Methodology Methodology

View the most recent version.

Start of text box

End of text box

This document describes the concepts, data the sources and the methodology used to produce the population estimates. Population estimates are produced to measure the population counts according to various characteristics and geographies between two censuses. The demographic estimates are the official population estimates at the national, provincial, territorial and subprovincial levels.

Postcensal estimates are based on the 2011 Census.

Population Estimates

Types of estimates

Population estimates can either be intercensal or postcensal. Intercensal estimates are produced using counts from two consecutive censuses adjusted for census net undercoverage (CNU)^Note 1 (including adjustment for incompletely enumerated Indian reserves (IEIR)) and postcensal estimates. The production of intercensal estimates consists of updating the postcensal estimates using the counts from a new census adjusted for CNU^Note 1.

Postcensal estimates are produced using data from the most recent census adjusted for CNU^Note 1 and the components of population growth. In terms of timeliness, postcensal estimates are more up-to-date than data from the most recent census adjusted for CNU^Note 1, but as they get farther from the date of that census, they become less reliable.

Levels of estimates

Updating population estimates between censuses requires the use of data from administrative files or surveys. The quality of population estimates therefore depends on the availability of a number of administrative data files that are provided to Statistics Canada by Canadian and foreign government departments. Since some components are not available until several months after the reference date, three kinds of postcensal estimates are produced: preliminary postcensal (PP), updated postcensal (PR) and final postcensal (PD). The time lag between the reference date and the release date is three months for preliminary estimates and two to three years for final estimates. Though it requires more vigilance on the part of users, the production of three successive series of postcensal estimates is the strategy that best satisfies the need for both timeliness and accuracy of the estimates.

Calculation of postcensal population estimates

Population estimates – preliminary, updated and final – are produced using the component method. This method consists in taking the population figures from the most recent census, adjusted for CNU^Note 1 (undercoverage minus overcoverage), and adding or subtracting the number of births, deaths, and components of international and internal migration.

A. Subprovincial estimates

Population estimates for census metropolitan areas and census divisions

The component method is used to produce estimates for census metropolitan areas (CMAs) and census divisions (CDs) by age and sex. The method is applied to each age-sex cohort in the base population.

The component method formulas for estimating the population of CMAs and CDs by age and sex are as follows:

For age 0:

For ages 1 to 89:

For age group 90 and over:

where, for each subprovincial region

$(t,t+1)$ = interval between times t and t+1

$P_{(t+1)}$ = population estimates at time t+1

$P_t$ = base population at time t (census counts adjusted for net census undercoverage or the most recent estimate)

$\text{B}$ = number of births

$\text{D}$ = number of deaths

$\text{I}$ = number of immigrants

$\text{E}$ = number of emigrants

$\Delta \text{TE}$ = net temporary emigration

$\text{RE}$ = number of returning emigrants

$\text{NPR}$ = number of non-permanent residents

$\Delta \text{Ninter}$ = net interprovincial migration

$\Delta \text{Ninfra}$ = net intraprovincial migration

$Resid$ = residual deviation (for intercensal estimates).

To ensure concordance between the subprovincial estimates and the provincial and territorial estimates by age and sex, two-way raking is used.

Population estimates for economic regions

A different method is used to produce population estimates for economic regions (ERs). In this case the census division's (CD) aggregate method is used. First, the ERs are defined in terms of CDs using the most recent Standard Geographical Classification (SGC) specifications. When the geographic delineation of the CDs and ERs are the same, no adjustment is required; the population estimates for the CDs that make up the ER are simply added together.

However, when the geographic delineation of the CD does not match that of the ER, i.e., when a CD is in more than one ER, distribution of the CD's demographic components are allocated on the basis of its demographic weight in each ER in question. The proportions are referred to as conversion factors. They are calculated using the most recent census counts.

Thus, demographic components (births, deaths and migration) initially measured at the CD level can be allocated to each ER. Using the census division's aggregate method by the ERs' geographic delineation, the population and demographic components of ERs can be estimated.

