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

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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. With the exception of the territories, estimates of census families are available by family type, sex and age group of parents, family size and children's age group.

The Demography Division has restructured its program in order to estimate the census families. This is different from the components method^Note 1 used in previous years. The estimation method described in this chapter is the headship rates method. The series produced by this method goes back to 2006. However, readers can refer to the 2007 version of this report for further details on the components method.

The Demographic Estimates Program also produces estimates of economic entities and private households at the national, provincial and territorial levels by the headship rates method. Estimates for these two analytical units are used internally^Note 2 and are available on request. In this chapter, reference to the development of private households and economic entities are also presented as a 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 2011 Census^Note 3.

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 sex^Note 4. 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, adoption or a foster relationship. A couple may be of opposite or same sex.

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 census net 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.^Note 5

Table 10.1
Sources, references and role of data used to produce estimates of census families, economic entities and households

Table summary
This table displays the results of Source, reference and role of data used to produce estimates of census families, economic entities and households. The information is grouped by T1 Family File, Census, Census coverage studies and Population estimates (appearing as row headers) and Reference and role (appearing as column headers).

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 census net undercoverage

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 does 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 or 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 coefficient

Table summary
This table displays the results of situation. The information is grouped by situation (appearing as row headers) and level (appearing as column headers).

Situation	$\begin{array}{l}{\text{H}}_{\text{C}\text{F}}^{\text{T}1\text{F}\text{F}}\\ (\text{p},\text{a},\text{s},\text{f}\text{a}\text{m},\text{a}\text{'},\text{s}\text{'},\text{s}\text{f},\text{a}")\end{array}$	${\text{H}}_{\text{i}}^{\text{C}\text{e}\text{n}}(\text{X})$	${\text{E}}_{\text{i}}\left(\text{X}\right)$	Level
1	>0	>0	$\frac{{\text{H}}_{\text{i}}^{\text{C}\text{e}\text{n}}(\text{X})}{{\text{H}}_{\text{C}\text{F}}^{\text{T}1\text{F}\text{F}}(\text{p},\text{a},\text{s},\text{f}\text{a}\text{m},\text{a}\text{'},\text{s}\text{'},\text{s}\text{f},\text{a}")}$	8
2	=0	=0	0	0
3	>0	=0	0	0
4	=0	>0	See below

where

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.

In the fourth situation, the census correction coefficient is calculated using a special method involving the use of higher 'level' T1FF counts. The situation represents a very small portion of the estimates.

The correction coefficient is also used to estimate economic entities and private households from 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:       ${\text{E}}_{\text{i}}^{}\text{(X)}=\text{bias}\times \text{relationship}=\frac{{\text{H}}_{\text{i}}^{\text{Cen}}}{{\text{H}}_{\text{i}}^{\text{T1FF}}}\times \frac{{\text{H}}_{\text{i}}^{\text{T1FF}}}{{\text{H}}_{\text{CF}}^{\text{T1FF}}}=\frac{{\text{H}}_{\text{i}}^{\text{Cen}}}{{\text{H}}_{\text{CF}}^{\text{T1FF}}}$

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:      $\text{C}{\text{H}}_{\text{i}}(\text{X})={\text{E}}_{\text{i}}(\text{X})\times {\text{H}}_{\text{C}\text{F}}^{\text{T}1\text{F}\text{F}}(\text{X})$

where

Step 2 – Adjustment of the reference date

The T1FF is based on tax data, mostly collected no later than the end of April of the following year 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 adjusts the reference date from December 31 back to 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:      ${\text{CH}}_{\text{i}}^{\text{Jul1}}\text{(X)}=\frac{{\text{CH}}_{\text{i}}^{\text{CD}}(\text{X})}{{\text{Unadjust\_pop}}_{\text{CD}}^{\text{Dem}}\text{(p,a,s)}}\times {\text{Unadjust\_pop}}_{\text{Jul1}}^{\text{Dem}}\text{(p,a,s)}$

where

Step 3 – Adjustment of census coverage

Since some individuals are not counted during the census, a certain number of census families, economic entities and households is also omitted. A correction is therefore needed to take these omitted analytical units into account.

Social Survey Methods Division (SSMD) provided estimates of 2011 census net undercoverage for the households. Demography Division used these estimates to also calculate the census net undercoverage for census families and economic entities.

Two assumptions are being made in order to use this method of calculation. First assumption is that the rate of net undercoverage for census families, economic entities and households is the same. The second is that the characteristics of the 2011 census net undercoverage are the same as 2006.

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:      ${\text{EST}}_{\text{i}}\text{(X)}=\frac{{\text{H}}_{\text{CF}}^{\text{T1FF}}\text{(X)}\times {\text{E}}_{\text{i}}^{}\text{(X)}}{{\text{Unadjust\_pop}}_{\text{CD}}^{\text{Dem}}\text{(p,a,s)}}\times {\text{Unadjust\_pop}}_{\text{Jul1}}^{\text{Dem}}\text{(p,a,s)}+{\text{EST\_CNU}}_{\text{i}}\text{(X)}$

where

10.4 Characteristics of census families, economic entities and households

As seen in the previous section, estimates are produced for several characteristics and are estimated at the same time as the number of analytical units. These characteristics are:

• province or territory of residence
• 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)
• 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 or more persons.

Size of 1 to 5 persons

For these units, the estimate is direct:

Equation 10.5:      $\text{I}\text{N}{\text{D}}_{\text{i}}(\text{X}|\text{S}\text{i}\text{z}\text{e}\in [1,5])=\text{E}\text{S}{\text{T}}_{\text{i}}(\text{X}|\text{S}\text{i}\text{z}\text{e}\in [1,5])\times \text{S}\text{i}\text{z}{\text{e}}_{\text{i}}(\text{X})$

where

Size of 6 or more persons

For these units, since their actual size is suppressed in the construction of the model, we use provincial or territorial distributions from the last census to estimate the average size for analytical units of 6 or more persons, and then apply it to the estimates of each analytical unit. The number of persons in each analytical unit with size of 6 or more persons can be obtained by using the following equation:

Equation 10.6:      ${\text{IND}}_{\text{i}}\text{(X|Size}=\text{6}+\text{)}={\text{EST}}_{\text{i}}\text{(X|Size}=\text{6}+\text{)}\times {\text{AverageSize}}_{\text{i}}\text{(p)}$

where

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:      $\text{I}\text{N}{\text{D}}_{\text{i}}(\text{X})=\text{I}\text{N}{\text{D}}_{\text{i}}(\text{X}|\text{S}\text{i}\text{z}\text{e}\in \left[1,5\right])+\text{I}\text{N}{\text{D}}_{\text{i}}(\text{X}|\text{S}\text{i}\text{z}\text{e}=6+)$

10.6 Level of estimates

Postcensal estimates may be preliminary^Note 6 or final; the difference being in the level of timeliness of source files.

• Preliminary postcensal estimates:
  • Preliminary postcensal population estimates;
  • Projection of T1FF for the fiscal year corresponding to the reference year (for example, the projection of T1FF for the 2014 fiscal year for estimates at July 1, 2014);
• Final postcensal estimates:
  • Final postcensal population estimates;
  • T1FF for the fiscal year corresponding to the reference year (for example, the T1FF for the 2014 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 for postcensal estimates; only the parameters of the model are changed. The census correction coefficients, the average size 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.

Notes