On this page

• Overview
• Reference period
• Data sources and methodologies
• Revisions and seasonal adjustment
• Data accuracy
• Notes
• References
• Appendix

Overview

The consumer price index (CPI) plays a key role in the Bank of Canada's conduct of monetary policy.

In 1991, the Bank of Canada and the Government of Canada jointly established an inflation-targeting framework for the conduct of monetary policy. This framework is reviewed every five years, with the most recent renewal occurring in October 2016. Based on this framework, the Bank of Canada conducts monetary policy aimed at keeping inflation, as measured by the change in the All-items CPI, at 2 per cent, the midpoint of an inflation-control range of 1 to 3 per cent.

To help it achieve this target, the Bank of Canada uses a set of measures of core inflation. The purpose of these measures is to capture persistent price movements by eliminating transitory or sector-specific fluctuations in some components of the CPI. From 2001 until the most recent renewal of the inflation control target, the Bank of Canada's focal measure of core inflation was the All-items CPI excluding eight of its most volatile components (as defined by the Bank of Canada) as well as the effect of changes in indirect taxes on the remaining components (CPIX). For more information, see the Bank of Canada Review article (Macklem [2001]).

As discussed in the Renewal of the Inflation-Control Target – Background Information, the Bank of Canada has identified three preferred measures of core inflation to help assess underlying inflation in Canada.^Note 1 The Bank of Canada chose these three measures based primarily on analysis conducted in 2015 by its researchers (Khan, Morel and Sabourin [2015]). While the Bank's emphasis will be on these three measures, Statistics Canada will continue to calculate and publish CPIX.

Although no measure of core inflation was superior across all the evaluation criteria, three measures showed the best performance. Based on the results of this analysis, the Bank of Canada decided to change its approach by jointly using all three measures: i) a measure based on the trimmed mean (CPI-trim); ii) a measure based on the weighted median (CPI-median); and, iii) a measure based on the common component (CPI-common). For more information on how the three measures were chosen, see the background document on the renewal of the inflation-control target (Bank of Canada [2016]). In the rest of this document, we will present detailed information on the methodologies and data used to produce these measures of core inflation.^Note 2

Reference period

These measures are expressed as a year-over-year percentage change (i.e., comparing any month in a given year to the same month in the previous year). Accordingly, they are not available in the form of an index level and do not have a reference period (e.g., 2002=100).

Data sources and methodologies

The three preferred measures of core inflation are computed by Statistics Canada using data from the CPI Survey. For more information on the data sources, error detection, imputation rules, estimation and calculation of price indexes, quality evaluation of the data collected, and data disclosure control for the CPI survey, see the description of this survey. Below, we will describe the CPI data used and the methods for calculating these three measures of core inflation.

The three measures require historical series of consumer price indexes based on the disaggregation of the All-items CPI into a fixed number of components. These components are exhaustive and mutually exclusive. Therefore, the sum of their respective weights in the CPI basket is equal to 100. These measures are based on a 55-component disaggregation of the CPI basket; a complete list of these components is provided in Table A1 in the appendix of this document. These historical series are available on a monthly basis. Owing to data limitations, these 55 components are calculated since January 1989.^Note 3 Since we use price indexes calculated at the national level, the three measures are only calculated at that level of detail.

The consumer price indexes of the 55 components are first adjusted to remove the effect of changes in indirect taxes.

Measure of core inflation based on the trimmed mean (CPI-trim)

CPI-trim excludes from the 55 components those whose monthly rates of change in the CPI are located in the tails of the distribution of the monthly rates of change of all the price indexes in a given month. This measure is calculated as a weighted arithmetic average of the price changes of the non-excluded components. The weight of a component corresponds to its weight in the CPI basket at the basket link month. The procedure for calculating CPI-trim every month can be described as follows.

Step 1: The historical series of price indexes for the 55 components, adjusted to remove the effect of changes in indirect taxes, are seasonally adjusted. For more information on the seasonal adjustment methodology, see the "Revisions and seasonal adjustment" section below.

Step 2: We obtain the distribution of all monthly inflation rates calculated for the 55 components based on the percentage changes in price indexes for the current month versus those for the previous month. These monthly inflation rates are then sorted in ascending order (i.e., from lowest to highest). By ranking all the components' weights and monthly inflation rates together in this order, components with the lowest inflation rates are excluded, which accounts for 20 per cent^Note 4 of the total CPI basket. The same process is used to exclude components with the highest inflation rates, up to 20 per cent^Note 5 of the basket.

Step 3: We calculate a monthly trimmed inflation rate, ${\text{CPI-trim}}_t^{m/m}$, defined as the weighted arithmetic average of monthly inflation rates for components not excluded in Step 2, which make up 60 per cent of the total CPI basket. The weight of the excluded components will always be 40 per cent of the total CPI basket, but the excluded components are not necessarily the same from month to month.

Step 4: We produce the annual inflation rate for a given month, ${\text{CPI-trim}}_t^{y/y}$, using the cumulative monthly trimmed inflation rates for the 12-month period ending in the current month. The following formula is used for this purpose:

$${\text{CPI-trim}}_t^{y/y}=\left(\left(1+\frac{{\text{CPI-trim}}_{t-11}^{m/m}}{100}\right)\times \left(1+\frac{{\text{CPI-trim}}_{t-10}^{m/m}}{100}\right)\times \dots \times \left(1+\frac{{\text{CPI-trim}}_t^{m/m}}{100}\right)-1\right)\times 100.$$

In other words, the annual inflation rate, ${\text{CPI-trim}}_t^{y/y}$, measured for a given month $t$ is calculated as the cumulative monthly trimmed inflation rates over the 12-month period ending in month $t$.

Measure of core inflation based on the weighted median (CPI-median)

CPI-median represents, for a given month, the price change corresponding to the 50th percentile (in terms of CPI basket weights) of the distribution of price changes of the 55 components. As with CPI-trim, the weight of a component is represented by its weight in the CPI basket at the basket link month. The method for processing data for the CPI-median is similar to that for CPI-trim. The procedure for calculating CPI-median every month can be described as follows.

