6427.0.55.007 - Experimental Producer Price Index for the Output of the Retail Trade Industry, Australia, 2013  
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APPENDIX 1: TECHNICAL APPENDIX TO CHAPTER 3

INTRODUCTION

1. This appendix provides a detailed explanation of the new compilation process for the producer price index for the output of the retail trade industry. Details of the original retail trade margins index can be found in ABS Experimental Price Index for Retail Trade Margins, 2003 to 2006: Information Paper (cat.no. 6402.0).


THE NEW EXPERIMENTAL RTPI CONSTRUCTION PROCESS

2. The ABS RTPI is constructed using a Lowe index formula applied at each stage of the index aggregation process. The calculation of the new RTPIs is carried out in three stages as described below.

3. Stage 1 of the process calculates the state/territory level margin indexes for SUPCs. For each SUPC, the outlet weight in period 0, Image - symbol , is calculated as the product of the outlet retail trade margin share and the business retail trade margin share as shown by the formula below.



Image - equation
Where:
Image - symbol is the four quarter average retail trade margin (the difference between the total sales and cost of goods sold) at outlet i, in the state/territory, in period 0;

Image - symbol is the four quarter average retail trade margin for business E in the state/territory, in period 0;

Image - symbol is the number of outlets sampled in the state/territory, for business E; and

Image - symbol is the number of businesses sampled in the state/territory.

Note: The four quarter average margins are calculated from period 0 and the prior three quarters.

4. For each SUPC the outlet prices, Image - symbol are then calculated as follows.


Image - equation



Where:

Image - symbolis the final retail trade margin price at outlet i in period t;

Image - symbol is the total sales for the SUPC at outlet i in period 0;

Image - symbol is the total sales for the SUPC at outlet i in period t;

Image - symbol is the retail trade margin for the SUPC at outlet i in period t;

Image - symbolis the relative margin for the SUPC at outlet i in period t; and

Image - symbolis the sales on the ‘preserved volume’ for the SUPC at outlet i in period t.

5. The estimation of the margin price on the sales that would be realised on the ‘preserved volume’ is an important element of the stage 1 calculation. The purpose of this adjustment is to maintain a consistent volume of sales, across periods, from which final retail trade margin prices are then calculated. This ensures that the RTPIs are not influenced by changes in sales caused by price inflation.

6. The state/territory SUPC index, Image - symbol, is then calculated as;

Image - equation

Where:

Image - symbolis the number of outlets in the state/territory reporting on the selected SUPC;

Image - symbolis the final price relative between periods t and 0 for each outlet.


STAGES 2 AND 3, CALCULATION OF THE NATIONAL SUPC INDEXES AND THE RTPI

7. Stage 2 of this process calculates the national margin indexes for SUPC, Image - symbol. These indexes are calculated as a weighted sum of state/territory indexes as shown below;

Image - equation

The weights, Image - symbol, are state/territory retail trade margin shares given by,

Image - equation


8. Stage 3 of this process calculates the national RTPI as a weighted sum of national SUPC indexes, as shown below;

Image - equation

Where,Image - symbol, is the national retail trade margin share weights obtained from the S–U table, given by,

Image - equation

9. Stages 2 and 3 utilise national retail trade margins SUPC data sourced from the unpublished annual S–U Table. Retail trade margins data by state/territory (used in equation 5) are calculated from the national SUPC data and dis-aggregated using the Household Expenditure Survey (HES) data.


NUMERICAL EXAMPLE FOR THE NEW EXPERIMENTAL RTPI CONSTRUCTION PROCESS

10. This example illustrates the three stages to calculate the experimental PPIs for the output of the retail trade industry. For the purpose of simplicity, this example does not use a four quarter average retail trade margin in the calculation of the outlet weights, as described in paragraph 3 above.

11. A retail business trading in products represented by the SUPC, Clothing (excluding knitted or crocheted) is used. The business has three outlets, all of which are located in the state of NSW. Tables A1.1 and A1.2 show the survey data (Sales $ and COGS $) collected from this business at the enterprise level and at the outlet level for the price reference period 0 and period t respectively along with the derived items, Margin $ and Relative Margin.

12. In Stage 1 of the calculation process we restrict the scope of the example to show the calculation of the contribution made by a business to the state/territory SUPC Index.

13. Dollar margins are calculated as the difference between the Sales and the COGS, relative margins are calculated as the ratio of dollar margin to sales.

14. Table A1.1, survey data and derived items for Clothing (excluding knitted or crocheted) received for the business at the outlet level and the enterprise level for NSW in price reference period 0.


TABLE A1.1 – Price reference period 0 data for a Clothing business
.

NSW
Sales $
COGS $
Margin $
Relative Margin
Outlet1 Total
20,000
15,000
5,000
0.25
Outlet2 Total
30,000
21,000
9,000
0.30
Outlet3 Total
40,000
32,000
8,000
0.20
Business Total
120,000
90,000
30,000
0.25

15. The CPI for Clothing (excluding knitted or crocheted) for this period is 110.2.

16. Table A1.2, Survey data and derived items for Clothing (excluding knitted or crocheted) received for the business at the outlet level and the enterprise level for NSW. Period, t.


