Chapter 9
Population estimates by age, sex and marital status

9.1 Postcensal population estimates by age and sex, Canada, provinces and territories
9.2 Intercensal population estimates by age and sex, Canada, provinces and territories
9.3 Subprovincial postcensal and intercensal estimates by age and sex
9.4 Population estimates by age, sex and marital status, Canada, provinces and territories
9.5 Postcensal population estimates by legal marital status
9.6 Postcensal population estimates by marital status
9.7 Intercensal population estimates by marital status and legal marital status
9.8 Changes to the methodology

Analysis of population by age and sex is a fundamental aspect of most demographic studies. The age and sex structure of the population varies with time and place, while at the same time demographic behaviour is often a function of age and sex. For example, mortality rates are much higher in the older age groups. High migration rates are associated with young adults, as they move for personal and economic reasons. Population estimates by age and sex are widely used by other divisions of Statistics Canada. For example, these estimates are used in the calculation of employment and unemployment rates and crime rates, which tend to vary according to age and sex distributions. The addition of marital status builds the foundation for studying other demographic phenomena such as marriage and divorce rates and changes in family structure. Government and private sector planning and policies are largely driven by the age, sex and marital status profiles of certain populations.

Population estimates by age and sex are available at national, provincial/territorial, census division, census metropolitan area and economic region levels. The more detailed breakdown of these estimates by marital status is available only at the national and provincial/territorial levels. This chapter presents the methods used to produce population estimates disaggregated by age, sex and marital status.

9.1 Postcensal population estimates by age and sex, Canada, provinces and territories

9.1.1 Data sources and relevant concepts

Postcensal estimates of population by age and sex are produced using the cohort component approach. This is similar to the component method as used in the production of total population estimates, although additional data are required in its application. The data required for the cohort component method are related to demographic events (deaths, immigration, net non-permanent residents, emigration, returning emigration, net temporary emigration and interprovincial migration) that can be directly linked to persons belonging to the same birth cohort (i.e., persons having been born during the same period or year). Different components require unique treatment, according to the nature of the data used to generate the estimates, and their respective chapters elaborate upon the manner in which the estimate for each component is distributed by age and sex.

The data sources used in the production of the population estimates by age and sex are as follows1:

  • Births and deaths using vital statistics;
  • Immigration and non-permanent residents using data from Citizenship and Immigration Canada (CIC);
  • Emigration are distributed by age and sex using data from the Office of Immigration Statistics, U.S. Department of Homeland Security, and Income Statistics Division (ISD);
  • Net temporary emigration are distributed by age and sex using emigration distributions;
  • Returning emigrants are distributed by age and sex using the most recent census data on mobility data one year ago, after excluding non-permanent residents and immigrants;
  • Interprovincial migration by age and sex is derived from T1 family file by Income Statistics Division and counts from the last available census (one-year mobility variable).

9.1.2 Levels of estimates

The difference between preliminary2 and final postcensal estimates lies in the timeliness of the components. When all the components are preliminary, the estimate is described as preliminary postcensal (PP). When they are all final, the estimate is referred to as final postcensal (PD). Any other combination of levels is referred to as updated postcensal (PR).

9.1.3 Methods of estimation

Postcensal estimates of population by age and sex are produced using the cohort component approach. This approach requires a slight modification of the component approach described in Chapter 1, but the overall principles are the same.

Annual estimates

Estimates of population by age and sex are published annually with July 1st as the reference date. To calculate these estimates, birth cohorts (those persons born during the same year) for both males and females separately, are used. The cohort component approach factors in the aging of the cohorts over time. For example, persons aged 19 one year will be 20 years old the following year. The data required for the cohort component method include demographic events such as deaths, immigration, emigration, net temporary emigration, returning emigration, non-permanent residents and interprovincial migration that can be directly linked to persons belonging to the same birth and sex cohorts.

Demographers use a tool called a Lexis diagram (Figure 9.1) to aid in the linking of events to specific cohorts. Time is located on the horizontal axis (abscissa), while the vertical axis (ordinate) represents age. Specific cohorts are identified by the diagonals (lifelines) that cross the diagram. Using the cohort component approach, demographic events are organized to follow these lifelines.