Step 1: The historical series of price indexes for the 55 components, adjusted to remove the effect of changes in indirect taxes, are seasonally adjusted. For more information on the seasonal adjustment methodology, see the "Revisions and seasonal adjustment" section below.

Step 2: We obtain the distribution of all monthly inflation rates calculated for the 55 components based on the percentage changes in price indexes for the current month versus those for the previous month. These monthly inflation rates are then sorted in ascending order (i.e., from lowest to highest). By ranking all the components' weights and inflation rates together in this order, we identify the monthly inflation rate located at the 50th percentile^Note 6 (in terms of CPI basket weights) of the distribution of the monthly inflation rates for the 55 components. This value represents the monthly inflation rate based on the weighted median, ${\text{CPI-median}}_t^{m/m}$. The component corresponding to the weighted median value is not necessarily the same from month to month. This approach is similar to that for CPI-trim because it eliminates all the weighted monthly price variations at both the bottom and top of the distribution of price changes in any given month, except the price change for the component that is the midpoint of that distribution.

Step 3: We produce the annual inflation rate, ${\text{CPI-median}}_t^{y/y}$, for a given month, using the cumulative monthly inflation rates based on the weighted median for the 12-month period ending in the current month. The following formula is used for this purpose:

$${\text{CPI-median}}_t^{y/y}=\left(\left(1+\frac{{\text{CPI-median}}_{t-11}^{m/m}}{100}\right)\times \left(1+\frac{{\text{CPI-median}}_{t-10}^{m/m}}{100}\right)\times \dots \times \left(1+\frac{{\text{CPI-median}}_t^{m/m}}{100}\right)-1\right)\times 100.$$

In other words, the value of the annual inflation rate, ${\text{CPI-median}}_t^{y/y}$, in a given month $t$ is calculated as the cumulative monthly inflation rates based on the weighted median over the 12-month period ending in month $t$.

Measure of core inflation based on the common component (CPI-common)

CPI-common is a measure that tracks common price changes across the 55 components in the CPI basket.

As with CPI-trim and CPI-median, the input data for CPI-common are the CPI series for the 55 components adjusted to remove the effect of changes in indirect taxes. In addition, we use the historical series of the All-items CPI adjusted to remove the effect of changes in indirect taxes to scale CPI-common to the inflation rate. Unlike CPI-trim and CPI-median, this measure is based on year-over-year percentage changes in price indexes. Therefore, the price index series are not seasonally adjusted when calculating CPI-common.

This measure is based on a factor model. Factor models are statistical methods that represent the variation in a set of variables as the sum of one or more factors representing co-movements across variables and an idiosyncratic term capturing the part unexplained by this (those) common factor(s). In the context of estimating core inflation, these models are used to separate the common source underlying the changes in CPI series from idiosyncratic elements that are related to sector-specific events (Khan, Morel and Sabourin [2013]).^Note 7 For each of the 55 components, $i=1,2,\mathrm{...},55$, the model is written as follows (in the case of one common factor):

$${\pi }_{i,t}={\Lambda }_i{F}_t+{\epsilon }_{i,t};i=1,2,\mathrm{...},55;t=1,2,\mathrm{...},T,$$

where $T$ represents the total number of time periods available, ${\pi }_{i,t}$ represents the inflation rate of component $i$ for the period $t$, which is related to the common factor $F_t$ through factor loading ${\Lambda }_i$, and ${\epsilon }_{i,t}$ is an idiosyncratic error term representing sector-specific disturbances that are uncorrelated with the common factor. In this model, the measure of core inflation is then defined as follows:

$${\tilde{\pi }}_t=\Lambda F_t\text{ ,}$$

where $\Lambda$ is the matrix of factor loadings. For more information, see Khan et al. (2013).

In practice, CPI-common is calculated using the entire historical data of price index series and by following the steps below.

Step 1: We calculate annual inflation rates for the 55 components and for the All-items CPI excluding the effect of changes in indirect taxes. In a given month, the annual inflation rate for a given component is defined as the year-over-year percentage change in the price index for that month.

Step 2: The historical series of annual inflation rates for the 55 components are standardized. In other words, the historical series of annual inflation rates for each component is centred with respect to its average and then divided by its standard deviation.

Step 3: A factor model is estimated using data from the 55 historical series of annual standardized inflation rates. The principal components method is used for this purpose (Stock and Watson [2002a, 2002b]). This method involves creating 55 new variables, called principal components, each explaining a fraction of the variation found in all 55-historical series of annual inflation rates. The first principal component, which is associated with the highest eigenvalue, is the one that best explains the variation in the 55 historical series of annual inflation rates over the entire observation period. Only the first principal component is used in calculating CPI-common.^Note 8

Step 4: The final step is to scale the first principal component to the inflation rate. The measure of core inflation based on the common component, CPI-common, is defined and calculated as the series of predicted values from the simple linear regression of the annual inflation rates of the All-items CPI excluding the effect of changes in indirect taxes (obtained in Step 1) on an intercept and on the first principal component calculated in Step 3.

Since CPI-common is based on a factor model, a standardization and a linear regression requiring all data available, the historical values for this measure are subject to revisions. An analysis of the magnitude of the revisions, reported in a Bank of Canada's Staff Working Paper (Khan et al. [2013]), suggests that revisions are relatively negligible.

Revisions and seasonal adjustment

These three measures of core inflation, CPI-trim, CPI-median and CPI-common, are subject to revision. For CPI-median and CPI-trim, this results from the fact that these measures are based on seasonally adjusted price index series. For CPI-common, revisions are due to the statistical technique used as the factor model is estimated over all available historical data.

When Statistics Canada introduces the CPI-trim and CPI-median measures in its November 2016 CPI release, 44 of the 55 historical series will be identified as seasonally adjusted, whereas others do not present any identifiable seasonal pattern. Since the technical parameters for seasonal adjustment are updated once a year, the number of series that are seasonally adjusted may change in the future depending on the historical series available that have (or do not have) an identifiable seasonal pattern. As with other CPI series, the approach used for seasonal adjustment involves each series to be seasonally adjusted separately. For more information, see the section "Revisions and seasonal adjustment" in the CPI detailed information document.