However, the census division's aggregate method cannot be used to estimate the number of intraprovincial in-migrants and out-migrants, since it overestimates those figures. In-migrants to a given CD from another CD in the same ER should not be counted since the migration occurred within the ER's boundaries. These are false in-migrants. The same is true for out-migrants from one CD to another CD in the same ER: they are false out-migrants. However, the net intraprovincial migration calculated with the CD aggregate method is correct because the false in-migrants and out-migrants cancel each other out. As a result, only the net intraprovincial migration of ERs can be estimated accurately using the CD aggregate method. This is why the estimates for intraprovincial in-migrants and out-migrants are not available at the ER level.

Special treatment for preliminary postcensal estimates for Quebec and British Columbia

A different method is used to calculate preliminary postcensal population estimates for census divisions (CDs) and census metropolitan areas (CMAs) in Quebec. The total population estimates produced by the Institut de la statistique du Québec (ISQ) are used. These population estimates are based on data from the Fichier d'inscription des personnes assurées (FIPA), the insured persons register, from the Régie de l'assurance-maladie du Québec (RAMQ).

For British Columbia, preliminary postcensal estimates at the CMA and CD levels are calculated by applying the total population growth rates provided by BC Stats, British Columbia's statistical agency, to the previous year's estimates produced by the Demography Division. The total preliminary postcensal estimates are then distributed by age and sex using the Demography Division's component method. The British Columbia population estimates used to calculate the rates are produced using a regression model based on data from residential Hydro services and Ministry of Health Client Registry data as symptomatic indicators.

To ensure concordance between the subprovincial estimates and the provincial totals by age and sex, two-way raking is used.

B. Levels of estimates

For subprovincial regions in Quebec and British Columbia, the specific methods described in the previous section are used only for preliminary postcensal estimates. For updated and final postcensal estimates, the component method is used.

For the subprovincial regions in other provinces and territories, the difference between preliminary and final postcensal population estimates lies in the timeliness of the components. When all the components are preliminary, the population estimate is deemed preliminary postcensal (PP). When all the components are final, the population estimate is deemed final postcensal (PD). Any other combination of levels is considered updated postcensal (PR).

C. Base population and components of population growth

Base population

The base populations are derived from the quinquennial censuses between 2001 and 2011. The population universe of the 2011 Census includes the following groups:

• Canadian citizens (by birth or by naturalization) and immigrants with a usual place of residence in Canada;
• Canadian citizens (by birth or by naturalization) and immigrants who are abroad, either on a military base or attached to a diplomatic mission;
• Canadian citizens (by birth or by naturalization) and immigrants at sea or in port aboard merchant vessels under Canadian registry or Canadian government vessels;
• Non-permanent residents:
  • persons with a usual place of residence in Canada who are claiming refugee status and the family members living with them;
  • persons with a usual place of residence in Canada who hold study permits and the family members living with them;
  • persons with a usual place of residence in Canada who hold work permits and the family members living with them.

The population universe of the 2011 Census does not include foreign residents but, since 1991, non-permanent residents are included in the population universe.

Foreign residents have not been enumerated since the 1991 Census. Foreign residents are persons who belong to the following groups:

• government representatives of another country attached to the embassy, high commission or other diplomatic body of that country in Canada, and members of their families living with them;
• members of the Armed Forces of another country who are stationed in Canada, and family members living with them;
• residents of another country visiting Canada temporarily (for example, a foreign visitor on vacation or on business, with or without a visitor’s permit).

These base populations are adjusted as follows:

• adjustment of the population for census net undercoverage (CNU);
• addition of independent estimates for incompletely enumerated Indian reserves;
• at the provincial level, the first postcensal population estimate is July 1 of the census year. This is obtained by addition or subtraction of the components of growth between Census Day and June 30. At the subprovincial level, the estimate of the July 1 population estimate is obtained by applying to the annual components of growth, a fraction of the year that corresponds to the period between Census Day and June 30. These are adjusted to the appropriate provincial and territorial components.

Adjustment for census net undercoverage (CNU)

The adjustment for CNU is important. The CNU is the difference between the number of persons who should have been enumerated but were missed (undercoverage) and the number of persons who were enumerated but should not have been or who were counted more than once (overcoverage).

