Technical Guide on Demographic Estimates at Statistics Canada
Chapter 8
Emigrants

Although Canada is generally perceived as a country of immigration, every year, several thousand Canadians emigrate from Canada to settle in the rest of the world. Although emigration as a demographic phenomenon is not as numerically significant when compared with immigration, the cumulative number of emigrants over time suggests that several million Canadians could be living abroad.^Note This chapter describes the methods used to estimate the number of emigrants.

Definitions and concepts

Emigrants are Canadian citizens or immigrants (permanent residents) who have left Canada to establish a long-term or short-term residence in another country involving a change in their usual place of residence.

Emigration is divided into long-term and short-term emigration for the purpose of calculating the number of emigrants. According to the United Nations, short-term migration refers to a change in the usual place of residence of 3 to 12 months, while long-term migration implies a duration of at least one year.^Note

However, in the absence of data enabling a direct measurement of entries into and exits from Canada, Statistics Canada’s Demographic Estimates Program (DEP) distinguishes between these two categories based on the intention behind the length of the stay. For example, people moving to the United States may be considered long-term emigrants if they acquire permanent resident status in that country, but short-term emigrants if they hold a visa.

The total number of emigrants is calculated by adding long-term emigrants and short-term emigrants. Only estimates of the number of emigrants are published.

It is important to note that a non-permanent resident (NPR) who leaves Canada is not considered an emigrant; their departure from the country is measured in the NPR component.

Long-term emigrants

Final estimates

Data sources

Unlike immigration, there is no legal obligation in Canada to maintain records for individuals leaving the country, either on a long-term or a short-term basis. Therefore, estimates of the number of emigrants must be derived through secondary sources.

The number of long-term emigrants is estimated from three administrative sources: immigration data from the Office of Homeland Security Statistics of the U.S. Department of Homeland Security for emigrants to the United States, and data from the Canada child benefit (CCB) and the T1 Family File (T1FF) for emigrants to other countries.

Immigration data from the Office of Homeland Security Statistics provide information on Canadians who have acquired permanent resident status in the United States. These data are used to estimate the number of emigrants settling in that country.

For other destination countries, estimates are based primarily on the CCB, a tax-free monthly payment made to eligible families with children under 18. These data, provided annually by the Canada Revenue Agency (CRA), are used to identify child emigrants, broken down by province and territory.

Estimates are also based on the T1FF, an annual tax file produced by Statistics Canada. The T1FF contains demographic and income data at subprovincial and subterritorial levels. This file is constructed from various administrative sources, such as T1 and T4 forms, as well as CCB data provided by the CRA.

However, unlike the U.S. data, the CCB and T1FF data do not confirm whether an individual has acquired long-term residency rights in another country. It is therefore assumed that an individual who has cut ties with Canada, according to the CRA data, has established long-term residence in another country.

Method

Figure 8.1 shows a diagram illustrating the method used to estimate the number of long-term emigrants. The estimate is made in two parts, according to the emigrants’ destination country: the United States or other countries of the world.

Figure 8.1 start

Description for Figure 8.1

Figure 8.1 is a diagram illustrating the method for estimating the number of long-term emigrants. The method is divided into two parts: emigrants to countries other than the United States, and emigrants to the United States. The data used include the T1 Family File, the Canada child benefit and population estimates (Demographic Estimates Program) for emigrants to countries other than the United States, and Department of Homeland Security data for those emigrating to the United States. Adjustments are made to estimate the number of children emigrating to countries other than the United States to account for bias, partial completeness and incomplete coverage of data. An adult–child ratio is then applied to estimate the number of adult emigrants to countries other than the United States. Emigrants to the United States are taken directly from Department of Homeland Security figures. The total number of long-term emigrants is calculated by adding data for adults and children.

Figure 8.1 end

Estimates of the number of child emigrants must be adjusted because the CCB program is not universal and covers children only. Four adjustment factors are used to account for

1. the partial coverage of the program, that is, individuals who do not apply for the CCB or who are not eligible;^Note
2. the differential propensity to emigrate between all children and those who are eligible for the CCB;
3. the incomplete CCB coverage caused by delays in receiving and processing the files of eligible children;
4. the differential propensity to emigrate between adults and children.

