# Appendix 7A Principal methodology^{1} for computing estimators of personal expenditure on consumer goods

7A.1 In this appendix, a fictitious example is used to illustrate
the steps in the methodology required for computing approximately 40
seasonally unadjusted^{2} estimators of personal expenditure on consumer
goods (excluding sales tax) with data from the *Quarterly Retail Commodity
Survey*^{3} (QRCS) and the *Monthly Retail
Trade Survey* (MRTS).

7A.2 The purpose of this example is not to portray the two surveys
faithfully but to describe how their data are used. Hence, a simplified
scenario involving only a limited number of trade groups and commodities^{4} was used (see Table 7A.1).

7A.3 The example covers the estimation process for the two most
recent periods t-1 and t. The results of both surveys are available
in t-1, while only the Monthly Retail Trade Survey results are available for the
most recent period t.^{5}

7A.4 The QRCS data are the cornerstone of the methodology. The data for period t-1 are given in Table 7A.2, and the Monthly Retail Trade Survey results also appear implicitly in the "Total" portion of the table, since the total sales are benchmarked from one survey to the other at the trade group level.

Table 7A.2

Source data (Quarterly Retail Commodity Survey and Monthly Retail Trade Survey), period t-1

## Step 1: Convert the classification

7A.5 Step 1 involves mapping commodity sales based on the QRCS classification into the J series according
to the classification of personal expenditure.^{6} This
operation is carried out with a concordance table similar to Table 7A.3.
The mapping between a commodity and a J series is the same no matter
what the trade group is.

Table 7A.3

Concordance between Quarterly Retail Commodity Survey (QRCS) commodities and
personal expenditure series

7A.6 It is often a direct mapping, as in the case of calculation example 1 for commodity C0001, which maps exactly to series J001, and for commodities C0009 to C0013, which all map to series J101.

Cell J001_TG001 from Table 7A.4 |
= Cell C0001_TG001 from Table 7A.2 × Proportion C0001_J001 from Table 7A.3 |
= 37,900 × 1.00 |
= 37,900 |

Cell J101_TG006 from Table 7A.4 |
= (Cell C0009_TG006 from Table 7A.2 × Proportion C0009_J101 from Table 7A.3) + (Cell C0010_TG006 from Table 7A.2 × Proportion C0010_J101 from Table 7A.3) + (Cell C0011_TG006 from Table 7A.2 × Proportion C0011_J101 from Table 7A.3) + (Cell C0012_TG006 from Table 7A.2 × Proportion C0012_J101 from Table 7A.3) + (Cell C0013_TG006 from Table 7A.2 × Proportion C0013_J101 from Table 7A.3) |
= (61,900 × 1.00) + (48,700 × 1.00) + (64,500 × 1.00) + (16,600 × 1.00) + (147,800 × 1.00) |
= 339,500 |

7A.7 However, some commodities map to more than one J series
of personal expenditure. When a breakdown is required, it is based on
more detailed data from the Input-Output Tables or from the *Survey
of Household Spending* (SHS), or
on the analyst's
judgement. This is the case in calculation example 2 for commodity C0003,
which must be distributed across series J004, J005, J006 and J007.

Cell J004_TG002 from Table 7A.4 |
= Cell C0003_TG002 from Table 7A.2 × Proportion C0003_J004 from Table 7A.3 |
= 10,600 × 0.30 |
= 3,180 |

Cell J005_TG002 from Table 7A.4 |
= Cell C0003_TG002 from Table 7A.2 × Proportion C0003_J005 from Table 7A.3 |
= 10,600 × 0.20 |
= 2,120 |

Cell J006_TG002 from Table 7A.4 |
= Cell C0003_TG002 from Table 7A.2 × Proportion C0003_J006 from Table 7A.3 |
= 10,600 × 0.35 |
= 3,710 |

Cell J007_TG002 from Table 7A.4 |
= Cell C0003_TG002 from Table 7A.2 × Proportion C0003_J007 from Table 7A.3 |
= 10,600 × 0.15 |
= 1,590 |

7A.8 Finally, it is important to note that the purchase of certain commodities sold by retailers constitutes gross fixed capital formation rather than personal expenditure, such as hardwood flooring, which would appear under C0002, or renovation materials, which would appear under C0008. As shown in calculation example 3, such commodities are assigned to a dummy series (identified as Jxxx), which ensures that the totals remain unchanged following the process of converting the classification. This is reflected in the "Total" heading in Table 7A.4, which is identical to the "Total" heading in Table 7A.2.

