6 |
| Dec qtr 2008 | 121.5 | 99.8 |
| Mar qtr 2009 | 122.4 | 100.5 |
| Jun qtr 2009 | 123.1 | 101.1 |
| Financial year 2008–09 | 121.8 | 100.0 |
| Sep qtr 2009 | 124.2 | 102.0 |
| Dec qtr 2009 | 125.1 | 102.7 |
| Mar qtr 2010 | 126.2 | 103.6 |
| Jun qtr 2010 | 126.9 | 104.2 |
| Sep qtr 2010 | 128.7 | 105.7 |
| Dec qtr 2010 | 129.8 | 106.6 |
- Conversion factor: 2003–04 index reference period to 2008–09 index reference period = 100.0 / 121.775 = 0.8212.
11.6 Similar procedures are used to convert the 2008-09 index reference period back to a 2003–04 index reference period. For example, the December quarter 2010 index for the total hourly rates of pay excluding bonuses index for Australia was 106.6 which, when multiplied by the conversion factor of 1.2178 (121.775/100.0), gives an index number of 129.8 on the index reference period of 2003–04 = 100.0. It should be noted that a different conversion factor will apply for each index - that is, the factor for the total hourly rates of pay excluding bonuses index for WA will differ from the factor for the total hourly rates of pay excluding bonuses index for NSW.
11.7 Re-referencing should not be confused with re-weighting. Re-referencing does not change the relative movements between periods. However re-weighting involves introducing new weights and recalculating the aggregate index for each period which will affect the relative movements between periods.
Linking
11.8 The weights used to compile price indexes require regular updating to ensure the index remains representative. In the case of the WPI, weights need to be updated to reflect changes in the expenditure pattern of employers.
11.9 The WPI is a Laspeyres index. There are two options for updating weights. Option one, known as the the direct method, involves holding the weights constant over as long a period as seems reasonable, starting a new index each time the weights are changed. This means that a longer term series is not available. Option two is to update the weights more frequently and chain link the series together to form a long-term series. The latter is the method used for the WPI.
11.10 The difference between the two methods is explored in Table 11.2.
| Item | Period 0 | Period 1 | Period 2 | Period 3 | Period 4 |
|---|---|---|---|---|---|
| Price ($) | |||||
| Job 1 | 10 | 12 | 15 | 10 | 15 |
| Job 2 | 12 | 13 | 14 | 12 | 10 |
| Job 3 | 15 | 17 | 18 | 15 | 12 |
| Quantity | |||||
| Job 1 | 20 | 17 | 12 | 20 | 10 |
| Job 2 | 15 | 15 | 16 | 15 | 20 |
| Job 3 | 10 | 12 | 8 | 10 | 15 |
| Index Number | |||||
| Index Formula | |||||
| Laspeyres | |||||
| period 0 to 1 | 100.0 | 114.2 | |||
| period 1 to 2 | 100.0 | 112.9 | |||
| period 2 to 3 | 100.0 | 78.8 | |||
| period 3 to 4 | 100.0 | 107.5 | |||
| chain | 100.0 | 114.2 | 128.9 | 101.6 | 109.2 |
| direct | 100.0 | 114.2 | 130.2 | 100.0 | 107.5 |
11.11 In period 3, prices and quantities are returned to their index reference period values and in period 4 the index reference period prices and quantities are shuffled between items. The period 3 situation is sometimes described as time reversal and the period 4 situation as price bouncing.
11.12 The index number under direct estimation returns to 100.0 when prices and quantities of each item return to their index reference period levels; however, the chained index numbers do not.
11.13 This situation poses a quandary for prices statisticians when using a fixed weighted index. There are obvious attractions in frequent chaining; however, chaining in a fixed weighted index may lead to biased estimates. This can occur if there is seasonality or cycles in the price, and chaining coincides with the top or bottom of each cycle. For this reason it is generally accepted that indexes should not be chained at intervals less than annual.