To estimate census net undercoverage (CNU) at the subprovincial level, provincial and territorial CNU rates by age and sex are applied to census subdivisions (CSDs), which are aggregated to create the base population of higher subprovincial levels (census metropolitan areas (CMAs) and census divisions (CDs) in the province).

D. Births and deaths

The numbers of births and deaths at the census division (CD) and for the census metropolitan areas (CMAs) levels are derived directly from the vital statistics database of Statistics Canada’s Health Statistics Division. Although Statistics Canada manages the National system of vital statistics, the central vital statistics registries of the provinces and territories are responsible for collecting and processing the information from those administrative files. Under provincial / territorial vital statistics statutes (or similar legislation), all live births and all deaths must be registered, and all provinces and territories provide the information to Statistics Canada.

The vital statistics universe closely parallels the census universe. Both universes include births and deaths of all Canadians, immigrants and non-permanent residents (NPR) and exclude foreign residents.

Vital statistics by province or territory of residence are used to produce our final estimates of births and deaths.

When there are no vital statistics, the number of births is estimated using fertility rates by mother’s age. The number of deaths is estimated using mortality rates by age and sex. These methods are used to calculate preliminary estimates at the provincial and territorial levels.

Levels of estimates

Births and deaths estimates are categorized as final when they are directly taken form the Health Statistics Division’s vital statistics. They are then adjusted to the provincial and territorial totals using two-way raking to ensure their concordance.

When no births or deaths data are available, preliminary provincial or territorial estimates are broken down, using the most recent known subprovincial distribution derived from Health Statistics Division's vital statistics, to produce estimates by region. In that case, the births and deaths estimates are categorized as preliminary. They are then adjusted to the provincial and territorial totals using two-way raking to ensure their consistency.

Special treatment for preliminary postcensal estimates for Quebec and British Columbia

A special case is relevant to the provincial totals on which subprovincial estimates are prorated. Quebec and British Columbia provide their most recent estimates of births and deaths at the provincial level. These estimates are used for the preliminary estimates. However, the final estimates of births and deaths for these provinces are derived directly from the vital statistics database of Statistics Canada’s Health Statistics Division.

E. Immigration

Like the numbers of births and deaths, Canadian immigration statistics must be kept by law. In Canada, immigration is regulated by the Immigration and Refugee Protection Act (IRPA) of 2002. This statute superseded the Immigration Act, which was passed in 1976 and amended more than 30 times in the years thereafter. Immigration Refugees Citizenship Canada (IRCC) collects and processes administrative files of immigrants. IRCC then provides Statistics Canada with information from Field Operational Support System (FOSS) files. The information is used to estimate at provincial and territorial level the number and characteristics of people granted permanent resident status by the federal government on a given date. For Demography Division, the terms immigrant and permanent resident are equivalent.

An immigrant is a person who is not a Canadian citizen by birth, but has been granted the right to live in Canada permanently by Canadian immigration authorities. The number of immigrants does not include persons born abroad to Canadian parents who are only temporarily outside the country.

Immigrants are usually counted on or after the date on which they are granted permanent resident status or the right to live in Canada.

Since we do not use subprovincial immigration data from Immigration Refugees Citizenship Canada (IRCC), the most recent known subprovincial distribution derived from the T1FF is used to produce immigrant estimates by subprovincial region. Because the data are available only by broad age groups (0-17, 18-24, 25-44, 45-64, 65+), they are broken down by age and sex based on the distribution from the most recent census or NHS (starting in 2011). The distribution stems from the NHS mobility question on place of residence one year ago. Since 2011/2012, NHS distributions have been modelled to minimize the impact of outliers found in some subprovincial regions, mostly for smaller geographies. To ensure their consistency, subprovincial estimates are then adjusted to the provincial and territorial totals using two-way raking.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the sources used to estimate this component. Since the subprovincial estimates of immigrants are adjusted to provincial and territorial estimates, the level of subprovincial estimates will be the same. Immigration estimates are preliminary the first year and final the following year.