Cell Jxxx_TG005 from Table 7A.4 |
= (Cell C0002_TG005 from Table 7A.2 × Proportion C0002_Jxxx from Table 7A.3) + (Cell C0008_TG005 from Table 7A.2 × Proportion C0008_Jxxx from Table 7A.3) |
= (5,500 × 0.60) + (72,900 × 0.10) |
= 10,590 |

7A.9 The results of all the computations in the conversion of classification are in Table 7A.4.

## Step 2: Convert sales into proportions

7A.10 In step 2, the proportion of each J series' sales relative to total sales is computed for each trade group, as shown in calculation example 4.

Cell J001_TG001 from Table 7A.5 |
= Cell J001_TG001 from Table 7A.4 ÷ Cell TOTAL_TG001 from Table 7A.4 |
= 37,900 ÷ 46,500 |
= 0.815 |

7A.11 The results of all the computations of the conversion of sales into proportions are in Table 7A.5.

7A.12 There are a number of advantages in converting sales into proportions. First, it is much easier to analyze their movements (i.e., their stability or volatility). Second, it allows total sales to be decomposed when Monthly Retail Trade Survey results are available for a given period while QRCS results are not, as is the case for the most recent estimation period t.

## Step 3: Decompose total sales

7A.13 In step 3, the proportions from a previous period computed in step 2 are applied to the Monthly Retail Trade Survey total sales for period t. The previous period is selected on the basis of seasonality; that is, the proportions for the same period of a previous year are generally used. It is important to note that the analyst may, when judged appropriate, adjust the proportions borrowed from a previous period to reflect recent trends in the retail trade sector.

7A.14 As shown in calculation example 5, the proportions for period t-1 from Table 7A.5 are applied to the Monthly Retail Trade Survey total retail sales for period t from Table 7A.6.

Cell J001_TG001 from Table 7A.7 |
= Cell TG001 from Table 7A.6 × Cell J001_TG001 from Table 7A.5 |
= 47,500 × 0.815 |
= 38,715 |

7A.15 The results of all the computations in the decomposition of total sales are in Table 7A.7.

## Step 4: Compute the estimators

7A.16 The estimators for the J series of personal expenditure excluding sales tax are computed by adding up the commodity sales for all trade groups. Calculation example 6 shows this process for the personal expenditure series J001 and J002.

Cell J001[t-1] from Table 7A.8 |
= Cell J001_TG001 from Table 7A.4 + Cell J001_TG002 from Table 7A.4 + Cell J001_TG003 from Table 7A.4 + Cell J001_TG004 from Table 7A.4 + Cell J001_TG005 from Table 7A.4 + Cell J001_TG006 from Table 7A.4 + Cell J001_TG007 from Table 7A.4 + Cell J001_TG008 from Table 7A.4 + Cell J001_TG009 from Table 7A.4 |
= 37,900 + 200 + 0 + 0 + 200 + 900 + 0 + 0 + 3,700 |
= 42,900 |

Cell J002[t] from Table 7A.8 |
= Cell J002_TG001 from Table 7A.7 + Cell J002_TG002 from Table 7A.7 + Cell J002_TG003 from Table 7A.7 + Cell J002_TG004 from Table 7A.7 + Cell J002_TG005 from Table 7A.7 + Cell J002_TG006 from Table 7A.7 + Cell J002_TG007 from Table 7A.7 + Cell J002_TG008 from Table 7A.7 + Cell J002_TG009 from Table 7A.7 |
= 204 + 0 + 0 + 0 + 2,208 + 0 + 0 + 0 + 196 |
= 2,608 |

7A.17 The results of all the estimator computations are in Table 7A.8.

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## Notes

1. See paragraph 7.47 for a list of estimators computed with this methodology. Alternative methodologies have been developed to compute the remaining estimators of personal expenditure on consumer goods which are not included in the list.

2. None of the data used are adjusted for seasonal variation. Only the estimators computed in the last step are seasonally adjusted.

3. While the QRCS results are officially published only on a quarterly basis for Canada, they are nevertheless benchmarked to the Monthly Retail Trade Survey results at the trade group level on a monthly basis. These national monthly series by trade group are provided to the Income and Expenditure Accounts Division (IEAD) by the Distributive Trades Division (DTD). The DTD also produces annual provincial and territorial estimates of commodity sales from these surveys for the Income and Expenditure Accounts Division.

4. The retail trade surveys include results for 19 trade groups based on special aggregations of the 2002 North American Industry Classification System (NAICS). The QRCS collects information on the sales of nearly 120 commodities.

5. QRCS data are usually available about two months after Monthly Retail Trade Survey data.

6. See Table 7.6 for a complete list of personal expenditure series on consumer goods and services.

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