Microsimulation model projecting small area populations using contextual variables: An application to the Montreal metropolitan area, 2006–2031

Most demographic projections are realized at the national or regional levels and are mainly used for planning of public policies at this broader level. Using cohort-component or multi-state approaches these models are not adequate for planning of local services and needs, such as places in childcare or services for the elderly because they are unable to account for all the spatial interactions (Harding, Vidyattama et al., 2011). Yet, local and municipal governments also need tools for planning, in particular to ensure public services under their responsibility (aqueducts, parks, waste collection, etc.) and urban planning (Isserman 1984; Foss 2002; Swanson & Pol 2008). Small area population projections have unquestionable value: they can be used for planning purposes, but also in a prospective approach such as measuring the impact of a change in public policy, such as zoning, on the spatial distribution of the population (Ballas, Clarke et al., 2005a; Wilson 2011).

In addition, population projections at the local and municipal level have to account for the dynamic of residential segregation (Yin 2009). While in many North American cities residential segregation is related to ethnic or racial groups, Montreal differs from other North American cities by the presence of two main linguistic groups: the francophone majority, descendants of the first colonists who came from France and founders of the city, and a wealthier English-speaking minority which gradually developed after the British conquest of New France (Brunet 1955; Vaillancourt 1985; Séguin 1987). Montreal is also the port of entry of a large majority of immigrants landing in the province of Québec and recent high levels of increasingly diverse immigration has favored the emergence of another, more heterogeneous, linguistic group: the allophones, a term which in Canada defines those who speak another language than French or English at home. While racial or ethnical spatial segregation doesn’t appear to be important in the Montreal area, a spatial pattern is clearly apparent in the residential choice of linguistic groups (Marois & Bélanger 2014, Marois and Bélanger 2014, Forthcoming).

The aim of this paper is to present the small area population projection model that we developed to project the population of municipalities of the Montreal Metropolitan Community (MMC). The model is innovative in its treatment of migration, the most technically and conceptually difficult component of change to model in small area population projections. To meet these challenges, we build a dynamic time-based microsimulation projection model in which the choice of municipality of residence is determined by a utility function that considers municipality-specific contextual factors. The time horizon of the projection is from 2006 to 2031. This model has an additional objective: assess the evolution of linguistic groups at a local level.

Small area population projection models are subject to specific methodological challenges that are less important for national population projections. Given the small size of the population, it is more difficult to accurately estimate the component of changes for small areas (Keyfitz 1972; Ballas, Rossiter et al., 2005b; Lutz 2009; Cameron & Poot 2011). This problem is particularly important for events that have a strong geographic dimension, such as internal migration and destination choice of external migrants (Ballas, Rossiter et al. 2005b). Furthermore, because for several origin-destination flows, the number of migrants is small to non-existent, a robust origin-destination matrix to determine the migration pattern can hardly be built.

Given the importance of migration on population growth and change at the local level and given the instability of migration patterns over time, the accuracy of the projection can be greatly affected by mobility assumptions (Sanderson, Dal et al. 2010, Cameron & Poot 2011). At this level, individual decisions regarding choice of a place of residence depends on the changes over time in each potential location relative to all other alternatives. Thus, another difficulty faced when projecting small area populations is related to the implementation of contextual factors which may highly influence individual decision-making and local population growth. A rigorous small area population projections model must also take into account those contextual variables that can be determining factors in the migrants’ decision-making, such as the distance from a central point, the socio-demographic composition or physical characteristics of the territory (Murdock, Hamm et al. 1991; Chi, Zhou et al. 2011). Similarly, urban planning can sometimes affect the projection since it has a major role in housing supply (Murdock, Hamm et al. 1991, Dittgen 2008, Bergouignan 2010). Geographical and contextual variables should thus be implemented as parameters to avoid the self-fulfilling effect of projections (e.g., when the urban plan is modified to integrate previous projection results). However, most small area projection models ignore contextual and environmental factors. Accordingly, traditional demographic methods such as the Hamilton-Perry method, the top-down method or the iterative proportional fitting method are generally used (Hamilton & Perry 1962; Birkin & Clarke 1989; Rees 1994; Rees, Norman et al. 2004; Simpson & Tranmer 2005; Ballas, Clarke et al. 2005a; Institut de la statistique du Québec 2010; Menthonnex 2010; Swanson, Schlottmann et al. 2010).

The method proposed in this paper to model internal migration and residential-choice combines elements from the life cycle approach and the random utility model. Most studies seeking to explain individual decisions regarding residential mobility are based on the life cycle approach (Glick 1947; Rossi 1955; Landale & Guest 1985; South & Crowder 1997; Kim, Horner et al., 2005; Æro 2006; Marois & Bélanger 2014). This approach suggests that events that mark the life cycle, such as union formations and dissolutions, births of children, or the departures of children from parental house, are determinants of residential mobility, because the residential needs of the family are changing after the occurrences of these events. Since they are generally correlated with age, this variable is therefore a key determinant of residential mobility.