F. Net non-permanent residents

Like the numbers of births and deaths, Canadian immigration statistics must be kept by law. In Canada, the non-permanent residents (NPR) are regulated by the Immigration and Refugee Protection Act (IRPA) of 2002. This statute superseded the Immigration Act, which was passed in 1976 and amended more than 30 times in the years thereafter. Immigration Refugees Citizenship Canada (IRCC) collects and processes the administrative files of NPRs in Canada. It then provides Statistics Canada with information from Field Operational Support System (FOSS) files. The information is used to estimate the number and characteristics of people granted NPR status by the federal government.

NPRs are persons who are lawfully in Canada on a temporary basis under the authority of a temporary resident permit, along with members of their family living with them. Non-permanent residents include foreign workers, foreign students, the humanitarian population and other temporary residents. The humanitarian population includes refugee claimants and temporary residents who are allowed to remain in Canada on humanitarian grounds and are not categorized as either foreign workers or foreign students. For Demography Division, the terms non-permanent resident and temporary resident are equivalent.

NPR estimates are based on the number of NPRs, not on the net. At the provincial and territorial levels, the number of people in IRCC’s administrative system is estimated for specific dates in each period of observation. First, the end-of-period number of NPR is estimated, and then the start-of-period number of NPR is subtracted from that estimate. That yields the net number of NPRs.

Anyone who received non-permanent resident status prior to the observation date is counted. For the refugee claimants we use the date of their demand. Permit holders and refugee claimants can be excluded for different reasons and those criteria are different for each category. Permit holders and refugee claimants are excluded from the population if their permit has expired, if they receive permanent resident status, or if they are deported. In addition, refugee claimants are excluded if their file has been inactive for two years.

At the subprovincial level, there are no reliable administrative data available to directly estimate net number of NPRs. To compensate for this lack of data, the provincial and territorial NPR estimates by age and sex are broken down by subprovincial region based on the distribution from the most recent census or NHS (starting in 2011). Since 2011/2012, NHS distributions have been modelled to minimize the impact of outliers found in some subprovincial regions, mostly for smaller geographies. To ensure their consistency, subprovincial estimates are then adjusted to the provincial and territorial totals using two-way raking.

For the 2005/2006 and 2010/2011 years, the net NPRs are calculated using two different distributions —the 2001 and 2006 censuses for the year 2005/2006, and the 2006 Census as well as the 2011 NHS for the year 2010/2011. This approach assumes that the two distributions are similar. If the two distributions vary by the regional breakdown of NPRs, the net NPRs for 2005/2006 and 2010/2011 will absorb all the changes attributable to the difference between the two distributions that were used. For this reason, the net NPRs for 2005/2006 and 2010/2011 should not be compared with the rest of the historical series.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the source used to estimate this component. Since the subprovincial estimates of the net number of NPRs are adjusted to provincial and territorial estimates, the level of the subprovincial estimates will be the same. NPR estimates are preliminary the first year and updated the following year. They become final two to three years after the reference year, when all other components are also final.

G. Emigration

The number of emigrants at provincial or territorial level is estimated using data from the Office of Immigration Statistics, U.S. Department of Homeland Security data collected by the Canada Child Tax Benefit (CCTB) program, and data from the T1 Family File (T1FF). The first source is used to estimate emigration to the United States. CCTB data are used to estimate emigration to other countries. The estimates of the number of child emigrants have to be adjusted because the CCTB is not universal and does not provide direct information on the number of adult emigrants. As a result, four adjustment factors are used to take into account:

