Technical Guide on Demographic Estimates at Statistics Canada
Chapter 10
Interprovincial migration

Interprovincial migration represents movement between provinces or territories involving a change in the usual place of residence. Intraprovincial migration also involves a change in usual place of residence, but these movements occur within the same province or territory. The term internal migration may refer to either interprovincial migration or intraprovincial migration, or both. This chapter focuses on the interprovincial migration component. For information on intraprovincial migration, see Chapter 11.

There is no provision for recording interprovincial migration in Canada. Consequently, this component of demographic growth is estimated using administrative data. The methods used to prepare estimates of interprovincial migration will be discussed in this chapter.

Definitions and concepts

Interprovincial migration is the movement of persons from one province or territory to another, involving a change to their usual place of residence. These movements are measured by comparing the place of residence at the beginning and end of the measurement period.

Canada Revenue Agency (CRA) provides Statistics Canada with data from the Canada child benefit (CCB) program and personal income tax returns (such as T1 and T4), which are used to estimate interprovincial migration. Monthly, quarterly and annual interprovincial migration estimates are produced using these sources.

Since 1976, personal income tax records have become the official data source for final interprovincial migration estimates. The population covered by tax data is more comprehensive than that of the CCB; in general, interprovincial migration estimates based on tax data are considered to be of higher quality than those produced using data from the CCB. However, tax data are not timely enough for use in preliminary estimates. Statistics Canada receives tax data only after annual processing, compared to CCB data which are available on a monthly basis. Therefore, final estimates are calculated annually using the T1 Family File (T1FF), while preliminary estimates^Note 1 are calculated using CCB data.

Interprovincial migration is a unique demographic phenomenon, in that it is closely tied to the measurement period. In fact, as a result of return migration and multiple migrations, the number of migrants may differ substantially depending on the duration of the measurement period. The following diagram illustrates this situation using a case of multiple migration.

Figure 10.1 start

Description for Figure 10.1

Figure 10.1 illustrates a hypothetical itinerary of someone migrating from province A to province B to province C, on a monthly, quarterly and annual basis. This figure also shows the impact of those migrations on consistency of the various time periods considered.

Figure 10.1 end

Even though the migrant moves twice in the same year, only one move is recorded at the annual level (A to C). As well, since both moves occur in the second quarter, only one move is recorded at the quarterly level (A to C). Lastly, since the moves occur in the fourth and sixth months, two moves are recorded at the monthly level (A to B and B to C). The result is different migration flows depending on the measurement period.

Since interprovincial migration estimates are calculated for the month, quarter and year, the number of migrants must be calculated for each measurement period. Although the number of migrants may differ, net interprovincial migration^Note 2 must be identical for each measurement period. For example, annual net migration in the figure above is -1 for A, 0 for B and +1 for C regardless of whether it is calculated using monthly periods or quarterly periods. However, given the nature of the administrative data and the fact that some individuals are absent at the beginning and end of each period, an adjustment must be made to ensure that the net migration is identical.

Final interprovincial migration estimates

Data sources

The T1 Family File (T1FF) is an annual administrative tax file processed by Statistics Canada. The T1FF contains income and demographic information of tax filers and their dependants for subprovincial geographic areas. The file is created using various administrative data including those provided by Canada Revenue Agency, such as the T1, T4, and the Canada Child Benefit.

The Canada Child Benefit (CCB) is a tax-free monthly payment made to eligible families with children under 18 years of age. Information from the Canada Child Benefit (CCB) program is provided by the Canada Revenue Agency on a monthly basis, and the data is used to identify migration of children.

Estimation methodology

Final estimates of interprovincial migration are produced using the T1FF. By comparing the place of residence at the time of filing, it is possible to identify for those persons who file returns for two consecutive years, those who move, their place of origin and their destination. The development of migration data involves four main steps:

1. geocoding of tax records;
2. estimation of non-filing dependants of tax filers, by age group and gender;
3. identification of migrant tax filers by age group and gender;
4. adjustment for the population not covered by the T1FF.

The four steps of the estimation methodology are described below.

Step 1 – Geocoding

The migration data developed from the taxation records are estimates of migration flows between census divisions (CDs) or census metropolitan areas (CMAs) and census agglomerations (CAs). The geographic coding of CDs, CMAs, and CAs on the tax records is done primarily on the basis of the postal code, which is a part of the mailing address. About 99% of all tax records are filed with a postal code, or are assigned one, based on the filer's address by matching the address to a file similar to the Postal Code Directory from Canada Post. As the tax return is usually submitted several months after the end of the tax year, the postal codes correspond to those existing in the spring of the year following the tax year.

Step 2 – Estimation of dependants

Since the tax records source file has no direct information on the number and characteristics of non-filing dependants, this information must be imputed. The estimation of tax filers' dependants is based on the T1FF. Families are created by linking all filing family members together, using spousal social insurance numbers, marital status, and matched addresses. Non-filing spouse is imputed whenever a filer has declared himself or herself married but was not linked to a filing spouse. Children are imputed based on CCB data, which carry the social insurance number of the parent receiving the benefit, as well as from previous T1FF. Newborns are added to tax filer records from Statistics Canada's Birth Database.

The family data from the T1FF are then used to create a file of individual tax filers for the migration system. The migration file contains information for each tax filer and assigns dependants to each tax filer based on the number of filers in the family, and the number of dependants. If only one parent in the family has filed a tax return, then all dependants, including the spouse, if one exists, are added to the tax filer's record. If both parents filed tax returns, and their family record contained dependant children, then each tax filer would receive half the count of dependants.

Step 3 – Identifying migrant tax filers

After assigning the geographic codes and non-filing dependants to each tax filer, records for two consecutive years are matched by social insurance number. Only records of tax filers who are present in both years are retained. Migrant tax filers are identified by comparing current and previous geography codes (CDs, CMAs, or CAs). Thus, it is only possible to determine migrant status for those who file in two consecutive years. The identification of migrants is based on their address at the time of filing, and thus the migration period is not precisely one year, but it is assumed to be close. The assumed reference period is around April to April, of the year following each tax year. However, in Statistics Canada’s Demographic Estimates Program, the given estimates cover the period from July to June. Tax filers' non-filing dependants are assumed to have the same migration behaviour as that of the filers to whom they are assigned.

Step 4 – Coverage adjustment factor

The final step in the estimation process is an adjustment for coverage, performed at the CD, CMA, and CA level for gender and specific age groups. This adjustment is required to estimate those migrants who did not file two consecutive personal income tax returns, which involves the calculation of coverage adjustment factors.

The coverage adjustment factors are calculated by dividing the population estimates from the Demographic Estimates Program of a given CD, CMA or CA with the T1FF counts, for each gender and age group.

The adjustment factors are applied to the counts of interprovincial migrants derived in Step 3 to obtain an estimate of total migrants. The basic assumption is that the population not covered by the taxation system has the same rate of migration as those for whom it can be measured.

The total migration estimates at the CD level are then aggregated to obtain the provincial/territorial estimates of in-migrants, out-migrants, and net migrants.

Final interprovincial migration estimates by age and gender

Final interprovincial migration estimates are derived from the T1FF file consisting of age and gender, as well as the province/territory of origin and destination. Unlike previously, where the estimates by single year of age were derived using a combination of T1FF, Census and Sprague’s multipliers, the data from T1FF is used directly instead. Please note that estimates from 2021/2022 onwards are based on this new method.

For details on the previous methodology, please refer to the 2015 edition of this publication.

Aligning estimates from different measurement periods

Final annual estimates are obtained directly from T1FF data. However, since these data are annual, models must be used to calculate monthly and quarterly final estimates. As well, these estimates must be adjusted to align the net interprovincial migration of the different measurement periods for which estimates are derived.

As is the case with preliminary estimates (see section Preliminary interprovincial migration estimates), matrix representations are used for final estimates. A matrix is used to represent interprovincial migration between 13 provinces and territories of origin (denoted by j) and 13 destination provinces and territories (denoted by k). Each item (j,k) of the matrix represents both the number of out-migrants from province or territory of origin j and the number of in-migrants to destination province or territory k.

Monthly estimates

Monthly interprovincial migration estimates are derived as follows.

First, a matrix containing the sum of the monthly number of migrants in the 12 months of the year is created using the annual matrix of the T1FF and the preliminary estimates derived from CCB data.

For each province or territory of origin j and destination province or territory k, item (j,k) of the matrix is calculated as follows:

Equation 10.1:           ${}_{j,k}{}^{D}S{M}_{t,t+11}={}_{j,k}{}^{P}S{M}_{t,t+11}^{**}\times \frac{{}_{j,k}{}^{D}A{}_{t,t+11}}{{}_{j,k}{}^{P}A{}_{t,t+11}}$

where

An adjustment is then applied to the matrix so that the sum of monthly net interprovincial migrants matches that of the annual matrix.

The adjustment involves calculating the difference between the net numbers of the two matrices for each combination of origin and destination:

Equation 10.2:           ${}_{j,k}{}^D\Delta {}_{t,t+11}=\left({}_{k,j}{}^{D}S{M}_{t,t+11}-{}_{j,k}{}^{D}S{M}_{t,t+11}\right)-\left({}_{k,j}{}^{D}A{}_{t,t+11}-{}_{j,k}{}^{D}A{}_{t,t+11}\right)$

where

The differences calculated above are then used to change the number of migrants to create a new matrix in which the net numbers match those of the annual migration matrix.

Each item (j,k) of the adjusted matrix is obtained as follows:

Equation 10.3:           ${}_{j,k}{}^{D}S{M}_{t,t+11}^{*}={}_{j,k}{}^{D}S{M}_{t,t+11}+{}_{j,k}{}^D\Delta {}_{t,t+11}\times \frac{{}_{j,k}{}^{D}S{M}_{t,t+11}}{{}_{j,k}{}^{D}S{M}_{t,t+11}+{}_{k,j}{}^{D}S{M}_{t,t+11}}$

where

Various adjustments are made to matrix ${}^{D}S{M}_{t,t+11}^{*}$ to avoid negative values or division by zero.

Lastly, for each of the 12 months, the adjusted monthly interprovincial migration matrix is derived using the matrix resulting from Equation 10.3 and preliminary monthly estimates derived from the CCB.

Equation 10.4:           ${}_{j,k}{}^{D}M{}_t^{*}={}_{j,k}{}^{P}M{}_t^{**}\times \frac{{}_{j,k}{}^{D}S{M}_{t,t+11}^{*}}{{}_{j,k}{}^{P}S{M}_{t,t+11}^{**}}$

where

This matrix contains the final monthly numbers of migrants adjusted so that the sum of the net numbers matches that of the annual matrix.

Quarterly estimates

When monthly interprovincial migration estimates are produced, quarterly migration estimates can be derived.

First, final quarterly matrices must be derived using information from preliminary matrices and final monthly matrices for the three months in each quarter produced above.

For each province or territory of origin j and destination province or territory k, each item (j,k) of the quarterly migration matrix is calculated as follows:

Equation 10.5:           ${}_{j,k}{}^{D}Q{}_{t,t+2}^{}={}_{j,k}{}^{P}Q{}_{t,t+2}^{*}\times \frac{{}_{j,k}{}^{D}S{M}_{t,t+2}^{*}}{{}_{j,k}{}^{P}S{M}_{t,t+2}^{**}}$

where

An adjustment is then applied to quarterly matrix ${}_{}{}^{D}Q{}_{t,t+2}$ to align net numbers with those of the sum of the three corresponding monthly matrices.

The adjustment involves calculating the difference between the net numbers of the quarterly matrix and those of the sum of the monthly matrices for the three months of the quarter. Note that net interprovincial migration in the final monthly matrices has already been aligned with the annual net numbers.

Equation 10.6:           ${}_{j,k}{}^D\Delta {}_{t,t+2}=({}_{k,j}{}^{D}Q{}_{t,t+2}-{}_{j,k}{}^{D}Q{}_{t,t+2})-({}_{k,j}{}^{D}S{M}_{t,t+2}^{*}-{}_{j,k}{}^{D}S{M}_{t,t+2}^{*})$

The differences are then used to change the number of migrants in the quarterly matrix to align the quarterly net numbers with those of the sum of the three monthly matrices for the three months of the quarter.

Each item (j,k) of the adjusted matrix is obtained as follows:

Equation 10.7:           ${}_{j,k}{}^{D}Q{}_{t,t+2}^{*}={}_{j,k}{}^{D}Q{}_{t,t+2}+{}_{j,k}{}^D\Delta {}_{t,t+2}\times \frac{{}_{j,k}{}^{D}Q{}_{t,t+2}}{{}_{j,k}{}^{D}Q{}_{t,t+2}+{}_{k,j}{}^{D}Q{}_{t,t+2}}$

where

Various adjustments are made to matrix ${}_{}{}^{D}Q{}_{t,t+2}^{*}$ to avoid negative values or division by zero.

This matrix contains the final quarterly numbers of migrants adjusted so that the net numbers match those of the sum of the three corresponding monthly matrices.

Final interprovincial migration estimates, subprovincial areas

The methodology used to produce final estimates of interprovincial migration at the subprovincial level is essentially the same as the provincial/territorial estimates, and are based primarily on the T1FF. As the migration estimates are produced initially at the CD, CMA and CA level (see section Final interprovincial migration estimates), the calculation of in-migrants, out-migrants, and net migrants can also be performed at these subprovincial levels. A calibration step is also included to ensure consistency with the provincial/territorial estimates.

For interprovincial migration by economic regions (ERs), the final estimates are produced by aggregating CD totals for each corresponding ER. The estimates are then calibrated to ensure consistency with the provincial/territorial estimates.

Limitations of final interprovincial migration estimates

Although the T1FF has strong coverage of the population,^{Note 3} adjustments are still required to cover the entire population. An assumption is introduced through the adjustments where the migration patterns of those not captured in two consecutive T1FF are the same as those that were captured. It is possible for those not captured in the T1FF to behave differently in terms of migration.

The reference period of two consecutive T1FF is also slightly different from the reference period of annual estimates. The migrations captured in the T1FF (approximately from April to April) may vary from those that would have occurred from the reference period of July 1 to June 30.

The more notable limitation of the T1FF is the frequency and timing at which the data is available. The file is produced on an annual basis and are not available in time for production of preliminary estimates of a given reference period. As such, the CCB is used instead as the primary data source in producing the preliminary estimates of interprovincial migration.

Preliminary interprovincial migration estimates

Data sources

The Canada Child Benefit (CCB) is a tax-free monthly payment made to eligible families with children under 18 years of age. Information from the Canada Child Benefit (CCB) program is provided by the Canada Revenue Agency on a monthly basis, and the data is used to identify migration of children.

The T1 Family File (T1FF) is an annual administrative tax file processed by Statistics Canada. The T1FF contains income and demographic information of tax filers and their dependants for subprovincial geographic areas. The file is created using various administrative data provided by Canada Revenue Agency, including the T1, T4, and the Canada Child Benefit.

Estimation methodology

Preliminary estimates of migration between provinces and territories are produced using CCB data, along with data from T1FF. Because the CCB program is not universal and does not provide direct information on the number of adult migrants, this estimation requires three adjustment factors to derive the complete estimate of interprovincial migration:

1. the program’s partial coverage (i.e. to take into account those who have not applied for the CCB);
2. the differential propensity to migrate between children who are registered to the CCB program and all children;
3. the differential propensity to migrate of adults versus children.

The three adjustment factors use CCB and T1FF data. The methods for estimating the interprovincial migration rates of children (aged 0 to 17 years) and adults (aged 18 years and older) are described in the next section.

Interprovincial migration of children

Given that T1FF are produced annually and are not available when preliminary estimates are being produced, preliminary estimates of interprovincial migration are based on monthly microdata from CCB administrative files, from which the number of child migrants can be extracted. The data can be used to derive information on the usual province or territory of residence of children registered in the CCB program. Therefore, monthly, quarterly and annual migration can be estimated by comparing two CCB microdata files.

The estimation of interprovincial migration of children involves two adjustment factors. The first factor reflects the CCB program's coverage: the ratio of the number of children as estimated by the Demographic Estimates Program, to the number of children who are registered to the CCB program, for each month and province and territory. The second factor, which corrects for any biases resulting from the differential propensity to migrate between children who are registered to the CCB program and all children, is obtained by comparing the interprovincial out-migration rates of children who are registered to the CCB program with the out-migration rates for all children (aged 0 to 17). The adjustment factor is calculated for each province and territory and is based on the two last available years of the T1FF.

A matrix is used to represent interprovincial migration between 13 provinces and territories of origin (denoted by j) and 13 destination provinces and territories (denoted by k). Each item (j,k) of the matrix represents both the number of out-migrants from province or territory of origin j and the number of in-migrants to destination province or territory k.

The formula used to estimate each item (j,k) of the matrix for the interprovincial migration of children is as follows:

Equation 10.8:                       ${}_{j,k}M{}^{0-17}={}_{j,k}{}^{CCB}M{}^{0-17}\times \frac{1}{{}_j{}^{CCB}\Re }\times {}_{j}G$

where

The equation above includes the adjustments for incomplete coverage of CCB-children who are registered to the CCB program (Equation 10.9) and for the differences in the propensities of this group to migrate as compared to all children (Equation 10.10).

The coverage rates are calculated as follows:

For each province or territory,

Equation 10.9:                       ${}_j{}^{CCB}\Re =\left[\frac{{}_j{}^{CCB}P{}^{0-17}}{{}_j{}^{Dem}P{}^{0-17}}\right]$

where

The differential migration propensity is based on a set of Gj factors. Using tax data, the Gj factors are obtained by dividing the interprovincial out-migration rates for all children by the out-migration rates of children who are registered to the CCB program, as follows:

For each province and territory:

Equation 10.10:                     ${}_{j}G=\left[\frac{{}_j{}^{TIFF}Rate\_M^{0-17}}{{}_j{}^{CCB}Rate\_M^{0-17}}\right]=\frac{\left[\frac{{}_j{}^{TIFF}M{}^{0-17}}{{}_j{}^{TIFF}P{}^{0-17}}\right]}{\left[\frac{{}_j{}^{CCB}M{}^{0-17}}{{}_j{}^{CCB}P{}^{0-17}}\right]}$

where

The Gj factor will equal one if the migration rate of children who are registered to the CCB program and the migration rate of all children are identical. A value of Gj that is greater (or less) than one indicates that the propensity to migrate of children who are registered to the CCB program is less (or greater) than that of all children.

Interprovincial migration of adults

The second factor for adjusting the estimates produced using CCB data is used in the calculation of the number of adult migrants. Estimates of adults migrating across provincial or territorial boundaries are obtained by calculating modelled migration ratios of adults to children, called the F factors. The F factors, which are calculated using the most recent T1FF data, are the ratio of the adult migration rate to the child migration rate, by province or territory of origin and by destination province or territory, as follows:

For each province and territory of origin and each destination province and territory,

Equation 10.11: ${}_{j,k}F{}_{t-3,t}=\left[\frac{{}_{j,k}Avg\_Rate\_M^{18+}}{{}_{j,k}Avg\_Rate\_M^{0-17}}\right]=\frac{\left[\frac{{}_{j,k}{}^{T1FF}M{}_{t-3,t-2}^{18+}+{}_{j,k}{}^{T1FF}M{}_{t-2,t-1}^{18+}+{}_{j,k}{}^{T1FF}M{}_{t-1,t}^{18+}}{{}_j{}^{Dem}P{}_{t-2}^{18+}}\right]}{\left[\frac{{}_{j,k}{}^{T1FF}M{}_{t-3,t-2}^{0-17}+{}_{j,k}{}^{T1FF}M{}_{t-2,t-1}^{0-17}+{}_{j,k}{}^{T1FF}M{}_{t-1,t}^{0-17}}{{}_j{}^{Dem}P{}_{t-2}^{0-17}}\right]}$

where

The Fj,k factors once applied to the child migration rates (based on adjusted CCB data) produces estimates of adult interprovincial migration rates. These are then multiplied by the provincial or territorial populations to obtain estimates of the number of adults migrating between provincial and territorial borders, as follows:

For each province and territory,

Equation 10.12:                     ${}_{j,k}M{}^{18+}=\frac{{}_{j,k}M{}^{0-17}}{{}_j{}^{Dem}P{}^{0-17}}\times {}_j{}^{Dem}P{}^{18+}\times {}_{j,k}F{}_{t-3,t}$

where

Finally, after estimates for the total numbers of interprovincial child and adult migrants have been separately calculated by province or territory of origin j and destination province or territory k, interprovincial migration estimates are obtained by adding the number of interprovincial child and adult migrants as follows:

For each province and territory,

Equation 10.13:                     ${}_{j,k}M={}_{j,k}M{}^{0-17}+{}_{j,k}M{}^{18+}$

Preliminary interprovincial migration estimates by age and gender

To produce the preliminary interprovincial migration estimates by age and sex at the provincial and territorial level, the average of three most recent age and gender distributions of final estimates is applied. This procedure has been used for estimates from 2021/2022 onwards.

For details on the previous methodology, please refer to the 2015 edition of this publication.

Aligning estimates from different measurement periods

The monthly, quarterly and annual number of migrants can be calculated using monthly CCB microdata. However, adjustments must be made to the numbers of migrants to align the net interprovincial migration of the different measurement periods for which estimates are derived, similarly to those performed for final estimates (see section Final interprovincial migration estimates).

Aligning monthly net numbers with quarterly net numbers

Each quarter, monthly data must be adjusted to align the monthly net numbers with the quarterly net numbers.

First, the difference between the net values of the sum of the three monthly matrices and those of the quarterly matrix is calculated for each combination of origin and destination:

Equation 10.14:                     ${}_{j,k}{}^P\Delta {}_{t,t+2}=\left({}_{k,j}{}^{P}S{M}_{t,t+2}-{}_{j,k}{}^{P}S{M}_{t,t+2}\right)-\left({}_{k,j}{}^{P}Q{}_{t,t+2}-{}_{j,k}{}^{P}Q{}_{t,t+2}\right)$

where

These differences are used to change the number of migrants to create a new matrix in which the net numbers match those of the quarterly matrix.

Each item (j,k) of the adjusted matrix is obtained as follows:

Equation 10.15:                     ${}_{j,k}{}^{P}S{M}_{t,t+2}^{*}={}_{j.k}{}^{P}S{M}_{t,t+2}+{}_{j.k}{}^P\Delta {}_{t,t+2}\times \frac{{}_{j.k}{}^{P}S{M}_{t,t+2}}{{}_{j.k}{}^{P}S{M}_{t,t+2}+{}_{k.j}{}^{P}S{M}_{t,t+2}}$

where

Various adjustments are made to matrix ${}_{}{}^{P}S{M}_{t,t+2}^{*}$ to avoid negative values or division by zero.

Lastly, for each of the three months in the quarter, the adjusted monthly interprovincial migration matrix is derived using the matrix resulting from the equation above. Each matrix item (j,k) is adjusted as follows:

Equation 10.16:                     ${}_{j,k}{}^{P}M{}_t^{*}={}_{j,k}{}^{P}M{}_t\times \frac{{}_{j,k}{}^{P}S{M}_{t,t+2}^{*}}{{}_{j,k}{}^{P}S{M}_{t,t+2}}$

where

This matrix contains the preliminary monthly numbers of migrants adjusted so that net numbers match the quarterly net interprovincial numbers.

Aligning monthly net numbers with annual net numbers

Each year, the monthly interprovincial migration estimates must be adjusted to align the monthly net numbers with the net numbers of the annual matrix.

The adjustment involves calculating the difference between the net numbers of the sum of the 12 monthly matrices ${}_{}{}^{P}M{}_t^{*}$ and the net numbers of the annual matrix for each combination of origin and destination:

Equation 10.17:         ${}_{j,k}{}^P\Delta {}_{t,t+11}=\left({}_{k,j}{}^{P}S{M}_{t,t+11}^{*}-{}_{j,k}{}^{P}S{M}_{t,t+11}^{*}\right)-\left({}_{k,j}{}^{P}A{}_{t,t+11}-{}_{j,k}{}^{P}A{}_{t,t+11}\right)$

where

These differences are then used to change the number of migrants to create a new matrix in which the monthly net numbers match the annual net numbers.

Each item (j,k) of this matrix is calculated as follows:

Equation 10.18:         ${}_{j,k}{}^{P}S{M}_{t,t+11}^{**}={}_{j,k}{}^{P}S{M}_{t,t+11}^{*}+{}_{j,k}{}^P\Delta {}_{t,t+11}\times \frac{{}_{j,k}{}^{P}S{M}_{t,t+11}^{*}}{{}_{j,k}{}^{P}S{M}_{t,t+11}^{*}+{}_{k,j}{}^{P}S{M}_{t,t+11}^{*}}$

where

Adjustments are made to matrix ${}_{}{}^{P}S{M}_{t,t+11}^{**}$ to avoid negative values or division by zero.

Lastly, for each of the 12 months, the adjusted monthly interprovincial migration matrix is derived by obtaining each item (j,k) as follows:

Equation 10.19:         ${}_{j,k}{}^{P}M{}_t^{**}={}_{j,k}{}^{P}M{}_t^{*}\times \frac{{}_{j,k}{}^{P}S{M}_{t,t+11}^{**}}{{}_{j,k}{}^{P}S{M}_{t,t+11}^{*}}$

where

This matrix contains the preliminary monthly numbers of migrants adjusted so that the net numbers match the annual net interprovincial numbers.

Aligning quarterly net numbers with annual net numbers

Each year, when the annual matrix is created, the quarterly net numbers must also be aligned with the annual net numbers.

The adjustment involves calculating the difference between the net numbers of the quarterly matrix and those of the sum of the matrices for the three months of the quarter. Note that net interprovincial migration in the preliminary monthly matrices has already been aligned with annual net numbers.

Equation 10.20:         ${}_{j,k}{}^P\Delta {}_{t,t+2}^{*}=\left({}_{k,j}{}^{P}Q{}_{t,t+2}-{}_{j,k}{}^{P}Q{}_{t,t+2}\right)-\left({}_{k,j}{}^{P}S{M}_{t,t+2}^{**}-{}_{j,k}{}^{P}S{M}_{t,t+2}^{**}\right)$

where

The differences are then used to change the quarterly number of migrants so that the net numbers of the quarterly matrix match those of the sum of the net numbers of the monthly matrices for the three corresponding months.

Each item (j,k) of the adjusted matrix is obtained as follows:

Equation 10.21:         ${}_{j,k}{}^{P}Q{}_{t,t+2}^{*}={}_{j,k}{}^{P}Q{}_{t,t+2}+{}_{j,k}{}^P\Delta {}_{t,t+2}^{*}\times \frac{{}_{j,k}{}^{P}Q{}_{t,t+2}}{{}_{j,k}{}^{P}Q{}_{t,t+2}+{}_{k,j}{}^{P}Q{}_{t,t+2}}$

where

Adjustments are made to matrix ${}_{}{}^{P}Q{}_{t,t+2}^{*}$ to avoid negative values or division by zero.

This matrix contains the preliminary quarterly number of migrants adjusted so that the net numbers match the annual net interprovincial numbers.

Preliminary interprovincial migration estimates, subprovincial areas

For preliminary estimates of interprovincial migration at the CD, CMA and CA level, CCB administrative files are used to estimate the migration of children (aged 0 to 17), while the migration of adults is derived using rates based on previous year’s final data. A calibration step is also included to ensure consistency with the provincial/territorial estimates.

For interprovincial migration by economic regions (ER), the preliminary estimates are produced by aggregating CD totals for each corresponding ER. The estimates are then calibrated to ensure consistency with the provincial/territorial estimates.

Limitations of preliminary interprovincial migration estimates

The adjustments for coverage as well as propensity for the CCB implies some assumptions in the estimation. The first is that the migration pattern of children not captured in the CCB is the same as those that are captured. The other assumption is that the differential propensity of migration is the same as the previous year. Although both assumptions are considered as reasonable, it is possible for the migration pattern and the propensity to be different.

With regards to provincial estimates, as the information from the CCB focuses on children, the migrations of adults are calculated based on the migration ratios of adults to children. However, the migration patterns of the two groups can diverge at times. For subprovincial estimates, the migration of adults is derived using rates based on previous year’s final data. It is certainly possible for migrations of adults to change abruptly from one year to the next. These limitations are addressed once the T1FF data becomes available, with the production of final estimates of interprovincial migration.