CCB and T1FF data are used to calculate these adjustment factors.

The number of emigrants to the United States is taken directly from immigration data provided by the Office of Homeland Security Statistics of the U.S. Department of Homeland Security.

Finally, the total number of long-term emigrants is calculated by adding the estimates for adults and children for both destinations.

Because of the logic behind the calculation methods, the methods for estimating the number of emigrants to countries other than the United States are presented first.

Long-term child emigrants

Children emigrating to countries other than the United States

The CCB file provides the numbers of dependent children (under 18 years of age) whose parents are eligible for the program, according to the CRA definition. As mentioned, the CCB program is not universal, consequently, the data are incomplete in terms of estimating all child emigrants, hence the need for adjustments.

The first correction factor considers the partial coverage of the file resulting from the non-universality of the CCB program. The correction factor is calculated and applied to the population registered for the CCB program. The factor is the ratio of the number of children registered in the program to the number of children in the overall population estimated by the DEP for each month and each province and territory.

The second correction factor is applied to the CCB data to account for the differential propensity for emigration between children registered for the CCB program and all children. This factor is obtained on an annual basis by calculating a ratio of the emigration rate for all children (aged 0 to 17) to the rate for CCB-eligible children. This factor is calculated for each province and territory and is based on the last three available years of the T1FF. It is calculated simultaneously for all Atlantic provinces to mitigate the effect of variations attributable to the small numbers of emigrants observed for these provinces. The Canadian factor is applied to the territories for the same reason.

The third correction factor considers the partial completeness of the emigration information derived from the CCB data files because of delays in recording it. By comparing files produced two, three and four years after the reference period, it appears that the CCB files become complete enough to be used two years after the year of emigration, and that they can be considered fully complete around four years after the reference period. Since CCB data are used within this four-year timeframe, a correction factor is applied to account for this situation. The same factor is applied to the monthly data of each province and territory.

The formula to estimate child emigrants is as follows for each province and territory:

Equation 8.1:           ${}_{j}E{M}^{0-17}={}_j{}^{CCB}E{M}^{0-17}\times \frac{1}{{}_j{}^{CCB}\Re }\times {}_{j}G\times D$

where

The factors used in Equation 8.1 are detailed in equations 8.2 to 8.4c.

First, the factor for incomplete coverage of children by the CCB program is calculated monthly as follows for each province and territory:

Equation 8.2:           ${}_j{}^{CCB}\Re =\left[\frac{{}_j{}^{CCB}P{}^{0-17}}{{}_j{}^{DEP}P{}^{0-17}}\right]$

where

Secondly, the differential propensity to emigrate of CCB-registered children and non-CCB children is obtained by dividing the emigration rates for all children by the corresponding emigration rates for children registered for the CCB program, as follows for each province and territory:^Note

Equation 8.3:           ${}_{j}G=\frac{{}_{{}_j}{}^{T1FF}RateE{M}^{0-17}}{{}_{{}_j}{}^{CCB\_T1FF}RateE{M}^{0-17}}=\frac{\left[\frac{{}_j{}^{T1FF}E{M}^{0-17}}{{}_j{}^{T1FF}P{}^{0-17}}\right]}{\left[\frac{{}_j{}^{CCB\_T1FF}E{M}^{0-17}}{{}_j{}^{CCB\_T1FF}P{}^{0-17}}\right]}$

where

A three-year average of ${}_{j}G$ factors, based on the latest available factors, is used to mitigate the potential effects of annual factor variations.

Thirdly, completeness factors are used to compensate for the incompleteness of the CCB data file attributable to delays in registering child emigration. These factors are calculated by comparing different versions of the CCB files available over several years.

