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Population and Family Estimation Methods at Statistics Canada
Chapter 10
Estimates of census families, economic entities and households
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10.1 Definitions and relevant concepts
10.2 Data sources
10.3 Postcensal estimates of census families, economic entities and households
10.4 Characteristics of census families, economic entities and households
10.5 Postcensal estimates of number of persons living in analytical units
10.6 Level of estimates
10.7 Intercensal estimates of census families
10.8 Previous methods of estimating census families
In addition to population estimates, Statistics Canada produces annual estimates of census families for Canada, provinces and territories. These estimates are available from 1986 onwards. Estimates of the number of census families can be either postcensal or intercensal. Except for the territories, estimates of census families are available by family type, sex and age group of parents, family size and children's age group.
Due to a reorganization of the Demographic Estimates Program, the Demography Division has used a case-specific method to produce postcensal estimates for the 2007 to 2009 period. This is different from the components method1 that was used for the previous years and the headship rates method (using income tax files) that is implemented in 2011. The following discussion on the estimation method will focus on the headship rates method and readers can refer to the previous version of this report on details of the components method. The interim case-specific method will also be discussed in this chapter, as the changes in methods affect the consistency of the historical series of estimates.
The Demographic Estimates Program also produces estimates of economic entities and private households at the national and provincial/territorial levels by the headship rates method. Estimates for these two analytical units are used internally2 and are available on request. In this chapter, reference to the development of private households and economic entities is also presented as harmonized estimation of these three demographic indicators can be attained with the new headship rates method.
10.1 Definitions and relevant concepts
For the purpose of generating these estimates, the definitions of the three concepts are the same as those in the 2006 Census3.
A census family refers to a married couple (with or without children of either or both spouses), a couple living common-law (with or without children of either or both partners) or a lone parent of any marital status, with at least one child living in the same dwelling. A couple may be of opposite or same sex4. "Children" in a census family include grandchildren living with their grandparent(s) but with no parents present. For the estimates, married couples and couples living common-law are grouped into a single category.
An economic entity is derived from the concept of economic family. It includes economic families and persons not living in an economic family (who accordingly constitute economic entities of size 1). According to the census, an economic family is defined as a group of two or more persons who live in the same dwelling and are related to each other by blood, marriage, common-law or adoption. A couple may be of opposite or same sex. For 2006, foster children are included.
A household refers to a person or a group of persons (other than foreign residents) who occupy the same dwelling and do not have a usual place of residence elsewhere in Canada. It may consist of a family group (census family) with or without other persons, of two or more families sharing a dwelling, of a group of unrelated persons, or of one person living alone. Household members who are temporarily absent on Census Day (e.g., residing temporarily elsewhere) are considered as part of their usual household. For census purposes, every person is a member of one and only one household. Unless otherwise specified, all data in household reports are for private households only.
10.2 Data sources
Four sources of statistical data, all described previously in this document, are needed to produce estimates of these three entities: tax data from the T1 Family File (T1FF), census data, data on undercoverage from coverage studies, and population estimates. Table 10.1 shows the sources, references and role of the data used for estimating these analytical units.
Table 10.1
Sources, references and role of data used to produce estimates of census families, economic entities and households
| Source | Reference | Role |
|---|---|---|
| T1 Family File | Income Statistics Division, Statistics Canada | Creation of census correction coefficients |
| Census | Statistics Canada | Creation of census correction coefficients Distribution of size of analytical units of 6 or more persons |
| Census coverage studies | Social Survey Methods Division, Statistics Canada | Adjustment of census net undercoverage |
| Population estimates | Demography Division, Statistics Canada | Adjustment of reference date |
10.3 Postcensal estimates of census families, economic entities and households
Annual estimates of census families, economic entities and private households are based on T1FF tax data with different adjustments. Even though the T1FF data do not create economic entities and private households, it can be used to estimate these analytical units. The method can be divided into three steps: correct the biases inherent in the T1FF, adjust the reference date and adjust the census coverage.
Step 1—correction of biases inherent in the T1FF
The coverage provided by T1FF tax data, while excellent, is not complete. Also, some operational definitions in the T1FF do not directly correspond to census definitions. Therefore, it is necessary to make corrections to the T1FF by comparing the number of heads of census families in the T1FF with the number in the census for each of the three analytical units. The way of determining heads varies depending on the concept:
- Census families:
- Couples: each spouse shares the role of family head and is therefore equivalent to half a head;
- Single-parent families: the parent is the head;
- Non-family: each individual is a head.
- Economic entities:
- Couples: each spouse is equivalent to half a head, as in the case of census families;
- Single-parent families: the parent is the head;
- Non-family: each individual is a head.
