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INTRODUCTION TABLE 9.1: DISAGGREGATION OF EXPENDITURE DATA
9.8 In this example, a reasonable outcome would be to decide to construct pricing samples for varieties 1, 3, 5 and 6. Separate pricing samples would not be constructed for items 2 and 4 due to their relatively small market share. Pricing samples would also not be constructed for bread rolls and specialty breads (items 7 and 8) as they would prove difficult to price to constant quality due to the tendency for these items to be sold by number rather than weight. Elementary aggregates must have a price sample 9.9 When no more information is available to further disaggregate the expenditure values, the resulting product definitions are called elementary aggregates. Each elementary aggregate has its own price sample. Ideally, all the products covered (and there should only be a few) would be homogeneous goods or services and would be substitutes for each other. In the Australian CPI there are approximately 1,000 elementary aggregates for each of the eight capital cities. This gives around 8,000 price samples at the national level. The expenditure aggregates for the items that are not explicitly priced are reallocated across the elementary aggregates of closely related goods or services under the assumption that the price movements for these products will be similar. 9.10 In the bread example, the reallocation would be carried out in two stages. First, the expenditure aggregate for unsliced white sandwich loaves would be added to sliced white sandwich loaves resulting in an elementary aggregate for white sandwich loaves (as it will be the characteristics of being white and sandwich loaves that make them likely to experience similar price movement pressures). White high fibre loaves would be treated similarly. In the second stage, the expenditure aggregates for bread rolls and speciality breads, which have no closely matching characteristics with any of the other types of bread, would be allocated, on a proportional basis, across the remaining elementary aggregates under the assumption that the average movement of prices for all other bread types will be the best estimate. The outcome of this process is presented in table 9.2. 9.11 In summary, the rationale for this allocation is as follows. Price behaviour of item 2 (white, sandwich, unsliced) is likely to be best represented by the price behaviour of item 1 (white, sandwich, sliced). Items 4 (white high top) and 3 (white high fibre) are treated similarly. The price behaviour for items 7 and 8 (bread rolls and specialty bread respectively) is likely to be best represented by the average price behaviour of all other breads. TABLE 9.2: OUTCOME OF ELEMENTARY AGGREGATE RATIONALISATION
Determining outlet types 9.12 Having settled on the product definitions for which price samples are to be constructed, the next step is to determine the outlet types (respondents) from which prices will be collected. In order to accurately reflect changes in prices paid by households for bread, prices need to be collected from the various types of outlets from which households purchase bread. Data are unlikely to be available on the expenditures at the individual elementary aggregate level by type of outlet. It is more likely that data will be available for expenditure on bread in total by type of outlet. Suppose industry data indicates that supermarkets accounted for about 80% of bread sales and bakery outlets the remainder. A simple way to construct a pricing sample for each elementary aggregate that is representative of household shopping patterns is to have a ratio of four supermarkets to every bakery. COLLECTING PRICE DATA Selecting respondents 9.13 When pricing samples have been determined, ABS field staff determine from which individual supermarkets and bakeries the prices will be collected. The individual outlets are chosen to be representative of the two types of outlets taking into account the demographics of the city and the numbers required for the sample. Prices will be collected from any particular respondent at the same time of each collection period (e.g. first Monday of each month). Selecting items to price 9.14 When a pricing sample contains respondent standard specifications (refer to Chapter 8 for an explanation of this term) field staff will determine, in conjunction with the outlet management, which specific items are most representative of the required type of product. Using the bread example, at one outlet it might be decided that the 680 g sliced white sandwich loaf best represents white sandwich bread while at another outlet it might be a 700 g white sandwich loaf. Once selected, the same product will be priced at that respondent while ever it is the most representative example. 9.15 An important part of the price collection process is the continual monitoring of the items for quality change. In the bread example, quality change could occur with, say, a change in the size (weight) of the loaf of bread. In this case, the price movement directly attributable to the change in loaf size would be removed to derive a pure price movement for the loaf. ESTIMATION OF PRICE MOVEMENTS FOR ELEMENTARY AGGREGATES 9.16 Price relatives are calculated for each price in the sample and the geometric mean of these is calculated. The ratio of the current period’s geometric mean of price relatives to the previous period’s geometric mean of price relatives provides the change in the average price for the elementary aggregate. Using the hypothetical bread sample, table 9.3 shows price relatives being used to estimate the price movement for bread. These estimates of price movements are used to revalue the expenditure aggregates to current period prices, by applying the period to period price movement to the previous period’ ;s expenditure aggregate for each elementary aggregate. The updated expenditure aggregate provides an estimate of the cost of acquiring the base period quantity of the elementary aggregate’s products in the current period. (footnote 1) TABLE 9.3: ESTIMATING PRICE MOVEMENT FOR AN ELEMENTARY AGGREGATE
