Technical Guide on Demographic Estimates at Statistics Canada
Chapter 12
Estimates of census families, economic entities and households

In addition to population estimates, Statistics Canada produces annual estimates of census families, economic entities and private households for Canada, the provinces and territories. These estimates are available from 2006 onward and are used, notably, to calibrate the survey weights for many Statistics Canada social surveys.

The estimation method described in this chapter produces coherent estimates of these three analytical units. As with population estimates, these estimates can be postcensal or intercensal. Except for the territories, estimates are available by different characteristics, such as family type, gender and age group of parents, age group of children, and size of the family, economic entity or household.

Definitions and concepts

Definitions

For the purposes of these estimates, the definitions of the three analytical units are based on the 2021 Census definitions available in the Census Dictionary.^Note

A census family is defined as a couple, with or without children; or a parent in a one-parent family, living with at least one child. All members of a particular census family live in the same dwelling. Children can be biological or adopted children, regardless of age, as long as they live in the home without their own spouse or child.

The concept of economic entity includes economic families and persons living outside 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 living in the same dwelling and related by blood, marriage, common-law union, adoption or foster relationship. By definition, all persons who are members of a census family are also members of an economic family.

A household is defined as a person or group of persons who occupy the same dwelling and have no usual place of residence elsewhere in Canada or abroad. The dwelling can be a collective dwelling or a private dwelling. The household may consist of a family group (census family), of two or more families sharing a dwelling, of a group of unrelated persons or of a person living alone. Household members who are temporarily absent on reference day are considered part of their usual household. The methods presented here are for private households only.

In the estimation method presented below, the term “head” refers to the census reference persons and T1FF tax filers. The way to determine heads depends on each concept:

• Census families:
  • Couples: each spouse shares the role of head of the family and is therefore equivalent to half a head
  • One-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 for census families
  • One-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 can have more than one maintainer).

Characteristics of census families, economic entities and households

Estimates are produced for several characteristics and are estimated at the same time as the number of analytical units.^Note The following are the characteristics:

• Province or territory of residence;
• Age group of heads;
• Gender of heads;
• Type of census family (couple, one-parent family, people not in a census family);
• Size of census family (two, three, four, five, six or more members);
• Age group of children;
• Type of economic entity (couple, one-parent family, non-economic family);
• Size of economic entity (one, two, three, four, five, six or more members);
• Size of household (one, two, three, four, five, six or more members).

Final postcensal estimates

The data and methodology presented in this section are associated with the final postcensal estimates, but also apply to the preliminary and intercensal postcensal estimates, except for some specific aspects discussed in the sections on preliminary postcensal estimates and intercensal estimates.

Data sources

Four data sources are required to produce estimates for these three analytical units: tax data from the T1 Family File (T1FF),^Note census data, census net undercoverage data from coverage studies, and population estimates. Table 12.1 shows the sources, references and role of the data used to produce estimates for these analytical units.

T1FF data are derived primarily from tax returns, most of which are completed in the spring following the reference year. As a result, the annual estimates as of July 1 of year t use T1FF data of fiscal year t-1. Similarly, the calculation of census correction coefficients for year t requires the T1FF file for tax year t-1.

Methodology

Annual estimates of the number of census families, economic entities and private households are based on T1FF tax data with various adjustments. Although the T1FF does not include economic entities and private households, the number of these analytical units can be estimated using this file. The method comprises three steps: adjusting for T1FF biases; adjusting the reference date; and adjusting census coverage.

Step 1 – Adjusting for T1FF biases

T1FF tax data have three limitations in calculating estimates of census families, economic entities and private households. First, they provide coverage that, while excellent, is not complete. Second, the T1FF does not provide information on economic entities and private households. For these reasons, adjustments need to be made to the T1FF by comparing the number of heads of families in the T1FF and the census for each of the three analytical units using census correction coefficients.

These census correction coefficients are calculated for each combination of the characteristics mentioned above. The calculation of this coefficient depends on the number of heads counted in the census, as shown in Table 12.2.

where:

In Table 12.2, the level refers to the characteristics of census families. For example, in the first case, the correction coefficient is available for each combination of the eight characteristics. In the second and third cases, a correction coefficient of 0 indicates that there is no head of family in the census. The same applies to heads of economic entities and heads of households.

In the fourth case, the correction coefficient is calculated with a specific method that uses T1FF figures at a more aggregated level. This represents a very small portion of the estimates.

These census correction coefficients are calculated in each census year and are assumed to be constant for the entire postcensal period. T1FF biases are adjusted on an annual basis by multiplying the number of heads of families in the T1FF by the census correction coefficients, taking into account the level of each coefficient.

