Methods and concepts

Base Population
Updating of variables, estimation of parameters and data sources

The Demosim microsimulation population projections model was used to develop the projected data that are the subject of this report. This model, which simulates the individuals in the population one by one rather than proceeding on the basis of aggregate data, was also used to prepare Projections of the Diversity of the Canadian Population, 2006 to 2031, released in 2010. However, a number of additions have since been made to that model to make it possible to carry out the projections presented here. As a result of these recent developments, Demosim lends itself to a detailed projection of Aboriginal populations at the same time as non-Aboriginal populations (see Box 1).

Although the more general capabilities of Demosim have already been described elsewhere (Statistics Canada, 2010), it is useful to present here, albeit briefly, a few of its characteristics that will give the reader a better understanding of the exercise that was carried out. In this section, the emphasis is on the features of the model that are more specific to Aboriginal populations. Readers interested in other aspects of the model are invited to refer to the existing documentation. The section that follows, which merely supplements that body of information, contains a few inevitable repetitions.

Base population

The microdata file for the 20% sample of the 2006 Census serves as the base population for projections of populations according to Aboriginal identity to 2031. That file was initially adjusted to take account of net undercoverage in the census by age, sex and province/territory^{Note 1} of residence of the population living off reserve. This adjustment was made by modifying the sampling weights for the records in the initial file, for both Aboriginal and non-Aboriginal populations, who are consequently assumed to be equally undercovered in the targeted areas.^{Note 2} A similar adjustment was subsequently made for the population enumerated on Indian reserves, this time using undercoverage rates for two major regions: one consisting of all reserves enumerated in 2006 and located in Ontario or provinces further east, and the other consisting of the reserves in the rest of Canada. For these reserves, the distribution of net undercoverage by age and sex was assumed to be identical to that for the population living off reserve. For reserves incompletely enumerated in 2006, we assumed a population size equal to that estimated by Statistics Canada’s Social Survey Methods Division, and we then carried out imputation so that their population would have characteristics representative of the populations of enumerated reserves.^{Note 3} These adjustments were made with a view to ultimately obtaining a total population that would be representative of the population estimated by the Demography Division at May 16, 2006, by single year of age, sex and province/territory.

The base population includes a large number of variables such as  Aboriginal identity, Registered Indian status, place of residence, age, sex, highest level of education, number of children at home, marital status, place of birth, visible minority group, generation status and immigration period. Aboriginal identity, which is the main variable of analysis in this report, includes, as in the 2006 Census, the following categories:

• North American Indian, single response;
• Métis, single response;
• Inuit, single response;
• Other Aboriginal responses^{Note 4};
• Non-Aboriginal identity population.

The geography on which the projections are based corresponds to the standard geographic structure of the 2006 Census. It includes the following geographic entities:

• The 33 census metropolitan areas (CMAs), including the distinction between the Ontario portion and the Quebec portion of the Ottawa-Gatineau CMA^{Note 5};
• The portion of each province that is not included in a CMA (e.g., Non-CMA Manitoba);
• Indian reserves;
• Regions comprising Inuit Nunangat.

As for the other variables, even though they are not emphasized in the analysis provided in Section 4, they are nevertheless projected and updated in the course of simulation. Among other things, this ensures that they can be taken into consideration as explanatory variables for events likely to affect how Aboriginal and/or non-Aboriginal populations evolve in the future. For example, highest level of education serves as a determinant of mortality, fertility and also internal migration. Similarly, Registered Indian status is used in projecting fertility, highest level of education and internal migration.

The fact that the current model, unlike earlier models used in similar exercises, takes not only Aboriginal but also non-Aboriginal populations as a starting point and projects them simultaneously, offers certain advantages:

• It makes it possible to calculate, for each scenario, percentages of Aboriginal people within the overall population of a given region in a coherent manner; that is, without resorting to a set of external projections—which can be difficult to compare because of their methodology and assumptions—in order to obtain denominators;
• It lends itself to the dynamic simulation of transfers to and from Aboriginal populations, through either intergenerational or intragenerational ethnic mobility (see Box 1), with persons making “entries” and “exits” being selected within continually updated “populations at risk”;
• It increases the analytical potential of the results obtained, in particular by increasing the number of points of comparison.