9.17 Once price movements are calculated for each item, a geometric mean is calculated, which is used to derive priceupdated expenditure aggregates for each elementary aggregate. These are then summed to derive the current cost of the total (or any portion of the) basket of goods and services. Index numbers are calculated from the expenditure aggregates at every level of the index. Table 9.4 shows the calculation of the expenditure value for the total of bread (an expenditure class in the example). TABLE 9.4: AGGREGATION OF EXPENDITURE AGGREGATES FOR EXPENDITURE CLASS
9.18 Once the expenditure aggregates for all the elementary aggregates have been calculated from the price movements, the expenditure aggregates for all higher level components of the index structure are calculated by summing the expenditure aggregates of their components. A cutdown version of a CPI structure, incorporating the bread example, is shown in table 9.5. Price movements in period 2 are used to update the expenditure aggregates. CALCULATING INDEX NUMBERS AND POINTS CONTRIBUTIONS 9.19 Table 9.5 also shows the calculation of index numbers and points contribution. It has been assumed that index numbers already exist for the link period (June quarter 2000 for the 14th series CPI) and period 1. Assume the expenditure aggregate for Cereals has been calculated using the same method as that for Bread, so that the two can be added and a movement calculated for Bread and cereals. Similarly, assume the expenditure aggregates for period 2 have been calculated for Other Foods and Nonfood, so that expenditure aggregates can be calculated for Food and All groups. 9.20 When a price index has not been linked, indexes for any component can be calculated simply by dividing the current period expenditure aggregate by its expenditure aggregate in the reference period (when the index is set to 100.0). However, the CPI has been linked several times since its reference base (1989–90) and the index numbers must be calculated from (9.1) where I _{LP} is the index number in the link period (June quarter 2000 for the 14th series CPI), and V_{CP} and V_{LP} are the expenditure aggregates in the current period and link periods respectively. Thus the index number for Bread in period 2 is given by 108.0 x 8235 / 6500 = 136.8. 9.21 Points contributions are also calculated using the expenditure aggregates. In any period, the points contribution of a component to the All groups index number is calculated by multiplying the All groups index number for the period by the expenditure aggregate for the component in that period and dividing by the All groups expenditure aggregate for that period. This can be stated algebraically as (9.2) where is the index for All groups in period t, is the expenditure aggregate for component i in period t and is the expenditure aggregate for All groups in period t. 9.22 In the example in Table 9.5, the points contribution for Bread in period 2 is calculated as 141.3 * (8235 / 144268). 9.23 The change in index points contribution for a component between any two periods is found by simply subtracting the points contribution for the previous period from the points contribution for the current period. For example, the change in index points contribution for Bread between periods 1 and 2 is 8.07  7.84 = 0.23. 9.24 The CPI publication does not show the expenditure aggregates, but rather the index numbers derived from the expenditure aggregates. Expenditure aggregates vary considerably in size and showing them would make the publication difficult to read and interpret. The published index numbers and points contributions are a convenient presentation of the information. TABLE 9.5: AGGREGATION OF EXPENDITURE AGGREGATES FOR ENTIRE INDEX
SECONDARY INDEXES 9.25 A range of analytical indexes is published for the CPI. These include the ‘All groups excluding (each of the groups in turn)’ and ‘Goods and Services’ indexes. They are termed secondary indexes as they use the same weights (or expenditure aggregates) as the CPI  they are compiled from the summation of the appropriate value aggregates. For example, in Table 9.5 the starting point for compiling an index for All groups excluding Bread and cereals would be to add up the value aggregates for Other foods and Non food and then calculate index values as described in the previous section. TERTIARY INDEXES 9.26 A further range of analytical indexes is compiled from the price samples collected for the CPI. Price indexes compiled under the outlays approach are produced annually for four population subgroups: employees; age pensioners; selffunded retirees; and other government transfer recipients. These indexes, unlike the secondary indexes mentioned above, have their own weighting patterns and are compiled in a similar manner to the CPI. The purpose of the population subgroup indexes is to show any differences in the price changes faced by the four demographic groups, which would arise purely from their differing expenditure patterns. CPI ROUNDING CONVENTIONS 9.27 To ensure consistency in the application of data produced from the CPI, it is necessary for the ABS to adopt a set of consistent rounding conventions or rules for calculating and presenting data. The conventions strike a balance between maximising the usefulness of the data for analytical purposes and retaining a sense of the underlying precision of the estimates. These conventions need to be taken into account when CPI data is used for analytical or other special purposes. 9.28 Index numbers are always published relative to a base of 100.0. Index numbers and percentage changes are always published to one decimal place, with the percentage changes being calculated from the rounded index numbers. Points contributions are published to two decimal places, with points contributions change being calculated from the rounded points contributions. Index numbers for periods longer than a single quarter (e.g. for financial years) are calculated as the simple arithmetic average of the relevant rounded quarterly index numbers. Footnotes 1. Using terminology from the Laspeyres formula, the expenditure aggregates in period t are equivalent to . Index values can be derived from the corresponding . < Back
