CHAPTER 12 RE-REFERENCING AND LINKING PRICE INDEXES


REFERENCE PERIODS

12.1 The following reference periods are discussed in this chapter:

• Weight reference period is the period covered by the expenditure statistics used to calculate the weights. The weight reference period for the 16th series Consumer Price Index (CPI) is 2009-10.
• 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

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 historic data, especially for long series. In the March quarter 1992 the index reference period was changed from 1980-81 = 100.0 to 1989-90 = 100.0. The current CPI index reference period continues as 1989-90 = 100. The ABS has produced historical index numbers on the current base, so generally there is no need for users to do their own calculations.

12.3 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 group index for Perth from an index reference period of 1980-81 = 100.0 to 1989-90 = 100.0 (see Table 12.1). The index number for the 1989-90 Clothing group using an index reference period of 1980-81 is (181.5 + 186.4 + 185.8 + 188.6)/4 = 185.6 (rounded to one decimal place). Thus the conversion factor is 0.5388 (100.0/185.6) so that the March quarter 1989 index number, on an index reference period of 1989-90 = 100.0 is 95.4 (177.0×0.5388).

12.1 Converting index reference periods, Perth Clothing Group
	Index reference period(a)
Period	1980-81=100.0	1989-90=100.0
Mar qtr 1989	177.0	95.4
Jun qtr 1989	182.7	98.4
Sep qtr 1989	181.5	97.8
Dec qtr 1989	186.4	100.4
Mar qtr 1990	185.8	100.1
Jun qtr 1990	188.6	101.6
Financial year 1989-90	185.6	100.0
Sep qtr 1990	189.2	101.9
Dec qtr 1990	194.1	104.6
Mar qtr 1991	195.3	105.2
Jun qtr 1991	196.5	105.9
Sep qtr 1991	197.1	106.2
Dec qtr 1991	199.5	107.5
(a) Conversion factor: 1980-81 index reference period to 1989-90 index reference period = 100.0/185.6 = 0.5388.

12.4 Similar procedures are used to convert the 1989-90 index reference period to a 1980-81 index reference period. For example, the December quarter 1991 index for the Clothing group for Perth was 107.5 which, when multiplied by the conversion factor of 1.856 (185.6/100.0), gives an index number of 199.5 on the index reference period of 1980-81 = 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 group for Perth will differ from the factor for Automotive fuel for Perth, and for the Clothing group for Hobart.

12.5 Re-referencing should not be confused with reweighting. Re-referencing does not change the relative movements between periods. However reweighting involves introducing new weights and recalculating the aggregate index for each period which will affect the relative movements between periods.


LINKING

12.6 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.

12.7 There are two options in these situations if a fixed weighted 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 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 more common practice.

12.8 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.

12.9 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).

12.10 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. 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