The seasonally adjusted CPI series are subject to revision. Every month, the seasonally adjusted data for the previous seven years are revised.^Note 9 However, the models underlying the seasonal adjustment procedure are regularly revisited; as a result, they will be revised and updated when necessary.

Data accuracy

As with the CPI in general, statistical reliability is difficult to evaluate for the three preferred measures of core inflation. First, a statistical reliability indicator is not available for the price index series used as inputs to these measures. In addition, calculating these measures is complex, which makes it more difficult to evaluate their statistical reliability. For more information on the evaluation of the CPI data accuracy, see this Statistics Canada publication. In practice, since the three measures are based on price index series calculated at the national level, their level of accuracy should be relatively comparable to that of All-items CPI.

Appendix

Objectives, uses and users
Concepts, variables and classifications
Coverage and frames
Sampling
Questionnaire design
Response and non-response
Data collection and capture operations
Editing
Imputation
Estimation
Revisions and seasonal adjustment
Data quality evaluation
Disclosure control

1. Objectives, uses and users

1.1. Objective

The Monthly Retail Trade Survey (MRTS) provides information on the performance of the retail trade sector on a monthly basis, and when combined with other statistics, represents an important indicator of the state of the Canadian economy.

1.2. Uses

The estimates provide a measure of the health and performance of the retail trade sector. Information collected is used to estimate level and monthly trend for retail sales. At the end of each year, the estimates provide a preliminary look at annual retail sales and performance.

1.3. Users

A variety of organizations, sector associations, and levels of government make use of the information. Retailers rely on the survey results to compare their performance against similar types of businesses, as well as for marketing purposes. Retail associations are able to monitor industry performance and promote their retail industries. Investors can monitor industry growth, which can result in better access to investment capital by retailers. Governments are able to understand the role of retailers in the economy, which aids in the development of policies and tax incentives. As an important industry in the Canadian economy, governments are able to better determine the overall health of the economy through the use of the estimates in the calculation of the nation’s Gross Domestic Product (GDP).

2. Concepts, variables and classifications

2.1. Concepts

The retail trade sector comprises establishments primarily engaged in retailing merchandise, generally without transformation, and rendering services incidental to the sale of merchandise.

The retailing process is the final step in the distribution of merchandise; retailers are therefore organized to sell merchandise in small quantities to the general public. This sector comprises two main types of retailers, that is, store and non-store retailers. The MRTS covers only store retailers. Their main characteristics are described below. Store retailers operate fixed point-of-sale locations, located and designed to attract a high volume of walk-in customers. In general, retail stores have extensive displays of merchandise and use mass-media advertising to attract customers. They typically sell merchandise to the general public for personal or household consumption, but some also serve business and institutional clients. These include establishments such as office supplies stores, computer and software stores, gasoline stations, building material dealers, plumbing supplies stores and electrical supplies stores.

In addition to selling merchandise, some types of store retailers are also engaged in the provision of after-sales services, such as repair and installation. For example, new automobile dealers, electronic and appliance stores and musical instrument and supplies stores often provide repair services, while floor covering stores and window treatment stores often provide installation services. As a general rule, establishments engaged in retailing merchandise and providing after sales services are classified in this sector. Catalogue sales showrooms, gasoline service stations, and mobile home dealers are treated as store retailers.

2.2. Variables

Sales are defined as the sales of all goods purchased for resale, net of returns and discounts. This includes commission revenue and fees earned from selling goods and services on account of others, such as selling lottery tickets, bus tickets, and phone cards. It also includes parts and labour revenue from repair and maintenance; revenue from rental and leasing of goods and equipment; revenues from services, including food services; sales of goods manufactured as a secondary activity; and the proprietor’s withdrawals, at retail, of goods for personal use. Other revenue from rental of real estate, placement fees, operating subsidies, grants, royalties and franchise fees are excluded.

Trading Location is the physical location(s) in which business activity is conducted in each province and territory, and for which sales are credited or recognized in the financial records of the company. For retailers, this would normally be a store.

Constant Dollars: The value of retail trade is measured in two ways; including the effects of price change on sales and net of the effects of price change. The first measure is referred to as retail trade in current dollars and the latter as retail trade in constant dollars. The method of calculating the current dollar estimate is to aggregate the weighted value of sales for all retail outlets. The method of calculating the constant dollar estimate is to first adjust the sales values to a base year, using the Consumer Price Index, and then sum up the resulting values.

2.3. Classification

The Monthly Retail Trade Survey is based on the definition of retail trade under the NAICS (North American Industry Classification System). NAICS is the agreed upon common framework for the production of comparable statistics by the statistical agencies of Canada, Mexico and the United States. The agreement defines the boundaries of twenty sectors. NAICS is based on a production-oriented, or supply based conceptual framework in that establishments are groups into industries according to similarity in production processes used to produce goods and services.

Estimates appear for 21 industries based on special aggregations of the 2012 North American Industry Classification System (NAICS) industries. The 21 industries are further aggregated to 11 sub-sectors.

Geographically, sales estimates are produced for Canada and each province and territory.

3. Coverage and frames

Statistics Canada’s Business Register ( BR) provides the frame for the Monthly Retail Trade Survey. The BR is a structured list of businesses engaged in the production of goods and services in Canada. It is a centrally maintained database containing detailed descriptions of most business entities operating within Canada. The BR includes all incorporated businesses, with or without employees. For unincorporated businesses, the BR includes all employers with businesses, and businesses with no employees with annual sales that have a Goods and Services Tax (GST) or annual revenue that declares individual taxes.  annual sales greater than $30,000 that have a Goods and Services Tax (GST) account (the BR does not include unincorporated businesses with no employees and with annual sales less than $30,000).

The businesses on the BR are represented by a hierarchical structure with four levels, with the statistical enterprise at the top, followed by the statistical company, the statistical establishment and the statistical location. An enterprise can be linked to one or more statistical companies, a statistical company can be linked to one or more statistical establishments, and a statistical establishment to one or more statistical locations.