Table 8.1 illustrates the calculation of the completeness factors using fictitious figures. In this table, the production year is 2021. Therefore, the t‑3, t-2 emigration year in the first column corresponds to 2018/2019 and the t‑4, t‑3 emigration year corresponds to 2017/2018, and so on. The next three columns of the table show the numbers of child emigrants by period between the emigration year and the year of the file used. In this fictitious example, the number of child emigrants for the emigration year t-4, t-3 from the file available two years after the emigration year is 7,900; it is 8,500 from the file available three years after the emigration year (period of three years between the emigration year and the data file year). The objective of the completeness factor is to estimate what the numbers would be for the emigration years t-4, t-3, and t-3, t-2 four years after the emigration year.

First, completeness factors are calculated for the previous emigration years. The completeness factors ($D$) in the right-hand columns are derived from the numbers on the left. $D_{(2,3)}$ is the ratio of Duration 3 to Duration 2, while $D_{(3,4)}$ is the ratio of Duration 4 to Duration 3. For example, $D_{(3,4)}$ of 1.045 for the emigration year t-5, t-4 comes from the ratio of 8,200 to 7,850. This factor could be used to project one year ahead from Duration 3 to Duration 4. To project two years ahead from Duration 2 to Duration 4, the factor $D_{(2,4)}$ (the last column in the table) is calculated by multiplying the two most recent factors, $D_{(2,3)}$  and $D_{(3,4)}$ .

The formulas are as follows:

Equation 8.4a:           $D_{(2,3)}=\frac{{}^{CCB}E{M}_{(t-4,t-3)}^t}{{}^{CCB}E{M}_{(t-4,t-3)}^{(t-1)}}$

Equation 8.4b:           $D_{(3,4)}=\frac{{}^{CCB}E{M}_{(t-5,t-4)}^t}{{}^{CCB}E{M}_{(t-5,t-4)}^{(t-1)}}$

where

To project numbers for an emigration year that is three years earlier than the production year, the completeness factor for recording data on emigration from Duration 3 to Duration 4 (i.e., $D_{(3,4)}$) is used.

To project numbers for an emigration year that is two years earlier than the production year, then $D_{(2,4)}$  is used:

Equation 8.4c:           $D=D_{(2,4)}=D_{(2,3)}\times D_{(3,4)}$

When the demographic estimates are produced, a three-year average of each of the factors $D_{(3,4)}$ and $D_{(2,4)}$  is used based on the most recent factors available. For example, using data from Table 8.1, in year t, the number of child emigrants projected for the year t-3, t-2 is estimated with a three-year average of the most recent $D_{(2,4)}$ factor. The average is based on the factors 1.138, 1.142 and 1.124. This average factor (1.135) is then used to multiply the number of child emigrants in year t‑3, t‑2 at Duration 2 (7,700), and the result (Y=8,740) is the number of expected CCB child emigrants in the file four years after the emigration year. The same average calculation of the $D_{(3,4)}$ factor (1.048) is used to multiply the number of child emigrants in year t-4, t-3 at Duration 3 (8,500) to obtain the expected number of CCB child emigrants (Z=8,908) in the file four years after the emigration year.

Children emigrating to the United States

Data on Canadian adults and children who become immigrants in the United States are available from the U.S. Department of Homeland Security on an annual basis. These data provide the quarterly flow of immigrants to the United States emigrating from Canada. The number of child emigrants to the United States is subtracted from the estimated total number of child emigrants from CCB files to produce an estimated number of child emigrants to countries other than the United States. The calculations can be derived as follows:

Equation 8.5:           ${}^{OC}E{M}^{0-17}={}^{CCB}E{M}^{0-17}-\text{}\text{}\text{}{}^{HS}E{M}^{0-17}$

where

Long-term adult emigrants

Since the CCB program does not provide direct information on adult emigrants, an adjustment factor is used to estimate the number of adults emigrating to countries other than the United States. This factor is based on the emigration rate of children to other countries. Estimates for adults emigrating to the United States are taken directly from the U.S. Department of Homeland Security data.

