# Chapter 6 Emigrants, net temporary emigrants and returning emigrants

Emigration refers to citizens or immigrants who leave the country to establish a residence in another country. This residence abroad may be permanent or temporary. Emigration results in a loss of population. Taking into account all aspects of Canadian emigration, the calculation of population involves the estimation of emigrants, net temporary emigrants and returning emigrants.

Unlike immigration, there is no legal provision in Canada to maintain records for persons leaving the country either on a temporary or permanent basis. Therefore, estimates of the number of emigrants and persons living temporarily abroad and their characteristics must be derived through secondary sources such as Canadian administrative files or immigration statistics of the United States.

As emigration components are the most difficult components to estimate, the methods of estimation are constantly evolving in an attempt to produce more accurate emigration estimates, given available sources of information and feasible methods. This chapter presents current methods used to produce the estimates of the three components of population change resulting from emigration.

## 6.1 Data sources and relevant concepts

Despite recommendations by the United Nations to establish a universal definition of international migrants, as well as a uniform method of recording information regarding emigration and immigration, not much progress has been made (United Nations 1998). This has consequences on the ability to compare migration statistics between different countries, as well as the potential to use other nation's international migration statistics.

For the purpose of estimating Canada's population, the following three components relating to emigration are described. Emigration estimates require a distinction between persons establishing a permanent residence in another country (i.e., emigrants), persons living temporarily abroad (i.e., net temporary emigrants), and finally the portion of emigrants who have returned to Canada (i.e., returning emigrants). Different data sources and methods are necessary for the two types of emigrants, as well as for returning emigrants. Estimates of emigrants, net temporary emigrants and returning emigrants are provided as separate components in publications on Canadian population estimates.

Emigrants are Canadian citizens or immigrants who have left Canada to establish a permanent residence in another country (sometimes referred to as permanent emigration). For example, persons traveling to the United States may be considered permanent emigrants if they acquire permanent resident status there, but are considered temporary emigrants if they still hold a visa or are on visitor status. Permanent emigration is a misnomer as it is not necessarily irreversible; emigrants can always decide to return to Canada.

Emigrants are estimated from administrative sources in terms of the gross flow of migrants out of Canada. The Office of Immigration Statistics of U.S. Department of Homeland Security provides data on Canadians who acquire permanent immigrant status in the U.S. This data source is used in estimating emigration to the United States. In order to estimate emigration to other countries, information on notification of departure from the Canada Child Tax Benefit (CCTB) program and tax data from Canada Revenue Agency (CRA) is used.Note 1 For this portion of emigration, we cannot determine if someone has acquired permanent immigrant status in another country. In these cases, we must therefore assume that someone who has cut ties with Canada, according to CRA data, has established permanent residence in another country.

Some people leave Canada to live temporarily in another country while not maintaining a usual place of residence in Canada. Other temporarily leave Canada and then return. The net result of those departures and returns is the component known as net temporary emigration. Data from the Reverse Record Check (RRC), the most important census coverage study, are used to estimate the number of persons leaving the country temporarily; while data from the National Household Survey (NHS), combined with Demography Division's estimates of returning emigrant, are used to estimate the number of temporary emigrants returning.

Temporary migration constitutes many movements in and out of the country. This would not concern the overall population estimates if the net effect was nil or negligible. However, a census coverage study (Reverse Record Check) in 1996 has shown that this is not the case. The decision to account for persons living temporarily abroad was based on evaluations of the 1996 error of closure for postcensal population estimates and its components against Reverse Record Check estimates. These evaluations concluded that omitting departures of Canadians as temporary residents abroad and their consecutive returns to Canada has an important effect on the quality of the country's population estimates (Michalowski 1999). Including net change in temporary emigration in the Demographic Estimates Program is a practice that started in 1998, with revisions to estimates back to 1991.

Returning emigrants are Canadian citizens or immigrants having previously emigrated from Canada and subsequently returned to Canada to re-establish a permanent residence. Again, data from the CCTB program and from CRA's T1FF are used in estimating returning emigrants.

