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CHAPTER 12 RE-REFERENCING AND LINKING PRICE INDEXES
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.
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.
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