The formula for estimating the number of adult emigrants to a country other than the United States is as follows:

Equation 8.6:            ${}^{OC}E{M}^{18+}=\frac{{}^{OC}E{M}^{0-17}}{{}_{}{}^{DEP}P{}^{0-17}}\times {}_{}{}^{DEP}P{}^{18+}\times F_C$

where

where

The $F_C$ factor is the ratio of the rate of adult emigration to the rate of child emigration to countries other than the United States. This ratio is taken from the T1FF,^Note and it is calculated as follows:

Equation 8.7:           $F_C=\frac{\left[\frac{{}^{T1FF}E{M}^{18+}}{{}^{DEP}P{}^{18+}}\right]}{\left[\frac{{}^{T1FF}E{M}^{0-17}}{{}^{DEP}P{}^{0-17}}\right]}$

where

Estimates of adult emigration to the United States come directly from the U.S. Department of Homeland Security.

Finally, the total number of adult emigrants corresponds to the following:

Equation 8.8:            $E{M}^{18+}={}^{OC}E{M}^{18+}+{}^{HS}E{M}^{18+}$

where

Since the data from the U.S. Department of Homeland Security do not include the province or territory of origin of Canadian emigrants, provincial and territorial estimates of adult emigration must be derived from another source. The ratio of the number of adult to child emigrants by province or territory from the T1FF is used to estimate the distribution of adult emigrants by province or territory of origin.

The provincial and territorial distribution, as well as the monthly distribution of long-term adult emigrants, is estimated in five stages: the first three are dedicated to the provincial and territorial distribution, while the last two concern the monthly distribution.

1. To estimate the number of adult emigrants by province or territory, the adult–child ratio of emigrants from the T1FF is applied to the estimate of children from the CCB:

Equation 8.9:

$$\text{If}{}_j{}^{T1FF}E{M}^{0-17}\text{ or}{}_j{}^{CCB}E{M}^{0-17}=0\text{then}{}_j{}^{W}E{M}^{18+}={}_j{}^{T1FF}E{M}^{18+}$$

else,

$${}_j{}^{W}E{M}^{18+}=\left[\frac{{}_j{}^{T1FF}E{M}^{18+}}{{}_j{}^{T1FF}E{M}^{0-17}}\right]\times {}_j{}^{CCB}E{M}^{0-17}$$

where

To mitigate the effect of volatility induced by lower emigrant numbers in the territories, the fraction in Equation 8.9 is replaced by the national fraction for each territory. For Prince Edward Island, the fraction is replaced by the Atlantic provinces fraction for the same reason.

2. The distribution of adult emigrants by province or territory is then calculated:

Equation 8.10:

$$W_j=\frac{{}_j{}^{W}E{M}^{18+}}{{\displaystyle {\sum }_j{}_j{}^{W}E{M}^{18+}}}$$

where

$W_j$ represents the weight of each province and territory and establishes the provincial and territorial distribution of adult emigrants.

3. The distribution is then applied to the total of adult emigrants ($E{M}^{18+}$  from Equation 8.8):

Equation 8.11:

$${}_j{}^{\text{'}}E{M}^{18+}=E{M}^{18+}*W_j$$

4. The monthly distribution is then calculated for each province and territory:

Equation 8.12:

$${}_j{{\displaystyle R}}_m=\frac{{}_j{}^{\text{T1FF}}{{\displaystyle EM}}_m^{18+}}{{\displaystyle \sum _{m=7(t-x-1)}^{6(t-x)}{}_j{}^{\text{T1FF}}{{\displaystyle EM}}_m^{18+}}}$$

where

${}_j{{\displaystyle R}}_m$ represents the monthly distribution of adult emigrants for a year from July to June.

To limit the effect of volatility induced by lower emigrant numbers in the territories, the fraction in Equation 8.12 is replaced by the national fraction for each territory. For the Atlantic provinces, the fraction is replaced by a regional fraction, obtained by summing the data for the four Atlantic provinces.

5. This distribution is then applied to the total number of adult emigrants by province ($E{M}^{18+}$ from Equation 8.11):

Equation 8.13:

$${}_{j}E{M}_m^{18+}={}^{\text{'}}E{M}^{18+}*{}_j{{\displaystyle R}}_m$$

where

${}_{j}E{M}_m^{18+}$ represents the monthly estimates, for province or territory j, of adult emigrants aged 18 and over.

Finally, the monthly number of long-term emigrants by province or territory corresponds to the sum of the long-term child emigrants and the long-term adult emigrants.