Figure 9.1
Transition from a distribution of demographic events by age and period to a distribution by age and birth cohort

Description

Figure 9.1 Transition  from a distribution of demographic events by age and period to a distribution  by age and birth cohort

Take, for example, those aged 19 as of July 1, 2006, who belong to the cohort born between July 1, 1986 and June 30, 1987 (inclusive). The demographic events experienced by this cohort during the estimation period are represented by triangles "b" and "c".

The equations for estimating annual population by single years of age and sex, by the cohort component method (at the national and provincial/territorial levels) are as follows:

For each sex, by province/territory:

At age 03:

Equation 9.1:

Description

Equation 9.1

From 1 to 99 years:

Equation 9.2:

Description

Equation 9.2

For 100 years and over:

Equation 9.3:

Description

Equation 9.3

where

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

a  = age;

P(t+1)  = estimate of the population at time t+1;

Pt  = base population at time t (census adjusted for CNU4, or most recent estimate);

B  = number of births;

D  = number of deaths;

I  = number of immigrants;

E  =  number of emigrants;

ΔTE  = net temporary emigration;

RE =  number of returning emigrants;

ΔNPR  = net non-permanent residents;

ΔN  = net interprovincial migration.

Annual population estimates by single years of age and sex for persons aged 0 to 99, and 100 years and over are available from 2001 and onwards at the national, provincial and territorial level. Previously, the upper limit of the age category was age 90 and over.

9.2 Intercensal population estimates by age and sex, Canada, provinces and territories

Intercensal population estimates for reference dates between two censuses are produced following each census. They reconcile previous postcensal estimates with the new census counts. Like the total population by province/territory, intercensal population by age and sex are adjusted by distributing the error of closure uniformly across the age-sex cohorts.

9.3 Subprovincial postcensal and intercensal estimates by age and sex

Postcensal population estimates by age and sex for census divisions (CDs) and census metropolitan areas (CMAs) are produced by applying the component method to each age-sex cohort in the base population, whereby the population is aged from year to year and the components are tabulated according to age and sex cohorts. A different method called the census division (CD) aggregation method is used to produce population estimates by age and sex for economic regions (ERs). Descriptions of the methods used to estimate the populations by age and sex for CMAs, CDs and ERs are provided in Chapter 8.  At the subprovincial level, annual population estimates by age and sex are available for ages 0 to 89 and age 90 and over.

Special methods for preliminary postcensal estimates by age and sex are applied for CDs, CMAs and ERs in Quebec and British Columbia. These methods and the approach used to derive intercensal estimates by age and sex at subprovincial levels are described in Chapter 8.

9.4 Population estimates by age, sex and marital status, Canada, provinces and territories

There are two series of population estimates by marital status, the main difference between them being the treatment of persons living in "common law" unions. One of them is the series of estimates by legal marital status, i.e., a person's conjugal status under the law (for example, single, married, widowed or divorced). On the basis of this definition, people living "common law" are categorized by their legal marital status. If a person has never "married" and is living "common law", he or she is regarded as "single" under this definition.

The other is the series of estimates by marital status, i.e., a person's "de facto" conjugal status. For example, a person who reports being legally "widowed" and is living with another person as a couple but is not married to that person will be counted as "common law" in the marital status series and "widowed" in the legal marital status series.

Separate estimates for legal and "de facto" marital statuses at the national, provincial and territorial levels are available from 1991 onwards. However, estimates for the "de facto" marital status exist since 1971. Estimates of marital statuses are not produced for subprovincial levels.

9.4.1 Data sources and relevant concepts

Marital status refers to the conjugal status of a person. In demographic estimates, a distinction is made between "legal" marital status and marital status. The distinction between the two definitions lies in the concept of who is considered married. In the discussion of legal marital status, a person's marital status is determined by law. Common-law partners are not legally married to each other, thus are considered single, divorced or widowed according to their legal marital status. Separated couples are considered married under both concepts.

The following definitions represent those used by Statistics Canada for legal marital status and marital status, respectively.

Legal marital status refers to the marital status of the person under the law. Estimates are presented in the following categories: single, legally married, widowed or divorced.