TABLE A1.2 – Period t Survey data collected and derived data for a Clothing business
.

NSW
Sales $
COGS $
Margin $
Relative Margin
Outlet1 Total
25,000
17,500
7,500
0.30
Outlet2 Total
35,000
24,500
10,500
0.30
Outlet3 Total
45,000
33,750
11,250
0.25
Business Total
130,000
91,000
39,000
0.30

17. The CPI for Clothing (excluding knitted or crocheted) for this period is 109.9.

18. Stage 1, the calculation of state/territory SUPC indexes proceeds as follows.

19. This business contributes 10% to the retail trade margins for Clothing (excluding knitted or crocheted) within the state of NSW. The weight assigned to each outlet for period 0 is as follows:

Outlet margin sum = $5,000 + $9,000 + $8,000 = $22,000

Weight Outlet 1 = 5000/22,000 * 0.10 = 0.0227
Weight Outlet 2 = 9,000/22,000 * 0.10 = 0.0409
Weight Outlet 3 = 8,000/22,000 * 0.10 = 0.0364

(Refer to equation 1)

20. The ‘preserved volume of sales’ for each outlet for period t are calculated as follows from period 0 sales data and the relevant CPI figures (rounded to whole dollars);

Volume of sales Outlet 1 = (20,000 * 109.9/110.2) = $19,946
Volume of sales Outlet 2 = (30,000 * 109.9/110.2) = $29,918
Volume of sales Outlet 3 = (40,000 * 109.9/110.2) = $39,891

(Refer to equation 2)

21. A final retail trade margin price for each outlet is then calculated from the ‘preserved volume of sales’ and the relative margin at the outlet for period t as;

Final margin price Outlet 1 = 19,946 * 0.30 = $5,984
Final margin price Outlet 2 = 29,918 * 0.30 = $8,975
Final margin price Outlet 3 = 39,891 * 0.25 = $9,973

(Refer to equation 2)

22. The contribution to the state/territory Clothing (excluding knitted or crocheted) Index for NSW made by this business is then given by the weighted sum of final retail trade margin price relatives as shown below;

Business contribution to index = 5,984/5,000 * 0.0227 +
8,975/9,000 * 0.0409 +
9,973/8,000 * 0.0364
= 0.1133
(Refer to equation 3)

23. State/territory SUPC indexes are formed from the aggregation of these business contributions. This aggregation is then multiplied by the price reference period state/territory SUPC index. In this example, the derived index values are shown in Table A1.3.

24. Stage 2, the calculation of national SUPC indexes proceeds as follows.

25. Incorporating Stage 1 calculations for the businesses participating in the RTMS we have the following state/territory Clothing (excluding knitted or crocheted) Indexes presented in Table A1.3. Table A1.4 presents period 0 state/territory retail trade margins and margin shares.

TABLE A1.3, State/Territory, Clothing (excluding knitted or crocheted), Indexes calculated in stage 1 for periods 0 and t.

State/Territory
Index for Clothing
(excluding knitted or crocheted)
Period 0
Index for Clothing
(excluding knitted or crocheted)
Period t
NSW
101.1
100.0
Vic
102.3
101.4
Qld
100.5
99.5
SA
99.7
98.8
WA
98.0
99.2
Tas
99.9
99.9
NT
103.4
102.1
ACT
105.5
106.2

TABLE A1.4, State/Territory, Clothing (excluding knitted or crocheted), retail trade margins and margin shares for period 0.

State/Territory
Margin $’Millions
Period 0
Margin Share
Period 0
NSW
2,559
0.332
Vic
2,109
0.274
Qld
1,327
0.172
SA
513
0.067
WA
823
0.107
Tas
160
0.021
NT
59
0.008
ACT
160
0.021
Total Australia
7710
1.000



    26. The national value of retail trade margins for Clothing (excluding knitted or crocheted) in period 0 is $7,710 Million. The state/territory retail trade margins share is the ratio of the state/territory retail trade margin to the national retail trade margin value.

    27. The national Clothing (excluding knitted or crocheted) index is calculated as follows;

    Aggregation for Clothing (excluding knitted or crocheted)

    = 100.0/101.1 * 0.332 +
    101.4/102.3 * 0.274 +
    99.5/100.5 * 0.172 +
    98.8/ 99.7 * 0.067 +
    99.2/ 98.0 * 0.107 +
    99.9/ 99.9 * 0.021 +
    102.1/103.4 * 0.008 +
    106.2/105.5 * 0.021
    = 0.993
    (Refer to equations 4 and 5).

    28. This aggregation is then multiplied by the price reference period national SUPC index to obtain the period t national SUPC index for Clothing (excluding knitted or crocheted).

    29. Stage 3, the calculation of the national RTPI is a simple weighted aggregation of the state/territory SUPC indexes. The weights used in this aggregation process are retail trade margin shares calculated from the national S–U table.