Preliminary and updated estimates

Preliminary and updated estimates of the number of long-term emigrants follow a different method, because of the lack of sufficiently complete CCB data. This method applies to the current year, as well as to previous years, when estimates are not yet final.

Data sources

Preliminary and updated estimates of the number of long-term emigrants are calculated from the final estimates of the number of long-term emigrants and population estimates of the DEP.

Method

In the absence of sufficiently complete CCB data to estimate the number of long-term emigrants for recent years, a rate is calculated from the most recent final estimates of the number of long-term emigrants and the population at the start of the period corresponding to these estimates. In addition, the population at the start of the year to be estimated is also used. The number of long-term emigrants for recent years is estimated in four stages:

1. The rate is calculated at the Canadian level based on the final estimates of the number of long-term emigrants and the population at the beginning of the period, according to the following equation:

Equation 8.14:

$${{\displaystyle {}_{}QE}}_{t-x,t-x+1}^{LT}=\frac{{\displaystyle \sum _j{{\displaystyle {}_{j}E}}_{t-x,t-x+1}^{LT}}}{{\displaystyle \sum _j{{\displaystyle {}_j{}^{}P}}_{Julyt-x}}}$$

where

2. The number of emigrants for Canada is obtained by applying the calculated rate to the population on July 1 of year t:

Equation 8.15:

$${{\displaystyle E}}_{t,t+1}^{LT}={{\displaystyle {}_{}QE}}_{t-x,t-x+1}^{LT}*{{\displaystyle {}_{}{}^{}P}}_{Julyt}$$

where

3. The national number of long-term emigrants is then broken down by province or territory according to the distribution of long-term emigrants in year t-x, t-x+1. The distribution follows the equation below:

Equation 8.16:

$${{\displaystyle {}_{j}E}}_{t,t+1}^{LT}={{\displaystyle {}_{}E}}_{t,t+1}^{LT}*\frac{{{\displaystyle {}_{j}E}}_{t-x,t-x+1}^{LT}}{{\displaystyle \sum _j{{\displaystyle {}_{j}E}}_{t-x,t-x+1}^{LT}}}$$

4. The provincial and territorial data calculated in the previous step are then broken down by month, using the monthly distribution of long-term emigrants in year t-x, t-x+1. The calculation is as follows:

Equation 8.17:

$${{\displaystyle {}_{j}E}}_m^{LT}={{\displaystyle {}_{j}E}}_{t,t+1}^{LT}*\frac{{{\displaystyle {}_{j}E}}_{m\in \left(t-x,t-x+1\right)}^{LT}}{{{\displaystyle {}_{j}E}}_{t-x,t-x+1}^{LT}}$$

These steps produce estimates of the number of long-term emigrants per month, for each province and territory, based on available data.

Short-term emigrants

Some people leave Canada for a short-term stay in another country without maintaining a usual place of residence in Canada. Final estimates of the number of short-term emigrants for the intercensal period are calculated every five years when the base population for the demographic estimates is recalculated.

Final estimates

Data sources

Data from the Census Undercoverage Study (CUS; formerly known as the Reverse Record Check), the census coverage study used to estimate undercoverage, are used to estimate the number of short-term emigrants. Estimates of the number of long-term emigrants are also taken into account.

Method

The final number of short-term emigrants is estimated by month and by province or territory as follows:

1. The number of departures across Canada is estimated from the CUS; the CUS data provide an estimate of the number of people who left Canada in the short term^Note and are still outside the country on Census Day;
2. The estimated number of short-term emigrants is then broken down by province or territory,^Note according to the provincial and territorial distribution of long-term emigrants;
3. Provincial and territorial estimates are disaggregated using annual rates for each of the five years of the intercensal period;
4. Monthly estimates are calculated using the monthly distribution of long-term emigrants.

Preliminary and updated estimates

CUS data are available only after the census, i.e., every five years. Preliminary and updated estimates of the number of short-term emigrants are therefore calculated using a different method.

Data sources

Preliminary and revised estimates of the number of short-term emigrants are estimated based on final estimates of the number of long-term emigrants and the DEP’s population estimates.

