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CHAPTER 10 CONSUMER PRICE INDEX CALCULATION IN PRACTICE
10.8 In this example, a reasonable outcome would be to decide to construct pricing samples for varieties 1, 3, 5 and 6. Separate price samples would not be constructed for items 2 and 4 because of their small market share relative to the others. 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 because these items are usually sold by number and not by weight.
Elementary aggregates must have a price sample
10.9 When no more information is available to disaggregate the expenditure values any further, the resulting product definitions are called elementary aggregates. Each elementary aggregate has its own price sample. Ideally, all the products in an elementary aggregate (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 nationally. 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 are similar.
10.10 In the bread example, the reallocation is carried out in two stages. First, the expenditure aggregate for unsliced white sandwich loaves is added to sliced white sandwich loaves resulting in an elementary aggregate for white sandwich loaves (as being white bread and sandwich loaves makes them likely to experience similar price movements). White high top loaves would be treated similarly. In the second stage, the expenditure aggregates for bread rolls and specialty breads, which have no closely matching characteristics with any of the other types of bread, would be allocated proportionally across the remaining elementary aggregates under the assumption that the average movement in prices for all other bread types is the best estimate. The outcome of this process is presented in Table 10.2.
10.11 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 (bread rolls) and 8 (specialty bread) is likely to be best represented by the average price behaviour of all other breads.
Determining outlet types
10.12 The next step is to determine the outlet types (respondents) from which the prices will be collected. In order to accurately reflect changes in prices paid by households for bread, prices need to be collected from the types of outlets from which households normally 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 industrial data indicate that supermarkets account for about 80 per cent 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 for every bakery.
COLLECTING PRICE DATA
10.13 When the pricing samples are worked out, ABS field staff decide from which individual outlets the prices will be collected. The respondents are chosen to be representative of the types of outlets (in the example above, supermarkets and bakeries) taking into account the demographic characteristics of the city, and the numbers required for the sample. Prices are collected from any particular respondent on the same day in each collection period (e.g. the first Monday of each month).
Selecting items to price
10.14 When a pricing sample contains respondent standard specifications, the field staff will decide which specific items are most representative of the required type of product. Usually they do this by consulting with the manager of the outlet. Using the bread example above, at one outlet they might decide that a 680g sliced white sandwich loaf best represents white sandwich bread, but at another outlet it might be a 700g white sandwich loaf. Once selected, the same item will be priced at that respondent so long as it remains the most representative example of the product.
10.15 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 attributable to the change in loaf size would be removed to derive a pure price movement for the loaf.
ESTIMATING PRICE MOVEMENTS FOR ELEMENTARY AGGREGATES
10.16 Price relatives are calculated for each price in the sample, and mostly the geometric mean of these is used in the calculations. 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 example, Table 10.3 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.
CALCULATING THE CURRENT COST OF THE BASKET
10.17 The price updated expenditure aggregates for the elementary aggregates are then summed to derive the current cost of the basket of goods and services (or any portion of the basket) . Index numbers are calculated from the expenditure aggregates at every level of the index. The table below shows the calculation of the expenditure value for the total of bread (an expenditure class in this example).
CALCULATING INDEX NUMBERS AND POINTS CONTRIBUTIONS
10.18 Table 10.5 shows the calculation of index numbers and points contribution. It is assumed that index numbers already exist for the link period (June quarter 2005 for the 15th 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 Non-food so that expenditure aggregates can be calculated for Food and All groups.
10.19 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
where ILP is the index number in the link period (June quarter 2005 for the 15th series CPI), and VCP and VLP 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.
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
Where ItAG is the index for All groups in period t, Itiis the expenditure aggregate for component i in period t and is VtAG the expenditure aggregate for All groups in period t.
10.20 In the example in Table 10.5 below, the points contribution for Bread in period 2 is calculated as 141.3 * (8235 / 144268) = 8.07.
10.21 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.
10.22 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. Index numbers and points contributions are a better way to present the information.
Note: It is assumed the reference base period precedes period 1.
10.23 A range of analytical indexes are also published reusing data from the CPI. Examples of these are the All groups excluding (each of the groups in turn), Goods and Services, Tradables, Non-tradables, and Market goods and services (with exclusions). These are called secondary indexes as they use the same weights (or expenditure aggregates) as the CPI, and are compiled by summing the appropriate value aggregates. For example, in the table above, 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 previously.
10.24 A further range of analytical indexes are compiled from the price samples collected for the CPI. Price indexes compiled under the outlays approach are published annually for four population subgroups: employees; age pensioners; self funded retirees; and recipients of other government transfer. These indexes, unlike the secondary indexes, have their own weighting patterns. For each component in the population subgroup indexes, the movement in the corresponding CPI index is used to update the expenditure aggregate and index number for the population subgroup. The purpose of the population subgroup indexes is to show any differences in the price changes faced by each of the four demographic groups arising from their differing expenditure patterns.
CONSUMER PRICE INDEX ROUNDING CONVENTIONS
10.25 To ensure consistency from one publication to the next, the ABS uses a set of rounding conventions or rules for calculating and presenting the results. These conventions strike a balance between maximising the usefulness of the information 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.
10.26 Index numbers are always published relative to a base of 100.0. Index numbers and percentage changes are always published to one decimal place, and the percentage changes are calculated from the rounded index numbers. Index numbers for periods longer than a single quarter (e.g. for financial years) are calculated as the simple arithmetic average of the rounded quarterly index numbers.
10.27 Points contributions are published to two decimal places. Change in points contributions is calculated from the rounded points contributions. Rounding differences can arise in the points contributions where different levels of precision are used.
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