- Private Households:
- The primary household maintainer is the head (a household may have more than one maintainer).
It is therefore possible to create a census correction coefficient for each combination of characteristics, namely province/territory of residence, age group, sex, type of census family, age group of spouse, sex of spouse, size of census family and age group of children. The way to calculate this coefficient depends on the situation, as Table 10.2 shows.
Table 10.2
Possible situations for calculating census correction coefficients
| Situation | HCFTIFF(p,a,s,fam,a',s',sf,a") | HiCen(X) | Ei(X) | Level |
|---|---|---|---|---|
| 1 | >0 | >0 |
|
8 |
| 2 | =0 | =0 | 0 | 0 |
| 3 | >0 | =0 | 0 | 0 |
| 4 | =0 | >0 | See below | |
where
Ei(X) = Census correction coefficient is a ratio of census heads of census families, economic entities and households by characteristics (X) to T1FF heads of census families by (p,a,s,fam,a',s',sf,a").
HT1FF = T1FF heads
HCen = census heads
X = p,a,s,fam,a',s',sf,a",efam,se,sh
p = province/territory of residence
a = age group
s = sex
fam = type of census family
a'= age group of spouse
s'= sex of spouse
sf = size of census family
sh = size of household
a" = age group of children
efam = type of economic family
se = size of economic family
i = CF, EE, or HSD
CF = census families
EE = economic entities
HSD = households
In Table 10.2, 'Level' refers to census family characteristics. For example, in the first situation, the correction coefficient is available for each combination of the eight characteristics. In the second and third situations, a correction coefficient of 0 indicates no estimates of heads in the census.
The correction coefficient in the fourth situation is used to estimate economic entities and private households with T1FF. These census correction coefficients are calculated each census year and are assumed to remain constant for the entire postcensal period. They represent both an adjustment of coverage and an adjustment of conceptual bias which is illustrated in the following decomposition:
Equation 10.1:
Each year, it will be possible to correct the biases inherent in the T1FF simply by multiplying the number of heads in the T1FF by the census correction coefficients, taking the level of each coefficient into account.
Equation 10.2:
where
CHi(X) is the corrected number of heads in the T1FF.
Step 2—adjustment of the reference date
The T1FF is based on tax data that are mostly collected no later than the end of April and often refer to the situation on December 31, whereas the demographic estimates generally have different reference dates (such as July 1). The census correction coefficient in Step 1 takes into account the growth between December 31 and Census Day. Here, the correction applied to the T1FF data set adjusts the reference date from Census Day of the current year to July 1. This time lag is factored in using headship rates, constructed with population estimates. Since census net undercoverage will be taken into account in the next step, the population estimates used for the headship rates exclude the adjustment for census net undercoverage. For an estimate at July 1, the adjustment of the reference date is as follows:
Equation 10.3:
where
CHiJul1(X) = corrected number of heads in the T1FF at July 1;
CHiCD(X) = corrected number of heads in the T1FF at Census Day;
Unadjust_popCDDem(p,a,s) = PopCDDem(p,a,s) - Pop_CNU(p,a,s);
Unadjust_popJul1Dem(p,a,s) = PopJUL1Dem(p,a,s) - Pop_CNU(p,a,s);
Pop_CNU = population obtained on the basis of census net undercoverage;
CD = Census Day of current year.
Step 3—adjustment of census coverage
Since the census omits some individuals, it is logical that this also results in the omission of census families, economic entities and private households. A correction is therefore needed to take these omitted analytical units into account.
For census families, the adjustment method involves calculating the probability of an individual being omitted in the census in one of the following strata, according to his or her age group and de facto marital status:
- adult in a couple category with no children
- adult in a couple category with children
- single parent
- child
- adult in a non-family household
- adult in a collective dwelling
These probabilities are then applied to the figures for census net undercoverage by province/territory, age, sex and marital status to obtain the number of heads of census families. Finally, census weights are adjusted to include these new census families by characteristics, province/territory, sex, age group, de facto marital status, and household size. For economic entities and private households, a ratio between census family heads and economic entities and household heads is calculated for each combination of characteristics. This ratio is then applied to the estimates of census net undercoverage of census families to obtain the estimate of census net undercoverage of economic entities and households. These estimates of census net undercoverage are held constant for the entire postcensal period.
The new methodology proposed for 2006 census net undercoverage of families was modified due to a particular issue in the 2006 Reverse Record Check (RRC). The information used to ascertain the probabilities that a missed person was in a particular family stratum, given their demographic characteristics, was not available in a timely manner to produce the estimates. For that reason, the probabilities were based on data taken from the 2001 RRC findings.