Method

The number of short-term emigrants in recent years is estimated in four steps:

1. A rate for the entire country is derived from the quinquennial CUS data for the previous intercensal period;
2. This rate is applied to the population as of July 1 to obtain the number of short-term emigrants for year t, t+1 in Canada. This rate is assumed to be constant for the entire postcensal period;
3. National data are broken down by province or territory according to the distribution of long-term emigrants;
4. Provincial and territorial data are further broken down by month using the monthly distribution of long-term emigrants.

Finally, the number of emigrants is calculated by adding the long-term emigrants and the short-term emigrants.

Estimates of the number of emigrants by age and gender

The distributions by province or territory, age, and gender are taken from the numbers of emigrants in the T1FF, after adjusting these data for the incomplete coverage by province or territory, age, and gender. For this step, an emigrant in the T1FF is defined as a tax filer who reported a departure date on their tax return. The coverage adjustment is calculated as follows:

Equation 8.18:

$$\text{If}{}_{a,g,j}{}^{T1FF}P=0\text{then}{}_{a,g,j}{}^{T1FF-adj}EM=0$$

else,

$${}_{a,g,j}{}^{T1FF-adj}EM={}_{a,g,j}{}^{T1FF}EM\times \left(\frac{{}_{a,g,j}{}^{DEP}P}{{}_{a,g,j}{}^{T1FF}P}\right)$$

where

The adjusted emigrant numbers for the two most recent years of T1FF data are grouped by five-year age group for each province and territory and by gender. To mitigate the effect of volatility induced by lower emigrant numbers, the numbers for the four Atlantic provinces are grouped together, and national numbers are used for each of the three territories.

The numbers of emigrants are then produced by province or territory, age, and gender, using Sprague^Note coefficients. The age of emigrants, which is their age on December 31 in the T1FF, is adjusted to their age on July 1, using formulas adapted for each age group. These numbers represent the distribution of emigrants by age and gender for each province and territory for the year from the beginning of July of year t to the end of June of year t+1. Lastly, this distribution is applied to the total number of emigrants.

Subprovincial emigrant estimates

The distribution of long-term emigrants at the subprovincial and subterritorial levels is obtained by comparing the addresses provided in the T1FF over two consecutive fiscal years. For this step, an emigrant is defined as a tax filer whose tax address is in Canada in the first year examined and abroad in the second year. The estimates are initially calculated by broad age groups (0 to 17, 18 to 24, 25 to 44, 45 to 64, and 65 and over). They are then broken down by age and gender according to the provincial or territorial distribution of emigrants. They are subsequently adjusted to provincial and territorial totals using the bidimensional iterative method to ensure consistency.

Short-term emigrants follow the same distribution as long-term emigrants.

Limitations

Emigration is one of the most difficult components of population growth to estimate accurately, because of the absence of a registration system at Canada’s borders. Unlike immigrants and non-permanent residents, who settle in Canada by obtaining a permit issued by the federal government, the number of emigrants is calculated using indirect estimation methods.^Note As a result, statistics relating to emigrants generally display a higher degree of uncertainty than those for other components of population growth.

Estimates of the number of long-term emigrants are based on tax data taken from the CCB. These data use a tax concept of emigration and must be adjusted to better represent the population. Conceptual differences, adjustments and delays in obtaining data are the main sources of error.

Preliminary and updated estimates of the number of long-term emigrants are produced using the most recent final data, since CCB data are not deemed sufficiently complete at the time these estimates are calculated. Consequently, this method is based on the assumption that emigration trends remain stable for recent years. This assumption is not systematically valid and may affect the precision of the estimates.

In the absence of current information on short-term emigrants, final estimates are based on the CUS. The CUS is a sample survey that is not optimized for estimating the number of short-term emigrants. Several assumptions are made when using these data. Estimates for the intercensal period are distributed according to the distribution of long-term emigrants. Furthermore, certain additional assumptions must be made to break down national data by province or territory, and annual data by quarter. Since the CUS is available only after a census, further assumptions are required to estimate the number of short-term emigrants for the postcensal period, notably that the short-term emigration quotient is constant.