Updating of variables, estimation of parameters and data sources

The updating of variables during the projection process, as well as the addition of births and immigrants, is done in continuous time in Demosim. This updating is facilitated by Modgen, a programming language developed and maintained at Statistics Canada that is dedicated to microsimulation, and is performed using waiting times between a given moment in the life of an individual and the occurrence of events that the individual is likely to “experience” in the course of simulation.^{Note 6} Waiting times depend on a random process, individuals’ characteristics and the probabilities of experiencing each of the events included in the projection model (death, migration, etc.). They are recalculated a number of times in the course of simulation to take account of the changes that individuals “experience”; changes that are likely to alter their probabilities of subsequently “experiencing” other events. These probabilities, or parameters, which may vary over time and are dependent on various factors, are obtained from models or rates that were calculated using various data sources:

• Population censuses
• Surveys
• Administrative data
• Population estimates
• Data linkages

The availability of high-quality data for making these calculations poses a major challenge, especially regarding Aboriginal populations. The choice of the methods and independent variables selected when developing the projections was based on the available data, just as the choice of data sources (when more than one was available) was based on their quality, frequency and content. Sometimes, as was the case for mortality, it was necessary to use more than one source to calculate probabilities. Doing so necessarily entailed limitations with respect to coherence, but these limitations were considered preferable to those inherent in simply ignoring part of the available information.

The rest of this section will briefly describe the main methods and data sources used to calculate the parameters utilized in these projections. For a number of Demosim modules,^{Note 7} the methods used are identical to those used to develop the Projections of the Diversity of the Canadian Population, 2006 to 2031 (Statistics Canada, 2010), especially regarding the simulation of non-Aboriginal populations. Therefore, not all of those modules are described here (in which case, see their description in Statistics Canada, 2010). Table 1 summarizes the Aboriginal-related content of the main modules of the model used to prepare the results presented in this report.

Table 1 Key methods, data sources and variables used for parameter estimates specific to Aboriginal peoples in Demosim

Fertility

Since there were no direct data on the fertility of the three main Aboriginal identity groups projected, an indirect method—the own-children method,^{Note 8} was applied to data from the 2006 Census to obtain an estimate of this component.^{Note 9} On this basis, the fertility module was created in two main stages. In the first stage, we calculated the base risks of giving birth to a child, derived from fertility rates, age and number of children in the home. These rates were estimated separately for Aboriginal and non-Aboriginal peoples. In the second stage, using log-log regression models stratified by age group, number of children in the home and Aboriginal/non-Aboriginal status, we calculated the relative risks of giving birth to a child, and we used them to increase or decrease the base risks according to various independent variables. For the models relating to Aboriginal peoples, these variables are: Aboriginal identity, Registered Indian status, detailed place of birth (including CMAs, non-CMA portions of provinces, Indian reserves and Inuit Nunangat), marital status, highest level of education and age.^{Note 10} Since the fertility rates of Aboriginal and non-Aboriginal populations were modelled separately, projection assumptions were created for these two groups.

Intergenerational ethnic mobility

These data, derived from the 2006 Census by means of the own-children method, were also used to create parameters for intergenerational ethnic mobility. These parameters, which are intended to model the transmission of identity to newborns during simulation, were obtained by cross-tabulating the Aboriginal identity of the youngest children with that of their mother. The matrixes that were created take account of the mother’s place of birth, Registered Indian status and visible minority group. Thus, some Aboriginal women will give birth to children who will not be Aboriginal persons—or who will have an Aboriginal identity different from theirs—just as some non-Aboriginal women will give birth to children who will have an Aboriginal identity, in accordance with the estimates of the 2006 Census.

Intergenerational transmission of Registered Indian status

The assignment of Registered Indian status to newborns is subject to rules determined by the Indian Act that take the status of both the mother and the father into account, and therefore it was modelled somewhat differently. The link between children and their father was not simulated, unlike the link between the mother and her children. Accordingly, to determine the status of the newborn, we first considered both the mother’s status and the mixed/non-mixed nature of the union (i.e., Demosim can determine, by modelling, whether or not a woman in a union has a registered spouse) that she was in when she gave birth.^{Note 11} The general principle is as follows. If the mother is a Registered Indian in a non-mixed union, that is, if she is in a union with a Registered Indian, then the child will also be registered. If the mother is not registered and is not in a mixed union, then the child will also be non-registered.^{Note 12} If the woman is in a mixed union, regardless of whether she is registered, then we use mother-to-child status transmission matrices constructed like those used for modelling intergenerational ethnic mobility. These matrices take into account the marital status and Registered Indian status of mothers in mixed unions, as well as the identity of the newborns. Matrices are also used if the mother is not in a union at the time she gives birth. Registered Indian status is also assigned to newborns during the simulation in accordance with the provisions of paragraphs 1 and 2 of article 6 of the Indian Act of 1985, where possible. This status is then used to assign Registered Indian status to their own children.