## 6.2 Estimates of emigrants, net temporary emigrants and returning emigrants

### 6.2.1 Emigrants

The number of emigrants is estimated using data from the Office of Immigration Statistics, U.S. Department of Homeland Security, data collected by the Canada Child Tax Benefit (CCTB) program, and data from the T1 Family File (T1FF). The first source is used to estimate emigration to the United States while CCTB data is used to estimate emigration to other countries. The CCTB data covers all emigrant children, thus we can use this data to derive the children and adults emigrating to a country other than the United States. The estimates of the number of child emigrants have to be adjusted because the CCTB program is not universal. As a result, four adjustment factors are used to take into account:

1. the incomplete coverage due to a delay in the receipt and processing of the files of children eligible for the CCTB. Emigration estimates are usually finalized two or three years after the reference period. Based on historical files, it seems that CCTB data recordings reached a significant level two years after the year of emigration and that it takes four years for CCTB files to become complete. The data is adjusted as it is used within this four-year time frame;
2. the program's partial coverage, that is, people who do not apply for the CCTB or are not eligible;Note 2
3. the differential propensity to emigrate between children as a whole and those who are eligible for the CCTB; and
4. the differential propensity to emigrate between adults and children.

To calculate these adjustment factors, we make use of CCTB and tax data from T1FF. The estimation methods for child and adult emigrants are described in the following section.

#### Emigrant children

The CCTB file provides the numbers of dependent children (under 18 years of age) whose parents are eligible and have applied for the CCTB, but are no longer residents as defined by the CRA. These data are available on a monthly basis, but only provided by CRA to Statistics Canada annually for each province and territory. As mentioned, the CCTB program is not universal; therefore the data is incomplete in terms of estimation of total child emigrants and requires adjustments.

The first correction factor, that is the adjustment for partial coverage, corrects for the absence of universality of the CCTB program. The adjustment starts with a correction factor that is applied to the population registered for the CCTB program to account for its shortfall in total coverage. The correction factor uses the number of children registered for the CCTB program to the number of children in the total population, as estimated by Demography Division for each month, province and territory.

The second correction factor is used to adjust the differential emigration propensity between all children, and children registered for the CCTB program for each province and territory, on an annual basis. This factor is obtained by comparing the emigration rates for all children (aged 0 to 17) with the rates of CCTB-eligible children. This factor is calculated for each province and territory and is based on the last three available years of the T1FF. To eliminate variations due to small numbers in each of the Atlantic provinces, the differential propensity factor is estimated for these provinces as a group. In addition, the estimated factor for Canada is used for the territories.

The third correction factor is to take into account the incompleteness of the emigration information from the CRA's CCTB data files due to delays in the recordings of an emigration. Based on comparisons done with files that were two, three and four years after the reference period, it appeared that the CRA files could be considered complete about four years after the reference period. As we use CCTB data within this four year timeframe, we apply a correction factor. The same factor is applied to the monthly data of each province or territory.

The formula to estimate child emigrants is as follows:

For each province and territory:

Equation 6.1:      ${}_{\text{j}}\text{E}{\text{M}}^{0-17}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}^{0-17}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}\frac{1}{{}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{ℜ}}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}{}_{\text{j}}\text{G}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}\text{D}$

where

${}_{\text{j}}\text{E}{\text{M}}^{0-17}$
=
adjusted emigrant children aged 0 to 17 from province or territory j;
${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}^{0-17}$
=
number of emigrant children according to CCTB moving from province or territory j;
${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{ℜ}$
=
coverage rate of CCTB program for province or territory j;
${}_{\text{j}}\text{G}$
=
adjustment factor for emigration propensity of non CCTB children (derived from tax data), for all provinces, except for the Atlantic provinces, where the factor is measured as a whole and in the territories where the Canadian factor is used;
$\text{D}$
=
adjustment factor for the incompleteness of emigration data from CCTB files due to delays in the recordings of an emigration.

