CHAPTER 12 RE-REFERENCING AND LINKING PRICE INDEXES


REFERENCE PERIODS

12.1 The Weight reference period is the period of the expenditure data used to calculate the value aggregates (or weights). The weight reference period or weighting base period for the 15th Series CPI is 2003-04.

12.2 The Price reference period is the period whose prices are compared with the prices in the current period. It is the period whose prices appear in the denominators of the price relatives.

12.3 The Index reference period is the period in which all index numbers in the CPI have a value of 100.0 (with the possible exception of any items that have been newly introduced into the CPI since the base period).


RE-REFERENCING

12.4 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 reference base is inconvenient for users, particularly those who use the CPI for contract escalation. Also re-referencing may result in loss of detail in historic data, especially for long series. Since the March quarter 1992, the CPI uses an index reference base of 1989-90 = 100.0. In the June quarter 1982 the index reference base was changed from 1966-67=100.0 to 1980-81=100.0. The ABS has produced historical index numbers on the current base, so normally there is no need for users to do their own calculations.

12.5 The conversion of an index series from one index reference base to another involves calculating the ratio of the index numbers for the base period from the two series, and applying this to the index numbers. For example, consider converting the Clothing group index for Perth from an index base of 1980-81=100.0 to 1989-90=100.0 (see Table 12.1 below for the data). The index number for the group for 1989-90 on an index reference base of 1980-81 was 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 base of 1989-90=100.0 is 95.4 (177.0×0.5388).

12.1 Converting reference bases, Perth clothing Group
	Base	Base
	1980-81=100.0	1989-90=100.0
Mar 1989	177.0	95.4
Jun 1989	182.7	98.4
Sep 1989	181.5	97.8
Dec 1989	186.4	100.4
Mar 1990	185.8	100.1
Jun 1990	188.6	101.6
1989-90	185.6	100.0
Sep 1990	189.2	101.9
Dec 1990	194.1	104.6
Mar 1991	195.3	105.2
Jun 1991	196.5	105.9
Sep 1991	197.1	106.2
Dec 1991	199.5	107.5
Note: Conversion factor: 1980-81 base to 1989-90 base = 100.0/185.6 = 0.5388

12.6 Similar procedures are used to convert the current index base to a 1980-81 base. 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 reference base 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.

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


CHAINING INDEXES

12.8 The use of fixed weights (as in a Laspeyres formula) over a long period of time is clearly not 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 movements in relative prices, changes in preferences, and the introduction of new goods (and the displacement of older style goods).

12.9 There are two options in these situations if a fixed weighted index is used. 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. The second is to update the weights more frequently and to chain to produce a long term series. The latter is the more common practice.

12.10 The behaviour of the alternative index formulas under chaining are explored in Table 12.2 below. In period 3, prices and quantities are returned to their base period values and in period 4 the base 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.

12.11 Under the three formulae, the index number under direct estimation returns to 100.0 when prices and quantities of each item return to their base period levels. However, the chained index numbers do not (although the chained Fisher Ideal index might generally be expected to perform better than the chained Laspeyres or Paasche).

12.12 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 can sometimes lead to biased estimates. This can occur if there is seasonality or cycles in the price, and chaining coincides with the top and bottom of each cycle. For this reason it is generally accepted that indexes should not be chained at intervals less than annual. In effect, 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, 1993 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			10	12	15	10	15
2			12	13	14	12	10
3			15	17	18	15	12
Quantity
1			20	17	12	20	10
2			15	15	16	15	20
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	107.2
	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	128.4	99.9	100.3
		direct	100.0	114.0	128.5	100.0	100.4