Mortality

There are sizable data gaps in the case of Aboriginal mortality since, at the national level, vital statistics do not contain information on Aboriginal groups. Therefore, several data sources, each with a number of limitations, had to be combined to create this module.

For the non-Inuit population aged 25 and over, a two-stage method was used, similar to the one employed to develop fertility parameters. First, base risks of dying were derived from mortality rates by age and sex for the overall population, which were projected using a variant of the Lee-Carter model (Li and Lee, 2005) applied to vital statistics data from 1981 to 2006.^{Note 13} Relative risks of dying were then calculated using proportional risk regressions estimated on a database that matches the 1991 Census with vital statistics from 1991 to 2001 (census mortality follow-up study, 1991 through 2001).^{Note 14} The relative risks take the following variables into account: Aboriginal identity,^{Note 15} residence on or off reserve, province, visible minority group, immigrant status and immigration period, highest level of education and age. The models were calculated by broad age group and sex.

The latter database—the census mortality follow-up study, 1991 through 2001—does not include the population under 25 years of age. Moreover, because of the limitations inherent in the matching process that was used to create it, the database did not lend itself to modelling the mortality of Inuit aged 25 and over, unlike for the rest of the population. Therefore, alternative methods were used for those populations:

• For North American Indians under 25 years of age, we used mortality tables for Registered Indians^{Note 16} from the Indian Register for the period 1996-2000 (most recent tables available). We then calculated differences between Registered Indians and the population as a whole during this period and held these mortality differences constant until 2031.
• For Métis under 25 years of age, lacking tables specific to this population, we used the census mortality follow-up study, 1991 through 2001, to calculate differences between the Métis and the rest of the population aged 25 and over; we then applied these same differences below age 25 and held them constant until 2031.
• For the Inuit population, mortality rates by age and sex were obtained from vital statistics data from 2004 to 2007 for regions with a large proportion of Inuit, using the same method as described in Wilkins, Uppal, Finès, Senécal, Guimond and Dion (2008). Those rates were then projected until 2031, holding constant the differences between the rates for the Inuit population and those projected for Canada as a whole.^{Note 17} In the course of simulation, these mortality rates are applied to all Inuit and to them alone, regardless of their place of residence.

Internal migration

Internal migration parameters were developed so as to project two separate types of migration. The first type, interregional migration, refers to migration between the 47 main geographic entities included in the model, namely census metropolitan areas and the rest of each province. The second, intraregional migration, refers to migration between the reserve and off-reserve portions, as well as between Inuit Nunangat and non-Inuit Nunangat areas, within the portions of the 47 main regions that include Indian reserves and/or Inuit-owned lands. Interregional migration was modelled in two stages. First, the probabilities of leaving each of the 47 regions were obtained from log-log regression models that took account of age group, Aboriginal identity, Registered Indian status, living/not living on reserve or on Inuit-owned land where applicable, education, marital status, number of children at home and age of the youngest of these children, mother tongue, living/not living in province of birth, time elapsed since immigration and visible minority group.^{Note 18} Second, origin-destination matrices were calculated taking account of Aboriginal identity, Registered Indian status, age group, province of birth and mother tongue, in order to allocate migrants among the 46 possible destinations. Additional models were also produced to determine, where applicable, whether or not in-migrants would go to an Indian reserve or Inuit-owned land. In turn, the parameters for intraregional migration consist of migration rates by age group, Aboriginal identity and Registered Indian status.