The factors used in the equation above are detailed in equations 6.2 to 6.4c: factors for incomplete coverage of CCTB-registered children (Equation 6.2), factors for the differences in the propensities of CCTB-registered and non-registered subpopulations to emigrate (Equation 6.3), as well as factors used to correct the incompleteness of emigration data due to delays in the recordings of an emigration (Equations 6.4a to 6.4c).

The coverage rates are calculated on a monthly basis as follows:

For each province and territory:

Equation 6.2:      ${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{ℜ}=\left[\frac{{}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{P}{}^{0-17}}{{}_{\text{j}}{}^{\text{D}\text{e}\text{m}}\text{P}{}^{0-17}}\right]$

where

${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{ℜ}$
=
coverage rate of CCTB program for each province or territory j;
${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{P}{}^{0-17}$
=
number of children aged 0 to 17 years registered for the CCTB program in each province or territory j;
${}_{\text{j}}{}^{\text{D}\text{e}\text{m}}\text{P}{}^{0-17}$
=
population estimated by Demography Division of children aged 0 to 17 years in each province or territory j.

The differential propensity to emigrate is obtained by dividing the emigration rates for all children by the emigration rates for children registered for the CCTB program, as follows:

For each province and territory:Note 3

Equation 6.3:      ${}_{\text{j}}\text{G}=\frac{{}_{{}_{\text{j}}}{}^{\text{T}\text{A}\text{X}}\text{R}\text{a}\text{t}\text{e}\text{E}{\text{M}}^{0-17}}{{}_{{}_{\text{j}}}{}^{\text{C}\text{C}\text{T}\text{B}\text{_}\text{T}\text{A}\text{X}}\text{R}\text{a}\text{t}\text{e}\text{E}{\text{M}}^{0-17}}\text{ }=\text{ }\frac{\left[\frac{{}_{\text{j}}{}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}}{{}_{\text{j}}{}^{\text{T}\text{A}\text{X}}\text{P}{}^{0-17}}\right]}{\left[\frac{{}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}\text{_}\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}}{{}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}\text{_}\text{T}\text{A}\text{X}}\text{P}{}^{0-17}}\right]}$

where

${}_{\text{j}}\text{G}$
=
adjustment factor for emigration propensity of non-CCTB children (derived from fiscal data) for each province or territory of origin j;
${}_{{}_{\text{j}}}{}^{\text{T}\text{A}\text{X}}\text{R}\text{a}\text{t}\text{e}\text{E}{\text{M}}^{0-17}$
=
emigration rate of all children from each province or territory j;
${}_{{}_{\text{j}}}{}^{\text{C}\text{C}\text{T}\text{B}\text{_}\text{T}\text{A}\text{X}}\text{R}\text{a}\text{t}\text{e}\text{E}{\text{M}}^{0-17}$
=
emigration rate of CCTB-registered children from each province or territory j, derived from T1FF;
${}_{\text{j}}{}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}$
=
emigration of all children from province or territory j, according to income tax data;
${}_{\text{j}}{}^{\text{T}\text{A}\text{X}}\text{P}{}^{0-17}$
=
ISD estimate of children in province or territory j, based on income tax files;
${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}\text{_}\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}$
=
emigration of CCTB-registered children from province or territory j, derived from the T1FF by ISD;
${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}\text{_}\text{T}\text{A}\text{X}}\text{P}{}^{0-17}$
=
CCTB-registered children in the population of the income tax file provided by ISD by province or territory j.

We use delay factors to compensate for the incompleteness of the CCTB data file on child emigration due to registration delays.

Table 6.1 illustrates the calculation of the delay factors; all numbers in the table are fictitious. In this table, we suppose that the production year is 2011, therefore the t-3, t-2 emigration year in the first column corresponds to 2008/2009 and the t-4, t-3 emigration year corresponds to 2007/2008, etc. The subsequent three columns of the table show numbers of child emigrants by year of emigration and by duration between the emigration year and the year of the data file used. In the table, the numbers of child emigrants for the emigration year t-4, t-3 from the data file that is two years after the emigration year is 7,900 (duration of two years between the emigration year and the data file year) and the number is 8,500 from the data file that is three years after the emigration year (duration of three years between the emigration year and the data file year). Our objective is to estimate what the t-4, t-3 and also the t-3, t-2 emigration year numbers would be in a file that is four years after the emigration year.

Table 6.1
Calculation of the delay factors: An illustration for production year 2011

Table summary
This table displays the results of Calculation of the delay factors: An illustration for production year 2011. The information is grouped by Year of emigration (appearing as row headers), Number of child emigrants in the Canada Child Tax Benefit file after, Delay factor (2,3), Delay factor (3,4) and Delay factor (2,4) (appearing as column headers).
Year of emigration Number of child emigrants in the CCTB file after D(2,3) D(3,4) D(2,4)
2 years 3 years 4 years
t-7, t-6 (2004/2005) 6,300   2008 file 6,750 2009 file 7,100 1.071 1.052 1.138Table note 2
t-6, t-5 (2005/2006) 2008 file 6,700Table note 1 2009 file 7,250 2010 file 7,600 1.082 1.048 1.142
t-5, t-4 (2006/2007) 2009 file 7,200   2010 file 7,850 2011 file 8,200 1.090 1.045 1.124
t-4, t-3 (2007/2008) 2010 file 7,900   2011 file 8,500 Z=8,908 1.076 This cell is left blank intentionally This cell is left blank intentionally
t-3, t-2 (2008/2009) 2011 file 7,700   This cell is left blank intentionally Y=8,740 This cell is left blank intentionally This cell is left blank intentionally This cell is left blank intentionally
Average factors (3 years) This cell is left blank intentionally This cell is left blank intentionally This cell is left blank intentionally 1.083 1.048 1.135

We first calculate delay factors for the previous emigration years. The delay factors (D) in the right-hand columns are derived from the numbers on the left. D(2,3) is the ratio between duration 3 and duration 2; while D(3,4) is the ratio between duration 4 and duration 3. For example, D(3,4) of 1.045 for the emigration year t-5, t-4 comes from the ratio between 8,200 and 7,850. This factor could be used to project one year ahead from duration 3 to duration 4. But, to project two years ahead from duration 2 to duration 4, we calculate the factor D(2,4) (the last column in Table 6.1) by multiplying the two most recent factors, D(2,3) and D(3,4).

The formulas are as follows:

Equation 6.4a:      ${\text{D}}_{\left(2,3\right)}=\frac{{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}_{\left(\text{t}-4,\text{t}-3\right)}^{\text{t}}}{{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}_{\left(\text{t}-4,\text{t}-3\right)}^{\left(\text{t}-1\right)}}$

Equation 6.4b:      ${\text{D}}_{\left(3,4\right)}=\frac{{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}_{\left(\text{t}-5,\text{t}-4\right)}^{\text{t}}}{{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}_{\left(\text{t}-5,\text{t}-4\right)}^{\left(\text{t}-1\right)}}$

where

${}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}_{\left(\text{t}-\text{x}-1,\text{t}-\text{x}\right)}^{\text{t}}$
=
The number of child emigrants for the emigration year (t-x-1, t-x) from the CCTB file of year t.

If we want to project numbers for an emigration year that is three years before the production year, then we use the delay factor in the recordings of data on emigration from duration 3 to duration 4 (i.e., D(3,4)).

If we want to project numbers for an emigration year that is two years before production year, then we use:

Equation 6.4c:      $\text{D}={\text{D}}_{\left(2,4\right)}={\text{D}}_{\left(2,3\right)}×{\text{D}}_{\left(3,4\right)}$

In production, we use a three-year average of each of the D(3,4) and the D(2,4) factors based on the most recent factors available. For example, starting from data in table 6.1, in year t, we will project the emigration number for the year t-3, t-2 (7,700) with a three-year average of the most recent D(2,4). The average is based on the factors: 1.138, 1.142 and 1.124. This average factor (1.135) will then be used to multiply the number of emigrants in year t-3, t-2 at duration 2 (7,700) and the results (Y=8,740) will be the number of expected CCTB child emigrants in the file that is four years after the emigration year. The same average calculation of the D(3,4) factor (1.048) is used to multiply the emigration number of year t-4, t-3 at duration 3 (8,500) to obtain the expected number of CCTB child emigrants (Z=8,908) in the file that is four years after the emigration year.

Data on Canadian adults and children who became immigrants in the United States are available from the Department of Homeland Security on an annual basis. The Homeland Security data provides quarterly flow of immigrants to the United States emigrating from Canada. We then subtract this number of child emigrants to the United States from the estimated total number of child emigrants from CCTB files to produce an estimated number of child emigrants to countries other than the United States. The calculations can be derived as follows:

Equation 6.5:      ${}^{\text{O}\text{C}}\text{E}{\text{M}}^{0-17}={}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}^{0-17}\text{\hspace{0.17em}}-\text{\hspace{0.17em}}\text{​}\text{​}\text{​}\text{ }\text{ }{}^{\text{H}\text{S}}\text{E}{\text{M}}^{0-17}$

where

${}^{\text{O}\text{C}}\text{E}{\text{M}}^{0-17}$
=
number of emigrant children to countries other than the United States;
${}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}^{0-17}$
=
number of emigrant children based on CCTB data;
${}^{\text{H}\text{S}}\text{E}{\text{M}}^{0-17}$
=
number of emigrant children to the United States based on United States Department of Homeland Security data.

Estimates for adults emigrating to the United States are taken directly from the Homeland Security data. As the CCTB program does not provide direct information on emigrant adults an adjustment factor was used to estimate the number of adults emigrating to countries other than the United States, based on the emigration rate of children to other countries.

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

Equation 6.6:      ${}^{\text{O}\text{C}}\text{E}{\text{M}}^{18+}=\frac{{}^{\text{O}\text{C}}\text{E}{\text{M}}^{0-17}}{{}_{}{}^{\text{D}\text{e}\text{m}}\text{P}{}^{0-17}}×{}_{}{}^{\text{D}\text{e}\text{m}}\text{P}{}^{18+}×\text{R}\text{a}\text{t}\text{i}\text{o}\text{A}{\text{C}}_{}$

where

${}^{\text{O}\text{C}}\text{E}{\text{M}}^{18+}$
=
number of monthly adult emigrants to countries other than the United States;
$\frac{{}^{\text{O}\text{C}}\text{E}{\text{M}}^{0-17}}{{}^{\text{D}\text{e}\text{m}}\text{P}{}^{0-17}}$
=
monthly emigration rate of children moving to countries other than the United States;
${}_{}{}^{\text{D}\text{e}\text{m}}\text{P}{}^{18+}$
=
population estimate of adults at the beginning of the month;
RatioAC
=
annual ratio of adult emigration rate and child emigration rate to countries other than the United States.

where

The RatioAC is the rate of adult emigration divided by the rate of child emigration to countries other than the United States taken from tax data.Note 4 It is calculated as follows:

Equation 6.7:      $\text{R}\text{a}\text{t}\text{i}\text{o}\text{A}\text{C}=\frac{\left[\frac{{}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{18+}}{{}^{\text{D}\text{e}\text{m}}\text{P}{}^{18+}}\right]}{\left[\frac{{}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}}{{}^{\text{D}\text{e}\text{m}}\text{P}{}^{0-17}}\right]}$

where

${}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{18+}$
=
annual number of adult emigrants to countries other than the United States, measured from tax data;
${}^{\text{D}\text{e}\text{m}}\text{P}{}^{18+}$
=
estimate of adult population by Demography Division (based on the average of start-of-period and end-of-period populations);
${}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}$
=
annual number of child emigrants to countries other than the United States, measured from tax data;
${}^{\text{D}\text{e}\text{m}}\text{P}{}^{0-17}$
=
estimate of child population by Demography Division (based on the average of start-of-period and end-of-period populations);

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

Equation 6.8:      $\text{E}{\text{M}}^{18+}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{}^{\text{O}\text{C}}\text{E}{\text{M}}^{18+}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{}^{\text{H}\text{S}}\text{E}{\text{M}}^{18+}$

where

$\text{E}{\text{M}}^{18+}$
=
${}^{\text{O}\text{C}}\text{E}{\text{M}}^{18+}$
=
number of adult emigrants to countries other than the United States;
${}^{\text{H}\text{S}}\text{E}{\text{M}}^{18+}$
=
number of adult emigrants to the United States, according to U.S. Department of Homeland Security data.

The data provided by the U.S. Department of Homeland Security does not include the province of origin for Canadian emigrants. The estimates for adults' province of origin at the provincial and territorial level must be acquired from another source. The ratio between the number of adult and child emigrants provided by tax data (T1FF), is used to estimate the distribution of adult emigrants by province and territory of origin.

The provincial and territorial of adult migrants is estimated as follows:

Definitions of the symbols used:

${}_{\text{j}}{}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{18+}$
=
emigrants from province or territory j, aged 18 years or more, taken from tax data (T1FF);
${}_{\text{j}}{}^{\text{T}\text{A}\text{X}}\text{E}{\text{M}}^{0-17}$
=
emigrants from province or territory j, aged 0 to 17 years, taken from tax data (T1FF);
${}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}^{0-17}$
=
emigrants of province or territory j, aged 0 to 17 years, estimated from CCTB;
${}_{\text{j}}{}^{\text{W}}\text{E}{\text{M}}^{18+}$
=
estimate of emigrants from province or territory j, aged 18 years or more which will serve to calculate the provincial and territorial distribution of adult emigrants.

The method is composed of three steps:

1. To estimate the number of adult emigrants by province and territory, the ratio of adult to child emigrants from the T1FF is applied to the estimate of children from the CCTB

Equation 6.9:

Due to small results, for each of the individual territories the fraction in equation 6.9 is replaced by the national fraction. For Prince Edward Island, the fraction is replaced by Atlantic Provinces fraction.
2. The distribution by province and territory is then calculated for the estimated number of adult emigrants

Equation 6.10:      ${\text{W}}_{\text{j}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{{}_{\text{j}}{}^{\text{W}}\text{E}{\text{M}}^{18+}}{{\sum }_{\text{j}}{}_{\text{j}}{}^{\text{W}}\text{E}{\text{M}}^{18+}}$

Wj 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 adult emigrants (EM18+ from equation 6.8)

#### Estimates of emigrants by age and sex

The distribution by age, sex, province and territory of emigrants is taken from the emigrants in the tax data (T1FF) adjusted for the variability of the T1FF coverage by age, sex, province and territory. The adjustment is as follows:

Equation 6.11:

where

${}_{\text{a},\text{s},\text{j}}{}^{\text{T}1\text{F}\text{F}-\text{a}\text{d}\text{j}}\text{E}\text{M}$
=
number of T1FF emigrants adjusted for coverage based on age, sex and province or territory;
${}_{\text{a},\text{s},\text{j}}{}^{\text{T}1\text{F}\text{F}}\text{E}\text{M}$
=
number of T1FF emigrants based on age, sex and province or territory;
${}_{\text{a},\text{s},\text{j}}{}^{\text{E}\text{S}\text{T}}\text{P}$
=
Demography Division's population estimates by age, sex and province or territory on January 1st of the year following the T1FF year;
${}_{\text{a},\text{s},\text{j}}{}^{\text{T}1\text{F}\text{F}}\text{P}$
=
T1FF population by age, sex and province or territory.

The adjusted number of emigrants from the two most recent years of T1FF data are assembled into five year age groups for each province, territory and sex. Due to small numbers, Atlantic province numbers are grouped together and used for the each Atlantic province. The National numbers are used for each of the territories.

Using the Sprague coefficients, we then produce the numbers by age, sex, province and territory.Note 5 We bring back the age of a person, which is on December 31 on the T1FF to their age at July 1. These numbers represent the emigration distributions for the year that covers the beginning of July (x) to the end of June (x+1), by age and sex for each province and territory. Therefore if the distribution estimate was produced by combining the 2010 and 2011 T1FF, we apply the distributions to the year beginning in July 2010 and ending in June 2011.

#### Levels of estimates

The difference between preliminaryNote 6 and final estimates lies in the timeliness of the sources used to estimate this component. The same estimation method is used.

### 6.2.2 Net temporary emigration

Some people leave Canada to temporarily live in another country; others who were temporarily outside Canada return. The net result of those departures and returns is the component known as net temporary emigration. The following steps are used to estimate their monthly numbers by province or territory:

1. The estimate of the number of departures at Canada level is derived from the Reverse Record Check (RRC), the most important census coverage study. The RRC provides an estimate of the number of people who left Canada temporarilyNote 7 during an intercensal period and who are still out of the country at the end of the period.
2. The estimate of the number of temporary emigrants returning is done in two steps:
1. The number of all returning emigrants for Canada is taken from the National Household Survey (NHS). The NHS provides the number of persons who resided outside Canada at the previous census and who have since returned to the country during the intercensal period;
2. From the estimate of all returning emigrants for Canada (NHS estimates Step 2a) we subtract Demography Division's estimate of returning emigrants. The resultant estimate is the number of temporary emigrants returning.
3. The estimate of net temporary emigration for Canada is derived by subtracting returning persons (Step 2b) from departures (Step 1).
4. The estimate derived in Step 3 is then distributed by province or territory according to the provincial and territorial distribution of departures of temporary emigrants based on the RRC.Note 8 The number for the Atlantic provinces is estimated as a group and redistributed proportionately to each province according to their respective population size. The same is done for the three territories.
5. The provincial and territorial estimates are disaggregated equally into annual estimates for each of the five years of the intercensal period. The monthly estimates are assumed to have a seasonal distribution. This distribution is modeled after the seasonal patterns observed for permanent emigration. The seasonal patterns are assumed to be between an even flow of net temporary migrants and the proportional flow as measured for permanent emigration which is expressed as an average of the two seasonal patterns. The mathematical expression that gives each monthly flow is as follows:

Equation 6.12:      $\text{N}\text{T}{\text{E}}_{\text{m}}=\frac{\left[\left(\frac{\text{N}\text{T}\text{E}}{12}\right)+\left(\frac{\text{E}{\text{M}}_{\text{m}}}{\text{E}\text{M}}×\text{N}\text{T}\text{E}\right)\right]}{2}$

where

$\text{N}\text{T}{\text{E}}_{\text{m}}$
=
number of net temporary emigrants for the month m;
$\text{N}\text{T}\text{E}$
=
annual number of net temporary emigrants;
$\text{E}{\text{M}}_{\text{m}}$
=
number of emigrants for the month m;
$\text{E}\text{M}$
=
number of annual emigrants.

Net temporary emigration can only be estimated for the intercensal period preceding the most recent census. Postcensal estimates of net temporary emigration is assumed to be the same as those estimated in the previous intercensal period for each province and territory as no other source of information is available. They remain unchanged until the completion of the RRC in the next census (i.e., approximately two years after the census).

#### Estimates of net temporary emigrants by age and sex

To obtain the estimates of net temporary emigrants by age and sex, the same distributions as observed for emigrant are used.Note 9

#### Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the emigration estimate used to calculate the seasonal adjustment for the net temporary emigration. The same estimation method is used.

### 6.2.3 Returning emigrants

A returning emigrant is a person returning to Canada, after having been classified as an emigrant. In a manner similar to the procedure used to calculate the number of emigrants, data from the CCTB file and CRA's T1FF are used to estimate the number of returning emigrants. A citizen or an immigrant who has emigrated regains eligibility for the CCTB if he or she re-establishes residential, economic and social ties in Canada. A returning child emigrant is identified by the presence of both a departure date and return date on the CCTB file, as well as the parent's residency status. As with emigration, a person's return to Canada relies on their resident status for income tax purposes.

CCTB data for returning emigrants include children born outside Canada. These children are included in the returning emigrant population because the majority of foreign births to Canadian parents are not included in vital statistics (according to provincial registry offices). Their inclusion makes up for what would otherwise be an underestimation of population for the reason of incompleteness of data on births. As is the case with emigrants, estimates of the number of returning emigrant children and the number of returning emigrant adults are calculated separately.

#### Returning emigrant children

The CCTB file provides numbers of dependent children (under the age of 18 years) of CCTB recipients who have returned to Canada after a period of emigration. These data are available on a monthly basis but provided by CRA to Statistics Canada annually for each province and territory.

As with emigrant children, adjustment factors are applied to adjust the CCTB data. First, the CCTB data for returning child emigrants are adjusted with a factor reflecting the program's partial coverage, that is, people who do not apply for the CCTB or are not eligible. This factor is obtained by comparing the estimated number of children in the population with the number of children in CCTB files (Equation 6.2). The second adjustment factor is used to take into account the differential propensity to emigrate between children who are eligible for the CCTB and children who are not. In this case, it is assumed that the ratio is the same as the ratio for emigrants (Equation 6.3). Hence, the numbers for returning CCTB-eligible children are adjusted with the same differential propensity factors that are used for emigration. Finally, we adjust the data for the delay in completion of CCTB data (the delay factor), which is calculated the same way as was done for emigration, but this time with the number of returning emigrants. The formula provided earlier used to compute the estimate of child emigrants (Equation 6.1) is used to estimate returning child emigrants, where  $\left({}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{E}{\text{M}}^{0-17}\right)$ the number of child emigrants by province or territory, according to CCTB data, is replaced by  $\left({}_{\text{j}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{R}{\text{E}}^{0-17}\right)$ the number of children returning to Canada.

The number of adults returning to Canada after emigrating can be indirectly estimated using ISD estimates based on income tax files or NHS data. Both sources include returning permanent emigrants and returning temporary emigrants including persons who may have maintained residential ties with Canada. However, neither source can be used directly to provide the number of adult returning permanent emigrants. It is possible to obtain the adult to child ratio for the returning emigrant population as follows:

Equation 6.13:      ${\text{τ}}^{\text{R}\text{E}}=\frac{{}^{\text{C}}\text{R}{\text{E}}^{18+}}{{}^{\text{C}}\text{R}{\text{E}}^{0-17}}$

where

${\text{τ}}^{\text{R}\text{E}}$
=
ratio of adults and children in the returning emigrant population;
${}^{\text{C}}\text{R}{\text{E}}^{18+}$
=
number of returning emigrant adults according to NHS data;
${}^{\text{C}}\text{R}{\text{E}}^{0-17}$
=
number of returning emigrant children according to NHS data.

The number of adult returning emigrants is estimated by multiplying the estimate of returning child emigrants based on CCTB data by the adult to child ratio from Equation 6.13.

Equation 6.14:      $\text{R}{\text{E}}^{18+}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{}^{\text{C}\text{C}\text{T}\text{B}}\text{R}{\text{E}}^{0-17}\text{\hspace{0.17em}}×\text{\hspace{0.17em}}{\text{τ}}^{\text{R}\text{E}}$

where

$\text{R}{\text{E}}^{18+}$
=
estimated number of returning adult emigrants;
${}^{\text{C}\text{C}\text{T}\text{B}}\text{R}{\text{E}}^{0-17}$
=
estimated number of returning child emigrants according to CCTB data;
${\text{τ}}^{\text{R}\text{E}}$
=
Adult-child ratio for the returning emigrant population according to NHS counts.

The estimate of the number of returning children is produced monthly for each province and territory. The provincial and territorial distribution of returning children is assumed to hold for returning adults.

#### Estimates of returning emigrants by age and sex

The age and sex distribution of returning emigrants is based on NHS data. Characteristics of returning emigrants are derived from census mobility data for one year, after excluding non-permanent residents and immigrants. Since 2011-2012, we use a distribution by age and sex derived from the 2011 NHS. The NHS distribution by single years of age and sex is applied to children aged 0 to 17 years and to adults 18 years and over.

#### Levels of estimates

The difference between preliminary and final estimates lies in the timeliness of the sources used to estimate this component. The same estimation method is used.

## Notes

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