Equation 12.1:            $C{H}_i\left(X\right)=E_i\left(X\right)\times H_{CF}^{T1FF}\left(X\right)$

where

Step 2 – Adjusting the reference date

The T1FF data are collected by the end of April of the year following the fiscal year and reflect the situation as of December 31, while the population estimates have different reference dates (such as July 1). The census correction coefficients in step 1 adjust the reference date from December 31 to Census Day since they are based on the census and account for the change in the number of the three analytical units between December 31 and Census Day. Here, the correction applied to the T1FF data adjusts the Census Day reference date of the current year to July 1 of the same year. This time lag is considered using the rates calculated with the population estimates. Since census net undercoverage accounted for in the next step, the population estimates used to calculate the rates exclude net undercoverage adjustment. For an estimate on July 1, the reference date is adjusted as follows:

Equation 12.2:

$$C{H}_i^{Jul1}\left(X\right)=\frac{C{H}_i^{CD}\left(X\right)}{Unadjusted\_po{p}_{CD}^{Dem}\left(p,a,g\right)}\times Unadjusted\_Po{p}_{Jul1}^{Dem}\left(p,a,g\right)$$

where

Step 3   Adjusting census coverage

As for the population, an adjustment is needed for incomplete census coverage of census families, economic entities and private households. Coverage studies provide estimates for selected characteristics of census net undercoverage (CNU) of census families and households.

To incorporate characteristics not available in coverage studies, CNU estimates of census families and households are obtained using distributions from the most recent census.

To estimate the CNU of economic entities, the ratio of the number of heads of economic entities to the number of heads of census families is calculated for each combination of characteristics using data from the most recent census. This ratio is then applied to the CNU estimate of census families.

Final equation

By combining the three steps above, it is possible to build the final equation to produce the estimates. For an estimate as of July 1, the equation is as follows:

Equation 12.3:

$$ES{T}_i\left(X\right)=\frac{H_{CF}^{T1FF}\left(X\right)\times E_i\left(X\right)}{Unadjusted\_Po{p}_{CD}^{Dem}\left(p,a,g\right)}\times Unadjusted\_Po{p}_{Jul1}^{Dem}\left(p,a,g\right)+EST\_CN{U}_i\left(X\right)$$

where

Postcensal estimates of the number of people living in analytical units

In addition to producing estimates of the number of census families, economic entities and households, an estimate of the number of people associated with each of these analytical units can also be produced. It is produced in two parts: first, for units of one to five people, and second, for units of six or more people.

Units of one to five people

For these units, the estimate is direct:

Equation 12.4:            $IN{D}_i\left(X|Size\in \left[1,5\right]\right)=ES{T}_i\left(X|Size\in \left[1,5\right]\right)\times Siz{e}_i\left(X\right)$

where

Units of six or more people

Provincial or territorial distributions from the most recent census are used to estimate the average size of analytical units of six or more people. These distributions are then applied to the estimates for each analytical unit. The number of people in each analytical unit with six or more people is produced using the following equation:

Equation 12.5:            $IN{D}_i\left(X|Size=6+\right)=ES{T}_i\left(X|Size=6+\right)\times AverageSiz{e}_i\left(p\right)$

where

Estimated number of people

The total number of people living in each analytical unit can be calculated by adding the two results.

Equation 12.6:            $IN{D}_i\left(X\right)=IN{D}_i\left(X|Size\in \left[1,5\right]\right)+IN{D}_i\left(X|Size=6+\right)$

Preliminary postcensal estimates

For the first iteration of estimates for a reference date t, the last available T1FF is the T1FF of fiscal year t-2. Since the input needed to produce the final postcensal estimates is the T1FF of fiscal year t-1, it is necessary to produce preliminary postcensal estimates. For these estimates, the input used is the T1FF of year t-2, to which a one-year projection is applied. This projection is calculated using linear regression based on T1FF data from previous years.

Intercensal estimates

Once the postcensal cycle is completed, intercensal estimates can be calculated. The same method is used as for postcensal estimates; only the model parameters differ. The census correction coefficients, the average size for units of six or more people, and the units added to adjust for census net undercoverage are interpolated linearly, while the population estimates used are intercensal.

Limitations

Estimates of the number of census families, economic entities and households are based on integrated tax, census and survey data.

Using families from the T1FF helps to track recent trends and changes between censuses. However, coverage of the population in this file is incomplete. It should therefore be assumed that the census correction coefficients, calculated using the most recent census data, correct these limitations. It should also be assumed that the coefficients reflect the relationships between the three analytical units because they serve to shift from T1FF families to economic entities and households. The coefficients are held constant for the postcensal period in the absence of other available data.

CNU estimates for census families, economic entities and households are calculated using census coverage studies. These sample-based studies are not optimized to provide coverage estimates for these analytical units and do not have all the characteristics required. Characteristics that are not available must be obtained indirectly through the latest census.

Preliminary estimates are produced by making a short-term projection of T1FF data. This approach supposes that very recent family trends continue.