The target population for the MRTS consists of all statistical establishments on the BR that are classified to the retail sector using the North American Industry Classification System (NAICS) (approximately 200,000 establishments). The NAICS code range for the retail sector is 441100 to 453999. A statistical establishment is the production entity or the smallest grouping of production entities which: produces a homogeneous set of goods or services; does not cross provincial boundaries; and provides data on the value of output, together with the cost of principal intermediate inputs used, along with the cost and quantity of labour used to produce the output. The production entity is the physical unit where the business operations are carried out. It must have a civic address and dedicated labour.

The exclusions to the target population are ancillary establishments (producers of services in support of the activity of producing goods and services for the market of more than one establishment within the enterprise, and serves as a cost centre or a discretionary expense centre for which data on all its costs including labour and depreciation can be reported by the business), future establishments, establishments with a missing or a zero gross business income (GBI) value on the BR and establishments in the following non-covered NAICS:

• 4541 (electronic shopping and mail-order houses)
• 4542 (vending machine operators)
• 45431 (fuel dealers)
• 45439 (other direct selling establishments)

4. Sampling

The MRTS sample consists of 10,000 groups of establishments (clusters) classified to the Retail Trade sector selected from the Statistics Canada Business Register. A cluster of establishments is defined as all establishments belonging to a statistical enterprise that are in the same industrial group and geographical region. The MRTS uses a stratified design with simple random sample selection in each stratum. The stratification is done by industry groups (the mainly, but not only four digit level NAICS), and the geographical regions consisting of the provinces and territories, as well as three provincial sub-regions. We further stratify the population by size.

The size measure is created using a combination of independent survey data and three administrative variables: the annual profiled revenue, the GST sales expressed on an annual basis, and the declared tax revenue (T1 or T2). The size strata consist of one take-all (census), at most, two take-some (partially sampled) strata, and one take-none (non-sampled) stratum. Take-none strata serve to reduce respondent burden by excluding the smaller businesses from the surveyed population. These businesses should represent at most ten percent of total sales. Instead of sending questionnaires to these businesses, the estimates are produced through the use of administrative data.

The sample was allocated optimally in order to reach target coefficients of variation at the national, provincial/territorial, industrial, and industrial groups by province/territory levels. The sample was also inflated to compensate for dead, non-responding, and misclassified units.

MRTS is a repeated survey with maximisation of monthly sample overlap. The sample is kept month after month, and every month new units are added (births) to the sample.  MRTS births, i.e., new clusters of establishment(s), are identified every month via the BR’s latest universe. They are stratified according to the same criteria as the initial population. A sample of these births is selected according to the sampling fraction of the stratum to which they belong and is added to the monthly sample. Deaths occur on a monthly basis. A death can be a cluster of establishment(s) that have ceased their activities (out-of-business) or whose major activities are no longer in retail trade (out-of-scope). The status of these businesses is updated on the BR using administrative sources and survey feedback, including feedback from the MRTS. Methods to treat dead units and misclassified units are part of the sample and population update procedures.

5. Questionnaire design

The Monthly Retail Trade Survey incorporates the following sub-surveys:

Monthly Retail Trade Survey - R8

Monthly Retail Trade Survey (with inventories) – R8

Survey of Sales and Inventories of Alcoholic Beverages

The questionnaires collect monthly data on retail sales and the number of trading locations by province or territory and inventories of goods owned and intended for resale from a sample of retailers. The items on the questionnaires have remained unchanged for several years. For the 2004 redesign, the general questionnaires were subject to cosmetic changes only. The questionnaire for Sales and Inventories of Alcoholic Beverages underwent more extensive changes. The modifications were discussed withstakeholders and the respondents were given an opportunity to comment before the new questionnaire was finalized. If further changes are needed to any of the questionnaires, proposed changes would go through a review committee and a field test with respondents and data users to ensure its relevancy.

6. Response and non-response

6.1. Response and non-response

Despite the best efforts of survey managers and operations staff to maximize response in the MRTS, some non-response will occur. For statistical establishments to be classified as responding, the degree of partial response (where an accurate response is obtained for only some of the questions asked a respondent) must meet a minimum threshold level below which the response would be rejected and considered a unit non-response.  In such an instance, the business is classified as not having responded at all.

Non-response has two effects on data: first it introduces bias in estimates when non-respondents differ from respondents in the characteristics measured; and second, it contributes to an increase in the sampling variance of estimates because the effective sample size is reduced from that originally sought.

The degree to which efforts are made to get a response from a non-respondent is based on budget and time constraints, its impact on the overall quality and the risk of non-response bias.

The main method to reduce the impact of non-response at sampling is to inflate the sample size through the use of over-sampling rates that have been determined from similar surveys.

Besides the methods to reduce the impact of non-response at sampling and collection, the non-responses to the survey that do occur are treated through imputation. In order to measure the amount of non-response that occurs each month, various response rates are calculated. For a given reference month, the estimation process is run at least twice (a preliminary and a revised run). Between each run, respondent data can be identified as unusable and imputed values can be corrected through respondent data. As a consequence, response rates are computed following each run of the estimation process.

For the MRTS, two types of rates are calculated (un-weighted and weighted). In order to assess the efficiency of the collection process, un-weighted response rates are calculated. Weighted rates, using the estimation weight and the value for the variable of interest, assess the quality of estimation. Within each of these types of rates, there are distinct rates for units that are surveyed and for units that are only modeled from administrative data that has been extracted from GST files.

To get a better picture of the success of the collection process, two un-weighted rates called the ‘collection results rate’ and the ‘extraction results rate’ are computed. They are computed by dividing the number of respondents by the number of units that we tried to contact or tried to receive extracted data for them. Non-monthly reporters (respondents with special reporting arrangements where they do not report every month but for whom actual data is available in subsequent revisions) are excluded from both the numerator and denominator for the months where no contact is performed.

In summary, the various response rates are calculated as follows:

Weighted rates:

Survey Response rate (estimation) =
Sum of weighted sales of units with response status i / Sum of survey weighted sales

where i = units that have either reported data that will be used in estimation or are converted refusals, or have reported data that has not yet been resolved for estimation.

Admin Response rate (estimation) =
Sum of weighted sales of units with response status ii / Sum of administrative weighted sales

where ii = units that have data that was extracted from administrative files and are usable for estimation.

Total Response rate (estimation) =
Sum of weighted sales of units with response status i or response status ii / Sum of all weighted sales

Un-weighted rates:

Survey Response rate (collection) =
Number of questionnaires with response status iii/ Number of questionnaires with response status iv

where iii = units that have either reported data (unresolved, used or not used for estimation) or are converted refusals.

where iv = all of the above plus units that have refused to respond, units that were not contacted and other types of non-respondent units.

Admin Response rate (extraction) =
Number of questionnaires with response status vi/ Number of questionnaires with response status vii

where vi = in-scope units that have data (either usable or non-usable) that was extracted from administrative files

where vii = all of the above plus units that have refused to report to the administrative data source, units that were not contacted and other types of non-respondent units.

(% of questionnaire collected over all in-scope questionnaires)

Collection Results Rate =
Number of questionnaires with response status iii / Number of questionnaires with response status viii

where iii = same as iii defined above

where viii = same as iv except for the exclusion of units that were contacted because their response is unavailable for a particular month since they are non-monthly reporters.

Extraction Results Rate =
Number of questionnaires with response status ix / Number of questionnaires with response status vii

where ix = same as vi with the addition of extracted units that have been imputed or were out of scope

where vii = same as vii defined above

(% of questionnaires collected over all questionnaire in-scope we tried to collect)

All the above weighted and un-weighted rates are provided at the industrial group, geography and size group level or for any combination of these levels.

Use of Administrative Data

Managing response burden is an ongoing challenge for Statistics Canada. In an attempt to alleviate response burden and survey costs, especially for smaller businesses, the MRTS has reduced the number of simple establishments in the sample that are surveyed directly and instead derives sales data for these establishments from Goods and Service Tax (GST) files using a statistical model. The model accounts for differences between sales and revenue (reported for GST purposes) as well as for the time lag between the survey reference period and the reference period of the GST file.

For more information on the methodology used for modeling sales from administrative data sources, refer to ‘Monthly Retail Trade Survey: Use of Administrative Data’ under ‘Documentation’ of the IMDB.

Table 1 contains the weighted response rates for all industry groups as well as for total retail trade for each province and territory. For more detailed weighted response rates, please contact the Marketing and Dissemination Section at (613) 951-3549, toll free: 1-877-421-3067 or by e-mail at retailinfo@statcan.

6.2. Methods used to reduce non-response at collection

Significant effort is spent trying to minimize non-response during collection. Methods used, among others, are interviewer techniques such as probing and persuasion, repeated re-scheduling and call-backs to obtain the information, and procedures dealing with how to handle non-compliant (refusal) respondents.

If data are unavailable at the time of collection, a respondent's best estimates are also accepted, and are subsequently revised once the actual data become available.

To minimize total non-response for all variables, partial responses are accepted. In addition, questionnaires are customized for the collection of certain variables, such as inventory, so that collection is timed for those months when the data are available.

Finally, to build trust and rapport between the interviewers and respondents, cases are generally assigned to the same interviewer each month. This action establishes a personal relationship between interviewer and respondent, and builds respondent trust.

7. Data collection and capture operations

Collection of the data is performed by Statistics Canada’s Regional Offices.

Weighted Response Rates

Respondents are sent a questionnaire or are contacted by telephone to obtain their sales and inventory values, as well as to confirm the opening or closing of business trading locations. Collection of the data begins approximately 7 working days after the end of the reference month and continues for the duration of that month.

New entrants to the survey are introduced to the survey via an introductory letter that informs the respondent that a representative of Statistics Canada will be calling. This call is to introduce the respondent to the survey, confirm the respondent's business activity, establish and begin data collection, as well as to answer any questions that the respondent may have.

8. Editing

Data editing is the application of checks to detect missing, invalid or inconsistent entries or to point to data records that are potentially in error. In the survey process for the MRTS, data editing is done at two different time periods.

First of all, editing is done during data collection. Once data are collected via the telephone, or via the receipt of completed mail-in questionnaires, the data are captured using customized data capture applications. All data are subjected to data editing. Edits during data collection are referred to as field edits and generally consist of validity and some simple consistency edits. They are used to detect mistakes made during the interview by the respondent or the interviewer and to identify missing information during collection in order to reduce the need for follow-up later on. Another purpose of the field edits is to clean up responses. In the MRTS, the current month’s responses are edited against the respondent’s previous month’s responses and/or the previous year’s responses for the current month. Field edits are also used to identify problems with data collection procedures and the design of the questionnaire, as well as the need for more interviewer training.

Follow-up with respondents occurs to validate potential erroneous data following any failed preliminary edit check of the data. Once validated, the collected data is regularly transmitted to the head office in Ottawa.

Secondly, editing known as statistical editing is also done after data collection and this is more empirical in nature. Statistical editing is run prior to imputation in order to identify the data that will be used as a basis to impute non-respondents. Large outliers that could disrupt a monthly trend are excluded from trend calculations by the statistical edits. It should be noted that adjustments are not made at this stage to correct the reported outliers.

The first step in the statistical editing is to identify which responses will be subjected to the statistical edit rules. Reported data for the current reference month will go through various edit checks.

The first set of edit checks is based on the Hidiriglou-Berthelot method whereby a ratio of the respondent’s current month data over historical (last month, same month last year) or auxiliary data is analyzed. When the respondent’s ratio differs significantly from ratios of respondents who are similar in terms of industry and/or geography group, the response is deemed an outlier.

The second set of edits consists of an edit known as the share of market edit. With this method, one is able to edit all respondents, even those where historical and auxiliary data is unavailable. The method relies on current month data only. Therefore, within a group of respondents, that are similar in terms of industrial group and/or geography, if the weighted contribution of a respondent to the group’s total is too large, it will be flagged as an outlier.

For edit checks based on the Hidiriglou-Berthelot method, data that are flagged as an outlier will not be included in the imputation models (those based on ratios). Also, data that are flagged as outliers in the share of market edit will not be included in the imputation models where means and medians are calculated to impute for responses that have no historical responses.

In conjunction with the statistical editing after data collection of reported data, there is also error detection done on the extracted GST data. Modeled data based on the GST are also subject to an extensive series of processing steps which thoroughly verify each record that is the basis for the model as well as the record being modeled. Edits are performed at a more aggregate level (industry by geography level) to detect records which deviate from the expected range, either by exhibiting large month-to-month change, or differing significantly from the remaining units. All data which fail these edits are subject to manual inspection and possible corrective action.

9. Imputation

Imputation in the MRTS is the process used to assign replacement values for missing data. This is done by assigning values when they are missing on the record being edited to ensure that estimates are of high quality and that a plausible, internal consistency is created. Due to concerns of response burden, cost and timeliness, it is generally impossible to do all follow-ups with the respondents in order to resolve missing responses. Since it is desirable to produce a complete and consistent microdata file, imputation is used to handle the remaining missing cases.

In the MRTS, imputation is based on historical data or administrative data (GST sales). The appropriate method is selected according to a strategy that is based on whether historical data is available, auxiliary data is available and/or which reference month is being processed.

There are three types of historical imputation methods. The first type is a general trend that uses one historical data source (previous month, data from next month or data from same month previous year). The second type is a regression model where data from previous month and same month, previous year are used simultaneously. The third type uses the historical data as a direct replacement value for a non-respondent. Depending upon the particular reference month, there is an order of preference that exists so that top quality imputation can result. The historical imputation method that was labelled as the third type above is always the last option in the order for each reference month.

The imputation method using administrative data is automatically selected when historical information is unavailable for a non-respondent. Trends are then applied to the administrative data source (monthly size) depending on whether the structure is simple, e.g. enterprises with only one establishment, or the unit has a more complex structure.

10. Estimation

Estimation is a process that approximates unknown population parameters using only part of the population that is included in a sample. Inferences about these unknown parameters are then made, using the sample data and associated survey design. This stage uses Statistics Canada's Generalized Estimation System (GES).

For retail sales, the population is divided into a survey portion (take-all and take-some strata) and a non-survey portion (take-none stratum). From the sample that is drawn from the survey portion, an estimate for the population is determined through the use of a Horvitz-Thompson estimator where responses for sales are weighted by using the inverses of the inclusion probabilities of the sampled units. Such weights (called sampling weights) can be interpreted as the number of times that each sampled unit should be replicated to represent the entire population. The calculated weighted sales values are summed by domain, to produce the total sales estimates by each industrial group / geographic area combination. A domain is defined as the most recent classification values available from the BR for the unit and the survey reference period. These domains may differ from the original sampling strata because units may have changed size, industry or location. Changes in classification are reflected immediately in the estimates and do not accumulate over time. For the non-survey portion, the sales are estimated with statistical models using monthly GST sales.

For more information on the methodology for modeling sales from administrative data sources which also contributes to the estimates of the survey portion, refer to ‘Monthly Retail Survey: Use of Administrative Data’ under ‘Documentation’ of the IMDB.

The measure of precision used for the MRTS to evaluate the quality of a population parameter estimate and to obtain valid inferences is the variance. The variance from the survey portion is derived directly from a stratified simple random sample without replacement.

Sample estimates may differ from the expected value of the estimates. However, since the estimate is based on a probability sample, the variability of the sample estimate with respect to its expected value can be measured. The variance of an estimate is a measure of the precision of the sample estimate and is defined as the average, over all possible samples, of the squared difference of the estimate from its expected value.

11. Revisions and seasonal adjustment

Revisions in the raw data are required to correct known non-sampling errors. These normally include replacing imputed data with reported data, corrections to previously reported data, and estimates for new births that were not known at the time of the original estimates.

Raw data are revised, on a monthly basis, for the month immediately prior to the current reference month being published. That is, when data for December are being published for the first time, there will also be revisions, if necessary, to the raw data for November. In addition, revisions are made once a year, with the initial release of the February data, for all months in the previous years. The purpose is to correct any significant problems that have been found that apply for an extended period. The actual period of revision depends on the nature of the problem identified, but rarely exceeds three years. The revision period can be extended when historical revisions or restratitfication are done.

Retail trade data are seasonally adjusted using the X12-ARIMA method. This consists of extrapolating a year's worth of raw data with the ARIMA model (auto-regressive integrated moving average model), and of seasonally adjusting the raw time series. Finally, the annual totals of the seasonally adjusted series are forced to the annual totals of the original series.

The seasonally adjusted data also need to be revised. In part, they need to reflect the revisions identified for the raw data. Also, the seasonally adjusted estimates are calculated using X-12-ARIMA, and are sensitive to the most recent values reported in the raw data. For this reason, with the release of each month of new data, the seasonally adjusted values for the previous three months are revised.  A seasonally adjusted time series is a time series that has been modified to eliminate the effect of seasonal and calendar influences. For this reason, the seasonally adjusted data allows for more meaningful comparisons of economic conditions from month to month.

Once a year, seasonal adjustments options are reviewed to take into account the most recent data. Revised seasonally adjusted estimates for each month in the previous years are released at the same time as the annual revision to the raw data. The actual period of revision depends on the number years the raw data was revised.

12. Data quality evaluation

The methodology of this survey has been designed to control errors and to reduce their potential effects on estimates. However, the survey results remain subject to errors, of which sampling error is only one component of the total survey error. Sampling error results when observations are made only on a sample and not on the entire population. All other errors arising from the various phases of a survey are referred to as nonsampling errors. For example, these types of errors can occur when a respondent provides incorrect information or does not answer certain questions; when a unit in the target population is omitted or covered more than once; when GST data for records being modeled for a particular month are not representative of the actual record for various reasons; when a unit that is out of scope for the survey is included by mistake or when errors occur in data processing, such as coding or capture errors.

Prior to publication, combined survey results are analyzed for comparability; in general, this includes a detailed review of individual responses (especially for large businesses), general economic conditions and historical trends.

A common measure of data quality for surveys is the coefficient of variation (CV). The coefficient of variation, defined as the standard error divided by the sample estimate, is a measure of precision in relative terms. Since the coefficient of variation is calculated from responses of individual units, it also measures some non-sampling errors.

The formula used to calculate coefficients of variation (CV) as percentages is:

CV (X) = S(X) * 100% / X
where X denotes the estimate and S(X) denotes the standard error of X.

Confidence intervals can be constructed around the estimates using the estimate and the CV. Thus, for our sample, it is possible to state with a given level of confidence that the expected value will fall within the confidence interval constructed around the estimate. For example, if an estimate of $12,000,000 has a CV of 2%, the standard error will be $240,000 (the estimate multiplied by the CV). It can be stated with 68% confidence that the expected values will fall within the interval whose length equals the standard deviation about the estimate, i.e. between $11,760,000 and $12,240,000.

Alternatively, it can be stated with 95% confidence that the expected value will fall within the interval whose length equals two standard deviations about the estimate, i.e. between $11,520,000 and $12,480,000.

Finally, due to the small contribution of the non-survey portion to the total estimates, bias in the non-survey portion has a negligible impact on the CVs. Therefore, the CV from the survey portion is used for the total estimate that is the summation of estimates from the surveyed and non-surveyed portions.

13. Disclosure control

Statistics Canada is prohibited by law from releasing any data which would divulge information obtained under the Statistics Act that relates to any identifiable person, business or organization without the prior knowledge or the consent in writing of that person, business or organization. Various confidentiality rules are applied to all data that are released or published to prevent the publication or disclosure of any information deemed confidential. If necessary, data are suppressed to prevent direct or residual disclosure of identifiable data.

Confidentiality analysis includes the detection of possible "direct disclosure", which occurs when the value in a tabulation cell is composed of a few respondents or when the cell is dominated by a few companies.

About the maps

Volume II of the Standard Geographical Classification (SGC) 2016 provides a series of reference maps that show the boundaries, names and SGC codes of all census divisions (CDs) and census subdivisions (CSDs) in Canada, in effect on January 1, 2016. It also provides the names, codes and areal extent of census metropolitan areas (CMAs), census agglomerations (CAs), census metropolitan influenced zones (MIZs) and economic regions (ERs). Definitions for these terms are found in Volume I of the Standard Geographical Classification (SGC) 2016, Catalogue no. 12-571-X. Concordances between the 2016 classification and the 2011 classification as well as annual changes in the census subdivision names, types and codes are also available.

The maps in this volume are introduced by a set of four national maps, at a scale which permits Canada to fit on a single sheet (i.e., 1:7 500 000). Map A, illustrating the country's 293 census divisions, presents a numerical list of the census divisions by province and territory. Maps B shows the location (using dots) of the census metropolitan areas and census agglomerations of Canada and present a numerical and alphabetical list of CMAs and CAs by province and territory. This map is designed to give a general idea of where CMAs and CAs are situated within a province or territory, with large dots designating CMAs and small dots designating CAs. Map C shows the Statistical Area Classification - Variant of SGC 2016. This map illustrates the spatial distribution of CSDs among CMAs, CAs and MIZs. Map D shows the census division and economic region boundaries and codes within each province and territory. This is accompanied by a legend which lists the ER names in ER code order within which are listed (numerically) their component census division codes and names.

The next set of maps, the Census divisions - Census subdivisions (CD-CSD) maps, shows the location of census divisions and census subdivisions and their SGC codes as well as the CSD names. This set begins with an index map, which shows the areas covered by each map. The index map covers all of Canada and is presented on a single sheet. It may be used as a quick reference to determine the correct map number(s) for the area(s) of interest. There are 23 CD-CSD maps for the 10 provinces and 3 territories. These maps include, where applicable, the boundaries and codes for CMAs and CAs, and on each map face, a list of the appropriate CD and CMA/CA names and codes (numerical and alphabetical order).

The maps were designed with the objective of permitting users to identify the general location, boundaries, names and codes of the geographic areas presented in Volume I of the SGC 2016. The maps are not intended to serve as detailed legal or cadastral representations of the geographic areas shown.

Technical information and data sources

The following are key technical points relating to the production of the maps:

• The vector base map information (e.g., shorelines, rivers, and lakes) were taken from the National Geographic Database, version 2 (NGD v.2). The map series is represented in Lambert conformal conic projection. The standard parallels, central meridians and latitudes of origin are specific to each province and territory.
• Geographic boundaries, names, types and codes were obtained from the Statistics Canada Spatial Data Infrastructure (SDI) June 2016 Geographic Frame. The reference date for all geographic areas is January 1, 2016. The naming of CSDs is a provincial/territorial responsibility. River and lake names were taken from the Canadian Geographical Names Data Base (CGNDB). Names of geographic entities having 'pan-Canadian' significance, established by the Geographical Names Board of Canada (GNBC) (i.e., names of provinces, territories, major islands and major bodies of water) are shown in both official languages.

Status

This standard was approved as a departmental standard on May 16, 2016.

2016 version of the SGC

The Standard Geographical Classification (SGC) provides a systematic classification structure that categorizes all of the geographic area of Canada.

The SGC was developed to enable the production of integrated statistics by geographic area. It provides a range of geographic units that are convenient for data collection and compilation, and useful for spatial analysis of economic and social statistics. It is intended primarily for the classification of statistical units, such as establishments or households, whose activities are normally associated with a specific location.