• the incomplete coverage due to a delay in the receipt and processing of the files of children eligible for the CCTB. Since it takes four years after the reference period for CCTB administrative files to become complete, the adjustment is made if the estimates are finalized after two years. The factor is derived from the two-year ratios of emigrant children based on two versions of the CCTB files;
• the program’s partial coverage, that is, people who do not apply for the CCTB or are not eligible. This factor is obtained by comparing the estimated number of children in the population with the number of children in CCTB files;
• the differential propensity to emigrate between children who are eligible for the CCTB and children who are not. This factor is obtained by comparing the emigration rates of CCTB-eligible children with the rates for all children (aged 0-17). This factor is calculated for each province and territory and is based on the last three available years of T1FF;
• the differential propensity to emigrate between adults and children. This factor generates the emigration rate for the population aged 18 and over. It is obtained by (1) calculating the average ratio over three years of the adult and child emigration rates based on T1FF data, (2) calculating the average ratio over three years of the adult and child emigration rates based on data from the Office of Immigration Statistics, U.S. Department of Homeland Security, and (3) taking the average of the two rates. This factor is calculated for Canada only.

The adult emigration rate is applied to the adult population. Adult emigration is distributed by province and territory using data from the T1FF file. We calculate a ratio of the number of emigrant adults to the number of emigrant children from the T1FF file. We then apply this ratio to the number of emigrant children from the CCTB by province, which yields the number of adult emigrants whose provincial distribution will differ from that of the children.

The number of adult emigrants combined with the number of child emigrants (once adjusted for the coverage and differential emigration factors) generate the number of emigrants for the entire population.

Emigration is disaggregated by province and territory based on the number of child emigrants adjusted for coverage and differential emigration.

As with immigrants, the number of emigrants at the subprovincial level is derived from the T1FF. Because the estimates are available only by broad age groups (0-17, 18-24, 25-44, 45-64, 65+), they are broken down by age and sex based on the provincial or territorial distribution. They are then adjusted to the provincial and territorial totals using two-way raking to ensure their consistency.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the sources used to estimate this component. Since the subprovincial estimates of emigrants are adjusted to provincial and territorial estimates, the level of the subprovincial estimates will be the same.

H. Net temporary emigration

Some people leave Canada to live temporarily in another country; others who were temporarily outside Canada return. The net result of those departures and returns is the component known as “net temporary emigration”. Estimates of the number of departures are derived from the Reverse Record Check (RRC), the most important census coverage study. The RRC provides an estimate of the number of people who left Canada temporarily during an intercensal period and are still out of the country at the end of the period. Estimates of the number of returns are based on two sources: the Census and Demography Division’s estimates of returning emigrants. The census provides the number of people who were outside Canada at the time of the previous census and returned during the intercensal period. That number includes all returning emigrants. Then Demography Division’s estimate of the returning emigrants’ component is subtracted to produce the number of returning temporary emigrants. The estimated numbers of departures (RRC) and returns (Census and Demography Division) yield an estimate of net temporary emigration.

This estimate is for the whole intercensal period; it is disaggregated into estimates for each of the five years in the period and then into monthly estimates using a seasonal adjustment that is an average between zero seasonality and the seasonality of emigration.

Net temporary emigration is calculated first for the national level. It is then disaggregated by province or by groups of provinces based on the RRC estimates of temporary emigration. For the Atlantic provinces and the territories, the estimate for the group is disaggregated on the basis of each province / territory’s proportion of the group’s total population.

Net temporary emigration can be estimated only for the intercensal period preceding the most recent census. Net temporary emigration in the current period is assumed to be the same as in the previous period for each province and territory.

At the subprovincial level, provincial and territorial net temporary emigration estimates by age and sex are broken down based on the subprovincial distribution of emigrants. They are then adjusted to the provincial and territorial totals using two-way raking to ensure their consistency.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the net temporary emigration estimates.

I. Returning emigrants

A returning emigrant is a person who returns to Canada after having been classified as an emigrant. In a manner similar to the procedure used to calculate the number of emigrants, data from the Canada Child Tax Benefit (CCTB) file of Canada Revenue Agency (CRA) and from the T1FF are used to estimate the number of returning emigrants at provincial or territorial level. Adjustment factors are applied to compensate for the fact that the CCTB program is not universal, and an adult/child ratio is used to estimate the number of adult returning emigrants. As a result, four adjustment factors are used to take into account:

• the incomplete coverage due to a delay in the receipt and processing of the files of children eligible for the CCTB. Since it seems to take four years after the reference period for CCTB administrative files to become complete, the adjustment is made if the estimates are finalized after two years. The factor is derived from the two-year ratios of returning emigrant children based on two versions of the CCTB files;
• the program’s partial coverage, that is, people who do not apply for the CCTB or who are not eligible. This factor is obtained by comparing the estimated number of children in the population with the number of children in CCTB files;
• the differential propensity to emigrate between children who are eligible for the CCTB and children who are not. This factor is obtained by comparing the emigration rates of CCTB-eligible children with the rates for all children (aged 0 to 17). This factor is calculated for each province and territory and is based on the last three available years of T1FFs;
• the adult/child ratio, which is based on the census by age and sex.

As with immigrants and emigrants, the number of returning emigrants at the subprovincial level is derived from the T1FF. Because the estimates are available only by broad age groups (0-17, 18-24, 25-44, 45-64, 65+), they are broken down by age and sex based on the provincial or territorial distribution. They are then adjusted to the provincial and territorial totals using two-way raking to ensure their consistency.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the sources used to estimate this component. Since the subprovincial estimates of returning emigrants are adjusted to provincial and territorial estimates, the level of the subprovincial estimates will be the same.

J. Interprovincial migration

Interprovincial migration represents movement between provinces or territories involving a change in the usual place of residence. As with emigration, there is no provision for recording interprovincial migration in Canada. Interprovincial migration by broad age groups and sex for subprovincial regions is derived from the T1FF for each subprovincial region. The estimates by broad age groups and sex are broken down by age based on distributions stemming from the most recent census or NHS (starting in 2011) mobility question on place of residence one year ago. Since 2011/2012, NHS distributions have been modelled to minimize the impact of outliers found in some subprovincial regions, mostly for smaller geographies. Subprovincial estimates are then adjusted to the provincial and territorial totals using two-way raking to ensure their consistency.

Data from the T1FF are used to produce the final estimates.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the sources used to estimate this component. Since the subprovincial estimates of interprovincial migrants are adjusted to provincial and territorial estimates, the level of the subprovincial estimates will be the same.

K. Intraprovincial migration

As with interprovincial migration, the components of intraprovincial migration by broad age groups and sex are derived from the T1FF for each subprovincial region. The estimates by broad age groups and sex are broken down by age based on distributions stemming from the most recent census or NHS (starting in 2011) mobility question on place of residence one year ago. Since 2011/2012, NHS distributions have been modelled to minimize the impact of outliers found in some subprovincial regions, mostly for smaller geographies.

These sources are used for both preliminary and final estimates.

Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the T1FF data used to estimate this component.

Since there are no reliable data sources for preliminary intraprovincial migration estimates, the data for the most recent year, for which final estimates are available, are used. The assumption that intraprovincial migratory behaviours for the current year are similar to those for the previous year for which final estimates are available is adopted.

L. Intercensal population estimates

Intercensal estimates – population estimates for reference dates between two censuses – are produced following each census. They reconcile previous postcensal estimates with the new census counts.

There are three main steps in the production of intercensal estimates:

• the correspondence of the geographic boundaries between the two censuses
• calculation of the error of closure
• linear distribution of the error of closure (residual deviation).

To ensure geographical concordance, the base populations and components of population growth must be adjusted according to geographical boundaries at the time of the most recent census. For areas whose geographical boundaries changed between the two censuses (as measured by the SGC), historical conversion factors are used based on population transfers at the census subdivision level during the most recent intercensal period. In general, corrections to CDs, CMAs and ERs are minor (see the “Quality of demographic data” section).

Error of closure is defined as the difference between the postcensal population estimates on census day and the population enumerated in that census adjusted for census net undercoverage (CNU^Note 1). The error of closure is spread evenly over the intercensal period, based on the number of days in each month. Intercensal estimates by age and sex are adjusted the same way (i.e., by distributing the error of closure evenly across the age and sex cohorts). As with postcensal estimates, the intercensal subprovincial estimates by age and sex are adjusted to provincial and territorial estimates using two-way raking to ensure their consistency.

• Previous
• Next