A final point is that data on interregional and intraregional migration were produced using information on place of residence one year earlier reported in the 1996, 2001 and 2006 censuses, which were aggregated and to which a constant geography was applied. Despite major limitations (for example, see Norris and Clatworthy, 2003), in particular related to sample sizes, these data make it possible to model migration at detailed geographical levels according to a large number of characteristics.^{Note 19}

Intragenerational ethnic mobility

Finally, intragenerational ethnic mobility—in other words, changes in the reporting of Aboriginal identity during an individual’s lifetime—is projected on the basis of results from a cohort flow analysis based first on the 1996 and 2001 censuses, and then the 2001 and 2006 censuses. This method, similar to the one used by Guimond (1999) to analyse this phenomenon for previous periods, is based on a comparison of population counts for a given identity population at age X to counts at age X+5 in the following census. The difference, either positive or negative, is then considered as an estimation of net gains or losses through ethnic mobility. This method was applied, for these population projections, to adjusted census data in order to control for net undercoverage, fertility, mortality and migration. The estimates of net ethnic mobility computed were translated into net rates of ethnic mobility allowing, by region, for changes in Aboriginal identity from non-Aboriginal people to Métis, from non-Aboriginal people to North American Indian and, for a small number of regions, from North American Indian to non-Aboriginal people. The rates, which arise from an average for the periods 1996 to 2001 and 2001 to 2006, also take into account large age groups. They were computed for the population living off-reserve and outside the territories, and excluded Inuit, immigrants and person belonging to visible minority groups. The assumption made for the current projections is that these populations do not experience ethnic mobility. Moreover, for consistency purposes with the databases used to compute the different parameters, “ethnic migrants” continue to be submitted to the probabilities associated with their initial identity during the simulation, even after changing identity.

---

Notes

1. To be more precise, the rates used for Newfoundland and Labrador, Quebec and the Northwest Territories excluded Inuit Nunangat regions (see definition in Box 1). Specific rates were created for Inuit Nunangat as a whole and then applied to the residents of these regions.
2. The available information for the population living off reserve did not support another assumption.
3. The imputation was based on reserves of similar size enumerated in 2006 in the same province or, where possible, on data available in 2001 for reserves that had been enumerated at that time.
4. This category includes multiple Aboriginal responses as well as persons who, without reporting themselves as North American Indians, Métis or Inuit at question 18 of the 2006 Census, reported being Registered Indians or Treaty Indians at question 21, or members of an Indian band at question 20.
5. This makes for a total of 34 census metropolitan areas.
6. See the documentation on Modgen on the Statistics Canada website at Modgen (Model generator). For an overview of the use of microsimulations in the field of population projections, see Van Imhoff and Post (1997).
7. Demosim employs one module per simulated event.
8. This method associates young children (in this case, under one year of age) with the woman in the same census family who is the most likely to be the mother, and it considers this woman as having given birth recently (in this case, in the past year). See Grabill and Cho (1965) and Desplanques (1993) for a description of this method and Ram (2004) for an example of how it is applied for purposes of estimating the fertility of the Aboriginal populations in Canada.
9. Adjustments were made to the data in order to take account of the mortality of young children and women of childbearing age by Aboriginal identity, as well as the fact that some children were not living with their mother at the time of the census. Also, the 2006 Census data were adjusted for net undercoverage.
10. For non-Aboriginal people, the variables considered are immigrant status, immigration period, generation status, visible minority group, place of residence, place of birth, schooling, marital status and age.
11. Only children with an Aboriginal identity can be attributed Registered Indian status during simulation, which means that children are assigned identity prior to status.
12. Although this principle applies in the vast majority of cases, the analysis revealed a small number of registered children both of whose parents were non-registered as well non-registered children living with two registered parents. These numbers are taken into account in the projection.
13. This method is also used to project the mortality of the non-Aboriginal population under 25 years of age by province of residence.
14. For a description of this database, see Wilkins, Tjepkema, Mustard and Choinière (2008).
15. Since there was no question on Aboriginal identity in the 1991 Census, the latter was approximated using the variables available in 1991.
16. Data from the 1991 Census mortality follow-up database show only very small differences between Registered Indians and non-registered North American Indians regarding mortality beyond age 25. Accordingly, the assumption of a match between the mortality of Registered Indians and that of North American Indians overall seems reasonable.
17. Projection for Canada as a whole is carried out in the same way as for the population aged 25 and over.
18. The variables used differ from one region to another, based on population size and the composition of the region.
19. A number of actions were taken to offset the limitations of the data used. For example, the model makes no provision for migration in some regions where the numbers of migrants were insufficient, as well as for incompletely enumerated reserves, whose population was imputed. Additionally, despite the fact that models of internal migration were created so as to be able to simulate the migratory movements of the population as a whole, methodological choices were made with a view to optimizing the migration of Aboriginal peoples by assigning a special value to the variables and geography associated with Aboriginal populations.