The classification is organized in two volumes: volume I and volume II. Volume I describes the classification and related standard geographic areas and place names. It provides names and codes for the geographical regions of Canada, provinces and territories, census divisions (counties, regional municipalities) and census subdivisions (municipalities). The names and codes for census metropolitan areas, census agglomerations, census metropolitan influenced zones, economic regions, census agricultural regions and census consolidated subdivisions are shown in the classification variants of the SGC. Volume I explains the changes between the 2016 version of the SGC and the 2011 version that impact upon the classification, such as changes in name, type or code, and indicates how the new and old codes relate to one another. Volume II contains reference maps showing boundaries, names, codes and locations of the geographic areas in the classification.

Reference maps

Volume II consists of four maps of Canada that illustrate locations of individual census divisions, census metropolitan areas, census agglomerations, census metropolitan influenced zones and economic regions. These are referred to as the National maps. Also included are 23 maps that show the boundaries of census divisions and census subdivisions. These are referred to as the Census divisions - Census subdivisions (CD-CSD) maps.

• Information on reference maps
• Reference map

Status

This standard was approved as a departmental standard on May 16, 2016.

2016 version of the SGC

The standard classification version of the SGC 2016 provides standard names and codes for the geographical regions of Canada, provinces and territories, census divisions (counties, regional municipalities) and census subdivisions (municipalities).

The names and codes for census metropolitan areas, census agglomerations, economic regions, census agricultural regions and census consolidated subdivisions are shown in the variants of SGC 2016. The first use of the standard version of SGC 2016 and its variants was in the 2016 Census.

HTML format

• Introduction
• Definitions
• SGC 2016 - Classification structure

PDF format

• SGC 2016 - Volume I, The Classification (catalogue no. 12-571-X)

CSV format

• SGC 2016 - Classification structure - CSV version (CSV, 233.75 KB)
• SGC 2016 - Elements - CSV version (CSV, 2.15 MB)

Concordances and documentation on changes

• SGC 2016 - SGC 2011
• SGC 2011 - SGC 2016
• Annual changes 2011 - 2016
• Annual revisions to 2011

Variants of the SGC 2016

Statistical Area Classification - Variant of SGC 2016

This classification variant provides standard names and codes for census metropolitan areas, census agglomerations and census metropolitan influenced zones. It shows the hierarchical relationship between these geographic areas and census subdivisions (municipalities).

Statistical Area Classification by Province and Territory - Variant of SGC 2016

This classification variant provides standard names and codes for census metropolitan areas (CMAs), census agglomerations (CAs) and census metropolitan influenced zones (MIZs) by province and territory. It shows the hierarchical relationship between these geographic areas and census subdivisions (municipalities). This classification variant also shows the hierarchical relationship between the geographical regions of Canada, provinces and territories, CMAs, CAs and MIZs.

Economic Regions - Variant of SGC 2016

This classification variant provides standard names and codes for economic regions. It shows the hierarchical relationship with their component census divisions and census subdivisions by province and territory.

Agricultural Regions - Variant of SGC 2016

This classification variant provides standard names and codes for census agricultural regions. It shows the hierarchical relationship with their component census divisions, census consolidated subdivisions and census subdivisions by province and territory.

North and South - Variant of SGC 2016

This classification variant provides a definition of the North and South of Canada. It shows the hierarchical relationship with their component census divisions (CDs) and census subdivisions (CSDs) by province and territory. This variant was originally developed for the analysis of justice statistics. It is recommended for use by other program areas at Statistics Canada should it meet their needs, but there is no requirement for it to be used outside of the Canadian Centre for Justice Statistics.

Reference Maps

Volume II consists of four maps of Canada that illustrate locations of individual census divisions, census metropolitan areas, census agglomerations, census metropolitan influenced zones and economic regions. These are referred to as the National maps. Also included are 23 maps that show the boundaries of census divisions and census subdivisions. These are referred to as the Census divisions - Census subdivisions (CD-CSD) maps.

• Information on reference maps
• Reference maps

The changes to census subdivisions (CSDs) between the 2011 edition of the SGC and the 2016 edition are provided in concordance tables. In addition to the changes of CSD name, CSD type and revision of SGC code, the concordance table SGC 2011 – SGC 2016 presents the CSDs that have been deleted (change code 4) and the CSDs that have lost land through the creation of new CSDs (change code 6) whereas the concordance table SGC 2016 – SGC 2011 presents the newly created CSDs (change code 1) and the complete annexations of CSDs by another CSD (change code 5A).

In each concordance table, there is only one entry or CSD on the left-hand side with one or many entries (CSDs) on the right-hand side. The change code allows users to exactly know what part of the left-hand side entity has changed. Change codes 2 and 2C, 3 and 3C, 23 or 7 and 7C respectively indicate a change of CSD name, CSD type, CSD name and type or revision of SGC code. Change codes 1, 4, 5A or 6 respectively indicate a newly created CSD, a CSD deleted, a complete annexation of a CSD by another CSD, or a CSD created out of another CSD.

Contrary to the SGC 2011 – SGC 2016 and SGC 2016 – SGC 2011 concordance tables, the table of annual changes from 2011 - 2016 uses two change codes to explain the annual changes to CSD codes, names and types between 2011 and 2016. The former state of the census subdivision appears on the left-hand side while its revised state is on the right-hand side. The change codes 2, 2C, 23, 3, 3C, 7 and 7C are repeated on both sides while the others are combined to show different changes. For a dissolution (code 4) on the left-hand side, there is a creation of new CSD (code 1) or a complete annexation of a CSD by another CSD (code 5A) on the right-hand side. A CSD that has lost part of its land through the creation of a new CSD has a code 6 on the left-hand side and a code 1 for the new created CSD on the right-hand side. The symbols (** and ***) attached to SGC codes on the left-hand side are included to inform users that these SGC codes are new entities created after January 1, 2011 which were updated after their creation.

The change codes used here follow the definitions presented in the Standard Geographical Classification (SGC) 2016, introduction to the classification. The exceptions are change code 6 that only shows the creation of a new CSD from a part of another CSD and change code Y, introduced here and used in concordance tables SGC 2011 – SGC 2016 and SGC 2016 – SGC 2011. Code Y shows the remaining part of the CSD from which a part has been lost or the common part of the combination that now makes up the new CSD on account of the complete annexation of a CSD.