Final equation
By combining all three steps above, it becomes possible to construct the final equation for producing estimates. For an estimate at July 1, the equation is:
Equation 10.4:
where
= estimated number of census families, economic entities or households;
= estimate of census net undercoverage of census families, economic entities or households.
10.4 Characteristics of census families, economic entities and households
As seen in the previous section, estimates are produced for several characteristics. These are estimated at the same time as the number of analytical units. These characteristics are:
- province/territory of residence
- broad age group of heads
- sex of head(s)
- type of census family (couple, single-parent family, non-census family)
- size of census family (2, 3, 4, 5, 6 and more members)
- broad age group of children
- type of economic entity (couple, single-parent family, non-economic family)
- size of economic entity (2, 3, 4, 5, 6 and more members)
- size of household (2, 3, 4, 5, 6 and more members)
10.5 Postcensal estimates of number of persons living in analytical units
In addition to producing estimates of the number of census families, economic entities and households, it is also possible to produce an estimate of the number of persons associated with each of these analytical units. This estimate is produced in two parts: first, for units of which the size is 1 to 5 persons and second, for units of size 6 and more persons.
Size of 1 to 5 persons
For these units, the estimate is direct, since all that is needed is to multiply the size (Sizei(X)) by the number of units to( 
) obtain the number of persons in each analytical unit with size of 1 to 5 persons, denoted as ( 
):
Equation 10.5:
Size of 6 and more persons
For these units, since their actual size is suppressed in the construction of the model, we use provincial/territorial distributions from the last census to estimate the average size for analytical units of 6 and more persons, here denoted as (AverageSiz ei(p)), and then apply it to the estimates of each analytical unit (
). The number of persons in each analytical unit with size of 6 and more persons can be obtained by using the following equation:
Equation 10.6:
Estimated number of persons
We can obtain the total number of persons living in each analytical unit by summing the two results obtained.
Equation 10.7:
10.6 Level of estimates
Postcensal estimates may be preliminary5 or final; the difference being in the level of timeliness of source files.
- Preliminary postcensal estimates:
- Preliminary population estimates;
- T1FF for the fiscal year two years prior to the reference year (for example, the T1FF for the 2012 fiscal year for estimates at July 1, 2014);
- Final postcensal estimates:
- Final population estimates;
- T1FF for the fiscal year preceding the reference year (for example, the T1FF for the 2013 fiscal year for estimates at July 1, 2014).
10.7 Intercensal estimates of census families
Once the postcensal cycle is completed, intercensal estimates can be calculated. The method remains the same as in components method; only the parameters of the model are changed. The census correction coefficients, the average sizes for the units consisting of 6 or more persons and the units added to adjust for census net undercoverage are interpolated linearly, while the population estimates used are intercensal.
10.8 Previous methods of estimating census families
In the past, census families were estimated with the components method (for the number of census families) or by extrapolation (for characteristics), while households and economic entities were estimated by the headship rates method. Since those methods have limitations, they were replaced by the method (headship rates method using income tax files) described in this chapter.It is therefore important to note that estimates released before 2010 or with a reference date of 2005 and prior were produced using the old methods. Through the use of the headship rates method based on income tax files, same-sex couples are included in the estimation of census families.
Due to a reorganization of the Demography Estimates Program, the Demography Division has used a case-specific method to produce reliable postcensal census family estimates for the 2007 to 2009 period. The main source of information used in this method is the census (for the years 2001 and 2006) adjusted for census net undercoverage. The postcensal estimates for the total number of census families by province and territory, and for the family characteristics in the case of the provinces only, are produced using a methodology that comprises two steps: 1) in order to produce the postcensal estimates, the increase (in percent) observed between 2005 and 2006 was applied to the estimate of the number of census families for the year 2006 at 2008. This calculation was applied to the provinces and territories; 2) total number of families estimated in the previous step is distributed according to family type, sex and age of parents, family size and children's age by extrapolating changes in these distributions as observed between the two previous censuses.
Notes:
- For details on the components method, refer to Statistics Canada 2007b.
- These estimates are used in the calculation of demographic, social and economic indicators. They are used for planning, program evaluation and base population for various surveys and studies. In addition, these data are also used in calculating of weights for use in Statistics Canada surveys.
-
For more details, see the 2006 Census Dictionary
(http://www12.statcan.gc.ca/census-recensement/2006/ref/dict/index-eng.cfm). - Before the implementation of the headship rates method in 2011, same-sex couples were excluded in the estimation of census families, since it was impossible to establish trends with regard to the increase of this group by the components method.
- Unless otherwise noted, the term preliminary includes both preliminary and updated estimates.
- Date modified: