RE-REFERENCING AND LINKING PRICE INDEXES


REFERENCE PERIODS

12.1 The following reference periods are discussed in Re-referencing and linking price indexes:

• Weight reference period is the period covered by the expenditure statistics used to calculate the weights. The weight reference period for the 17th series Consumer Price Index (CPI) is 2015-16.
• Price reference period is the period for which prices are used as denominators in the index calculation. The price reference period for the 17th series CPI is the September quarter 2017.
• Index reference period is the period for which the index is set to 100.0. The current index reference period is 2011-12.

RE-REFERENCING

12.2 The ABS changes the index reference period (a process known as re-referencing) of the CPI from time to time, but not frequently. This is because frequently changing the index reference period is inconvenient for users, particularly those who use the CPI for contract escalation. Also re-referencing may result in the loss of some detailed historical data, especially for long series. The current CPI index reference period was updated in the September quarter 2012 to 2011-12. Prior to this the index reference period was 1989-90.

12.3 By convention, the ABS publishes price index numbers rounded to one decimal place. Re-referencing is necessary where price index numbers fall to levels which would result in a loss of precision of period-to-period index movements. An example of a series in the CPI where this could occur is the Audio, visual and computing equipment expenditure class. This series experiences a downward trend due to the technological improvements seen in these goods, resulting in pure price falls over time. Therefore, re-referencing is required in these cases so that price indexes accurately capture period-to-period movements.

12.4 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, consider converting the Clothing and footwear group index for Australia from an index reference period of 1989-90 = 100.0 to 2011-12 = 100.0 (see Table 12.1). The index number for the 2011-12 Clothing and footwear group using an index reference period of 1989-90 is (110.3 + 109.7 + 107.7 + 109.2)/4 = 109.2 (rounded to one decimal place). The published conversion factor is 0.9154 (approximately 100.0/109.2) so that the March quarter 2011 index number, on an index reference period of 2011-12 = 100.0 is 97.2 (106.2×0.9154).

12.5 Similar procedures are used to convert the 2011-12 index reference period to a 1989-90 index reference period. For example, the December quarter 2013 index for the Clothing group for Australia was 99.7 which, when multiplied by the conversion factor of 1.0920 (109.2/100.0), gives an index number of 108.9 on the index reference period of 1989-90 = 100.0. It should be noted that a different conversion factor will apply for each index and city - that is, the factor for the Clothing and footwear group for Australia will differ from the factor for the Transport group for Australia, and for the Clothing and footwear group for Sydney.

12.1 CONVERTING INDEX REFERENCE PERIODS, CLOTHING AND FOOTWEAR GROUP
	Index reference period(a)
Period	1980-90=100.0	2011-12=100.0
Mar qtr 2011	106.2	97.2
Jun qtr 2011	108.7	99.5
Sep qtr 2011	110.3	101.0
Dec qtr 2011	109.7	100.4
Mar qtr 2012	107.7	98.6
Jun qtr 2012	109.2	100.0
Financial year 2011-12	109.2	100.0
Sep qtr 2012	109.5	100.2
Dec qtr 2012	110.3	101.0
Mar qtr 2013	106.1	97.1
Jun qtr 2013	108.9	99.7
Sep qtr 2013	110.1	100.8
Dec qtr 2013	108.9	99.7
(a) Conversion factor: 1989-90 index reference period to 2011-12 index reference period = 0.9154.

12.6 Re-referencing does not change the relative movements between periods. Period-to-period percentage changes may differ slightly to those previously published due to rounding and the re-referencing. However, these differences do not constitute a revision.

12.7 For a full list of the conversion factors used in the most recent CPI re-reference, see table 17 in Consumer Price Index, Australia, Sep 2012 (cat. no. 6401.0).

12.8 Further information on re-referencing can be found in Appendix 1 'Re-referencing the Consumer Price Index' of Consumer Price Index, Australia, Sep 2012 (cat. no. 6401.0)


LINKING

12.9 The use of fixed weights (as in a Laspeyres formula) over a long period of time is not considered sound practice. For example, weights in a consumer price index have to be changed to reflect changing consumption patterns. Consumption patterns change in response to longer term price movements, changes in preferences, and the introduction or displacement of goods or services.

12.10 There are two options in these situations if a fixed weight index is used. Option one is to hold 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 time series is not available. Option two is to update the weights more frequently and chain link the series together to form a longer time series. The latter option is the more common practice and is what is used in the Australian CPI.

12.11 The behaviour under chain linking of the Laspeyres, Paasche and Fisher index formulas is explored in Table 12.2. 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.

12.12 Under the three formulas, 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. Note that the chained Fisher Ideal index might generally be expected to perform better than the chained Laspeyres or Paasche. More information on linking indexes is contained in section 9.105 - 9.126 in the international CPI Manual (ILO, 2004).

12.13 This situation creates a challenge for prices statisticians when using a fixed weight index. There are obvious attractions in frequent chaining, however, chaining in a fixed weight 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. The conceptual underpinning of chaining is that the traditionally expected inverse relationship between prices and quantities actually applies in practice (i.e. growth in quantities is higher for those items whose prices increase less than those of other items). The System of National Accounts, 2008 describes the practical situations in which chaining works best.

12.2 A CLOSER LOOK AT CHAINING
Item			Period 0	Period 1	Period 2	Period 3	Period 4
Price ($)
1 Boys' sport socks			10	12	15	10	15
2 Girls' sport Socks			12	13	14	12	10
3 Men's socks			15	17	18	15	12
Quantity
1 Boys' sport socks			20	17	12	20	10
2 Girls' sport socks			15	15	16	15	20
3 Men's socks			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
	Paasche
		period 0 to 1	100.0	113.8
		period 1 to 2		100.0	112.3
		period 2 to 3			100.0	76.8
		period 3 to 4				100.0	93.8
		chain	100.0	113.8	127.8	98.2	92.1
		direct	100.0	113.8	126.9	100.0	93.8
	Fisher
		period 0 to 1	100.0	114.0
		period 1 to 2		100.0	112.6
		period 2 to 3			100.0	77.8
		period 3 to 4				100.0	100.4
		chain	100.0	114.0	128.3	99.9	100.3
		direct	100.0	114.0	128.5	100.0	100.4