Single: Persons who have never been married or persons whose marriage has been annulled and have not remarried. All persons aged less than 15 are considered as never married (single);

Legally married: Persons whose spouse is living, unless a divorce has been obtained. Persons separated are also included in this category;

Widowed: Persons who have lost their spouse through death and who have not remarried;

Divorced: Persons who have obtained a divorce and who have not remarried.

Marital status indicates the conjugal arrangement of a person. Estimates are presented in the following categories: single, married (including persons living common-law and persons who are separated), widowed or divorced. Common-law status refers to whether the person aged 15 or over is living with a person of the opposite sex or of the same sex as a couple but is not legally married to that person. It includes situations where the members of such a couple are living apart temporarily because of illness, work or school.

Single: Persons who have never been married, or persons whose marriage has been annulled and who have not remarried, and do not live common-law. All persons aged less than 15 are considered as never married (single);

Married (including persons living common-law and persons who are separated): Persons whose spouse is living, unless a divorce has been obtained;

Widowed: Persons who have lost their spouse through death and who have not remarried, and who do not live common-law;

Divorced: Persons who have obtained a divorce and who have not remarried, and who do not live common-law.

To produce population estimates by age, sex and marital status, data about events resulting in a change of marital status (for example, marriage, divorce, death of a spouse) are also required. These data are available from the vital statistics database maintained by Health Statistics Division of Statistics Canada. The database was created in collaboration with provincial and territorial ministries as well as the federal department of Justice Canada. This collaboration allows Statistics Canada to obtain data on marriage certificates registered by the provinces/territories for legal purposes as well as data related to divorces from the Central Divorce Registry5 maintained by Justice Canada.

9.5 Postcensal population estimates by legal marital status

9.5.1 Methods of estimation

Population estimates by legal marital status are produced by the cohort component method. This method takes into account events that result in a change of legal marital status. All persons under the age of 15 years are assumed to be single. For persons aged 15 years and over, estimates by single year of age are prepared for four subpopulations: single, legally married, divorced and widowed, as previously defined for legal marital status. These estimates are based on the census counts, adjusted to July 1st, as well as for census net undercoverage.

The component method formulae used to estimate the four legal marital status subpopulations are as follows:

For each sex and age (15 years and older), by province/territory6:

Single:

Equation 9.4:

Description

Equation 9.4

Legally married:

Equation 9.5:

Description

Equation 9.5

Divorced:

Equation 9.6:

Description

Equation 9.6

Widowed:

Equation 9.7:

Description

Equation 9.7

where for each province and territory:

a  = age;

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

nm  = never married;

mar  = legally married;

v  = divorced;

w  = widowed;

Pa+1t+1  = estimate of the population at age a+1 at time t+1;

Pat  = base population at time t (census adjusted for CNU, or most recent estimates) at age a;

B = number of births;

D = number of deaths;

I = number of immigrants;

E = number of emigrants;

ΔTE = net temporary emigration;

RE = number of returning emigrants;

ΔNPR = net non-permanent residents;

ΔN = net interprovincial migration;

Mar = number of marriages;

Div = number of divorces;

Veu = new widowhoods.

The components of population growth are disaggregated by legal marital status as follows:

  1. deaths by age and sex are disaggregated by legal marital status using the latest death statistics published by Health Statistics Division;
  2. interprovincial migration is disaggregated by legal marital status using the counts from the census used in calculating the base population (one-year mobility question);
  3. immigration and non-permanent residents are disaggregated by legal marital status using the estimates derived from the files of Citizenship and Immigration Canada's Field Operational Support System (FOSS);
  4. emigration and net temporary emigration is disaggregated by legal marital status using the latest available data from the Office of Immigration Statistics, U.S. Department of Homeland Security;
  5. number of returning emigrants is disaggregated by legal marital status using the population counts from the census used in the base population (one-year mobility question);
  6. marriages are disaggregated by age, sex and legal marital status using the latest marriage statistics published by Health Statistics Division. The totals are estimated beforehand by Demography Division;
  7. divorces are disaggregated by age, sex and legal marital status using the latest Justice Canada divorce statistics published by Health Statistics Division. The totals are estimated beforehand by Demography Division;
  8. the difficulty with deaths of married persons is that the age of the surviving spouse is not recorded in the Vital Statistics Registry. Consequently, the age of the new widow or widower must be determined indirectly. New widowhoods are derived from estimates of deaths of married persons and husband-wife families based on the population counts from the census used in calculating the base population.

