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6419.0 - Producer and International Trade Price Indexes, 1995  
Latest ISSUE Released at 11:30 AM (CANBERRA TIME) 13/02/1995  Ceased
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Contents >> Chapter 13. Price index number compilation

Introduction

13.1. Producer and Foreign Trade Price Indexes are compiled using the Laspeyres fixed weight approach. This involves six main stages each quarter:

      • checking the accuracy of the prices collected;
      • calculating price movements (price relatives) for each specification in each sample;
      • replacing specifications, as necessary;
      • combining the specification price relatives to produce fine level component index numbers;
      • combining the fine level component index numbers to produce index numbers for published series; and
      • calculating percentage changes and index points movements to supplement the published index number series.

13.2. Each of these stages involves numerous detailed steps. It is beyond the scope of this document to explain all the steps in detail, but a broad outline of each stage is given in the rest of this chapter.


Checking the prices collected

13.3. As soon as the price collection forms are received by the ABS they are checked for completeness and the reported data is loaded into the computer. The data is in the form of 'raw price elements' such as list prices, various discounts, transport charges, sales tax, etc. from which the transactions prices are calculated for use in the index.

13.4. A series of checks, or edits, are applied to the transactions prices to ensure their accuracy. These include comparisons with prices previously collected from the same respondent, and with prices reported by other respondents for the same item. Any prices that appear to be unusual or abnormal are verified with the respondent and corrected where necessary.

13.5. The process of checking and verifying reported prices also provides one of the means of ensuring that the quality of the specification priced in the current period is the same as that priced in previous periods. The procedures for identifying and dealing with changes in quality are described in Chapter 14.


Calculating price relatives

13.6. Once the prices data have been verified, a price relative (or price movement from the base period) is calculated for each specification. This is a straightforward procedure which uses the formula:



Thus, if specification A has a price in the current period of $12.50 and had a price in the base period of $8.00 the price relative in the current period would be:



Replacement of specifications

13.7. From time to time specifications have to be replaced either because the respondent is no longer able to provide a price, or because market conditions have changed and the specification is no longer appropriate (for example, a new model car being sold). The general procedure in these situations is to collect prices for overlapping periods for both the old specification and the new one. The new specification is 'spliced' into the sample in such a way that its price relative reflects only price movements and is not affected by the change in specification.

13.8. This procedure is illustrated in the following example:


Price
Specification
Base Period
Period 1
Period 2

A
$8.00
$12.50
. .
B
. .
$15.00
$16.00


In period 1, the price relative for specification A would be calculated as:



In period 2, the price relative for specification B would be calculated as:



      = 166.67

13.9. Thus, only the price movement for specification B from period 1 to period 2 of 6.67 per cent has been included and not the price change from specification A to specification B.

13.10. This approach is equivalent to estimating a base period price for specification B using the assumption that the price movement from the base period to period 1 would have been the same as was recorded for specification A. That is, the nominal base period price for B:





      = $9.60

Using this nominal base period price, the price relative for B in period 2 becomes:



13.11. Sometimes the overlap period between old and new specifications reflects unusual price conditions, for example the old specification being sold at clearance prices. In these circumstances adjustments are made to the reported prices to remove the impact of the unusual conditions. At other times it may not be possible to obtain overlap prices, in which case an assessment of the extent of any quality change between the old and new specifications is made and the prices adjusted accordingly.


Calculating fine level component index numbers

13.12. The price relatives calculated for each specification in the samples that comprise a fine level component are combined using the base period sample weights for that component. The resulting figure is the index number for the component. In accordance with the Laspeyres formula the weights used to combine the price relatives are value weights, i.e. the relative proportion of the total value of expenditure for the sample contributed by expenditure on each specification.

13.13. This procedure is illustrated in the following example:


Base Period
Specification
Weight
Price Relative

A
0.40
126.83
B
0.42
150.21
C
0.10
98.36
D
0.08
130.20
1.00
134.07


The component index number is 134.07, which is the weighted average of the specification price relatives that comprise the sample for that component, that is:
     (0.40 x 126.83) + (0.42 x 150.21) + (0.10 x 98.36) + (0.08 x 130.20).

13.14. If any prices are missing in a compiling period a price is imputed using the price movements of similar specifications for which prices have been reported. Alternatively, the missing price is imputed using other data sources (for example, exchange rate movements may be used in the foreign trade price indexes).

13.15. Similar procedures to those described in paragraphs 13.7 and 13.8 are used whenever sample weights (i.e. weighting of specifications to a component) are changed, to ensure that the change in weights does not affect the movement in the index. This is illustrated in the following example of an across the board price increase of 10 per cent between periods 1 and 2, and further price increases in period 3:


Weights

Price Relatives

Specs
Period 1
Period 2
Period 1
Period 2
Period 3

A
0.40
0.30
120
132
134
B
0.42
0.45
150
165
173
C
0.10
0.05
100
110
110
D
0.08
0.20
130
143
150
1.00
1.00


The index number for period 1, derived using the base period weights, would be 131.40. If the period 2 weights were to be applied directly to the period 2 price relatives the index number would be 147.95, which implies a price increase of 12.6 per cent not the 10 per cent that actually occurred. This is because part of the implied increase is due to the change in weighting pattern and because the reference period for the weights (period 2) and the relatives (base period) are no longer consistent.

13.16. There are two methods for overcoming this problem. In the first, period 2 is established as the new base period and the resulting index numbers are converted to the original reference base using a conversion factor:

In subsequent periods, the price relatives are derived using period 2 prices as the base and combined using the period 2 weights and the conversion factor (see period 3 below). That is:


Price Relatives on

Weights

Base Period

Period 2 Base

Specs
Base Period
Period 2
Period 1
Period 2
Period 2
Period 3

A
0.40
0.30
120
132
100
101.4
B
0.42
0.45
150
165
100
104.8
C
0.10
0.05
100
110
100
100.0
D
0.08
0.20
130
143
100
104.9

Index Numbers (period 2 weights)
100.00
103.56

Conversion factor
1.4454
1.4454

Index Numbers (original base)
131.40
144.54
144.54
149.69


13.17. The second method involves revaluing the new weights to reflect the prices of the base period. That is:



Specification
(1)
Period 2 Weights
(2)
Period 2 Relatives
(3)
Revalued Weights (a)
(4)
New
Weights (b)
(5)

A
0.30
132
0.23
0.33
B
0.45
165
0.27
0.39
C
0.05
110
0.05
   0.08 (c)
D
0.20
143
0.14
0.20
0.69
1.00

(a) Column (2) x 100 / column (3).
(b) Column (4) x 1.00 / 0.69.
(c) Rounded up.



Weights

Price Relatives

Specification
Period 1
Period 2
Period 1
Period 2
Period 3

A
0.40
0.33
120
132
134
B
0.42
0.39
150
165
173
C
0.10
0.08
100
110
110
D
0.08
0.20
130
143
150

Index Numbers (period 2 weights)
145.31
150.49

Conversion factor
0.9947
0.9947

Index numbers
131.40
144.54
149.69


13.18. While both methods yield the same result, the second method has the advantage that it maintains continuous price series for each specification and ensures that all price relatives remain on the same base. This enables meaningful comparisons over time and across specifications, thus facilitating the editing of index calculations. As a consequence, this second method is generally followed in calculating producer price indexes.


Calculating published index series

13.19. The various published index series are derived from the fine level component series using the combining weights that are published at the time of the latest index rebase and reweight. Again, the weights used are value weights.

13.20. The procedure is identical to that used to calculate the fine level component series from specifications except that the weights used are fixed between index rebases and reweights. The problems of missing prices and changing weights referred to above do not apply here.

13.21. The particular weighting patterns used for each index are described in earlier chapters.


Calculation of other measures

13.22. A number of other measures are also calculated for each price index series, viz percentage changes, index points contributions and index points changes.

13.23. Percentage changes summarise the magnitude of the price movement in the index numbers between specified periods. They are calculated directly from the index numbers in the manner discussed in Chapter 16.

13.24. Index Points Contributions and Changes provide the most convenient method of analysing the contribution made by individual index series to the movement for the total index. The methodology used to calculate index points contributions is explained in Chapter 16.





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