New widowhoods

Using the age distribution of deaths to married males and females, compiled by age7 group, the surviving spouse is assigned to a five-year age group. Assignment is based on the distribution of legally married husband-wife families by age group of husband and age group of wife from the last census (see Table 9.1).

Table 9.1 Percent distribution of husband-wife families by age group of wife and age group of husband according to the legal marital status concept: Ontario, 2001 Census

The number of new widow(er)s by age group (a, a + 4), for a = 15, 20,…,85, is estimated as follows for each province/territory:

Equation 9.8:

Description

Equation 9.8

with
Equation 9.9:

Description

Equation 9.9

where

estimated number of new widow(er)s in age group (a, a + 4)= estimated number of new widow(er)s in age group (a, a + 4);

number of deaths of married persons (male or female) in age group (b, b + 4)= number of deaths of married persons (male or female) in age group (b, b + 4);

proportion of husband-wife families by five-year age group of husbands (wives) cross-classified by five-year age group of wives (husbands) (a, a + 4) = proportion of husband-wife families by five-year age group of husbands (wives) cross-classified by five-year age group of wives (husbands) (a, a + 4);

number of husband-wife families by five-year age group of husbands (wives) cross-classified by five-year age group of wives (husbands) (a, a + 4)= number of husband-wife families by five-year age group of husbands (wives) cross-classified by five-year age group of wives (husbands) (a, a + 4).

Table 9.2 provides an illustration of the above formulae. A sample calculation of the incidence of widowhood among females in the 45 to 49 year age group for the province of Ontario in 2001/2002 is presented. The percent distribution of husbands with a 45 to 49 wife is taken from column (7) in Table 9.1. This is applied to the 2001/2002 distribution of male deaths (column (1) in Table 9.2), and the results summed to estimate the number of new widows aged 45 to 49 years, as presented in column (3). To determine the number of widows in another age group, the appropriate distribution from Table 9.1 is substituted for column (2) of Table 9.2, and the same procedure is followed.

Table 9.2 Calculation of the incidence of widowhood according to the legal marital status concept: An example for females aged 45 to 49 years, Ontario, 2001/2002

These results by five-year age group are then disaggregated into single years of age using Sprague's multipliers8. This distribution of surviving spouses represents the spouse's age at the beginning of the reference period.

9.5.2 Levels of estimates

The difference between preliminary and final postcensal estimates of the population by legal marital status lies in the timeliness of the components. When all the components are preliminary, the estimate is described as preliminary postcensal (PP). When they are all final, the estimate is referred to as final postcensal (PD). Any other combination of levels is referred to as updated postcensal (PR).

9.6 Postcensal population estimates by marital status

9.6.1 Methods of estimation

Since there are no reliable sources of data on annual formations and dissolutions of common-law unions, an alternative method is used to produce postcensal estimates by marital status. The number of persons living common-law is estimated using estimates by legal marital status and proportions derived from the census adjusted for census net undercoverage. The proportion of never-married persons living common-law is obtained by dividing the number of never-married persons living common-law by the total number of never-married persons. The same procedure is used to calculate the proportion of divorced and widowed persons living common-law. The marital status proportions are generated for each age, sex, province and territory.

The derived proportions are then multiplied by the number of never-married, divorced and widowed persons respectively to produce the number of persons living common-law. The number of persons living common-law by marital status is then subtracted from the estimates by legal marital status and added to the married category to produce the population by marital status.

As for the estimates by age and sex, the base populations by marital status are adjusted to July 1st and for census net undercoverage.

Postcensal population estimates by marital status for a given age and sex can be expressed as follows:

For each province/territory, by sex:

Single:

Equation 9.10:

Married:

Equation 9.11:

Divorced:

Equation 9.12:

Widowed:

Equation 9.13:

where

Equation 9.14:

Description

Equation 9.14

Equation 9.15:

Description

Equation 9.15

Equation 9.16:

Description

Equation 9.16

where

(t+1)  = at time (t+1);

a  = age;

population of single persons according to the marital status concept= population of single persons according to the marital status concept;

population of single persons according to the legal marital status concept = population of single persons according to the legal marital status concept;

population of persons living in common-law unions, never previously married= population of persons living in common-law unions, never previously married;

population of married persons according to the marital status concept = population of married persons according to the marital status concept;

population of married persons according to the legal marital status concept= population of married persons according to the legal marital status concept;

population of persons living in common-law unions who were widowed by their previous spouse= population of persons living in common-law unions who were widowed by their previous spouse;

population of persons living in common-law unions who divorced their previous spouse = population of persons living in common-law unions who divorced their previous spouse;

population of divorced persons according to the marital status concept= population of divorced persons according to the marital status concept;

population of divorced persons according to the legal marital status concept= population of divorced persons according to the legal marital status concept;

population of widowed persons according to the marital status concept= population of widowed persons according to the marital status concept;

population of widowed persons according to the legal marital status concept= population of widowed persons according to the legal marital status concept;

censal estimate of population of single persons living in common-law unions= censal estimate of population of single persons living in common-law unions;

censal estimate of population of single persons according to legal marital status concept= censal estimate of population of single persons according to legal marital status concept;

censal estimate of population of divorced persons living in common-law unions= censal estimate of population of divorced persons living in common-law unions;

censal estimate of population of divorced persons according to the legal marital status concept= censal estimate of population of divorced persons according to the legal marital status concept;

censal estimate of population of widowed persons living in common-law unions= censal estimate of population of widowed persons living in common-law unions;

censal estimate of population of widowed persons according to the legal marital status concept= censal estimate of population of widowed persons according to the legal marital status concept.

The two series of population estimates by marital status sum to the corresponding age and sex estimates of population by province and territory.

9.6.2 Levels of estimate

The difference between preliminary and final postcensal estimates stems from the estimates by legal marital status. The same estimation method is used in both sets of estimates. As a result, the estimates by marital status have the same revision level as the estimates by legal marital status from which they are derived.

9.7 Intercensal population estimates by marital status and legal marital status

The production of intercensal estimates by age and sex is done by distributing the error of closure across age and sex cohorts. For a description on the calculation and distribution of the error of closure, see Chapter 1.

Adjusted census distributions by age, sex and marital status/legal marital status from the two most recent censuses are used to derive intercensal estimates of population by marital status/legal marital status. The census distributions are linearly interpolated to obtain the required series of distributions. The interpolated distributions are then applied to the intercensal population estimates by age and sex to obtain estimates by age, sex and marital status/legal marital status.

9.8 Changes to the methodology

The methodology presented in this chapter was used until the release of the July 1, 2007 estimates. A new method was used for the following releases.

Given the fact that marriage and divorce data are no longer available, Demography Division had to modify the estimation method to produce population estimates by marital status and legal marital status.

Since marital status patterns do not really change over a short period, Demography Division has opted for the method of census ratios. At each census, a series of ratios by age, sex, marital status and legal marital status will be produced. The ratios will remain stable for the entire postcensal period and will be applied to the annual population estimates by age and sex.

Intercensal estimates will continue to be produced according to the method presented in this chapter.


Notes:

  1. For the methodology used to produce estimates by age and sex for each component of demographic growth, refer to their respective chapters in this reporta.
  2. Unless otherwise noted, the term preliminary includes both preliminary and updated estimates.
  3. Age -1 refers to the cohort who had a demographic event at age 0 during the interval (t, t+1) but who was not born at the beginning of the interval.
  4. Unless otherwise noted, the adjustment for the census net undercoverage (CNU) also includes the incompletely enumerated Indian reserves.
  5. The Central Divorce Registry is a database containing all the information related to divorce decrees granted in Canadian courts.
  6. All parts of Equation 9.4 to Equation 9.7 refer to legal marital status.
  7. Age at the beginning of the estimation period.
  8. Sprague's multipliers are interpolation coefficients used to subdivide data.  For a detailed description of the use of Sprague's multipliers, see Shryock, Siegel et al. 1976.