The literature distinguishes two main urban forms in North American metropolitan areas: the inner city, which for conceptual and methodological reasons is often defined as the central municipality, and the suburb. The inner city can be seen as a place of transition, especially for young people who study or are in search for a first job and a partner (Kasarda, Appold et al., 1997; Glaeser, Kolko et al., 2001; Fréchette, Desmarais et al., 2004; Turcotte & Vézina 2010; Marois & Bélanger 2013). According to the life cycle perspective, when they will be professionally stable and will be ready to have children, their preferences will be for larger housing and a quieter environment rather than for employment accessibility. They will therefore leave for the suburbs, if they can. (Frey & Kobrin 1982; Feijten & Mulder 2002; Karsten 2007; Marois & Bélanger 2014).

Because of the large number of municipalities in the Montreal metropolitan area, it is not possible to estimate an origin-destination matrix, especially when the population is disaggregated by age and language groups. But, if the determinants of the decision to move from the central city to the suburb differ from those of a reciprocal move from suburbs’ residents, we can assume that they are similar for residents of all suburban municipalities. Thus, we propose, as a first step in the modeling of internal migration, to stratify migrants according to the type of move rather than by municipality of origin. In the Montreal metropolitan area, the inner city consists of only one municipality (the municipality of Montreal, which is the central city). Residential moves within the central municipality are therefore not considered as a migration event. We can therefore define three types of internal mobility:

1. From a suburb to the central municipality;

2. From the central municipality to a suburb;

3. From a suburb to another suburb.

   In a second step, a new municipality of residence has to be assigned to those internal migrants. In addition, a large number of external migrants also arrive each year in the metropolitan area, some from abroad (international immigrants), some from elsewhere in Canada (interprovincial migrants) and others from other regions of Quebec (intraprovincial migrants) and a municipality has to be assigned to these newcomers too. To account for the various profiles and preferences of these migrants in their location-decision, we regroup them into three additional groups of migrants:

4. International immigrants;

5. Interprovincial migrants;

6. Intraprovincial migrants.

For those who move from a suburb to the central municipality, the model does not need to be more complex, since there is only one possible destination by definition. For the other five groups of migrants, the model must assign a municipality of residence and this is done using the following random utility approach.

Assuming that migrants want to maximize the utility of attributes of the municipality they choose as destination, this approach can be defined as follow. Let $U_j^t$ be a utility function for each possible alternative j for individual of type t, where t is the type of migrants (from the central municipality, from another suburb, from another country, from another province and from the rest of Quebec) and j the number of municipalities which has a set of zn characteristics. Thus, we have:

where

${\text{U}}_{\text{j}}^{\text{t}}$ = Utility of a municipality j for a migrant type t, j=1…J; t=1…n

z_kj = Value of the independent variable k for the municipality j, j=1…J; k=1…n

β_k = Parameter of the independent variable k, k=1…n

Parameters β_k are estimated by a maximum likelihood method and are constant for each alternative. They estimate the net impact of municipalities’ characteristics. We seek to estimate the probability that an individual i of type t chooses the municipality j with $U_j^j$ utility function. Thus, we have:

In this way, contextual variables can be included as explanatory variables of migrants’ decision for a municipality of destination. In the context of Montreal, previous analysis has shown the importance of the municipality’s accessibility and housing offer, as well as of the linguistic composition of the municipality (Marois & Bélanger 2014, Forthcoming). Additional variables such as the average value of housing and the socio-economic composition of the municipality also became apparent from the analysis, but since reliable long-term assumptions for them are not available, they are not included in the population projection. Therefore, five municipality-specific variables are included in the model:

1. Distance from the downtown area;

2. Population size;

3. Number of new housings;

4. Linguistic composition;

5. Geographical position.

The proposed method for residential location modeling focuses on individual preferences which vary according to personal characteristics. The projection model must therefore use a micro approach and microsimulation is the preferred method. Microsimulation simulates processes and life events (e.g., mortality, fertility, residential mobility, etc.) of individuals following behavioral assumptions which parameters are derived from empirical data (Orcutt 1957). The probability that each type of events occurs is calculated for each individual and the occurrence of a particular event is determined using a Monte Carlo process. Following the event, characteristics of the simulated individual may change (life status is changed to dead, number of births is incremented, place of residence changes, etc.). Statistical indicators, such as population size, age structure, socio-demographic composition, etc. can then be computed from the aggregation of individual data. Post and Van Imhoff (1998) argue that microsimulation is particularly appropriate when “the problem requires a large state space” (p. 107). The possibility of including a large number of individual attributes is another major advantage of microsimulation compared to a component-cohort method. This method is then appropriate for local projections because of the large number of municipalities and individual characteristics that are simultaneously projected.

Montreal is the second most populous metropolitan area of Canada after Toronto. The Montreal Metropolitan Community (MMC)¹ regroups 82 municipalities into a supra-municipal entity². The population of the MMC is estimated to 3.7 million residents in 2010. The MMC is active in land use planning and economic development, public transit and metropolitan arterial road network developments, waste management planning and social housing. With more than 1.6 million people, the municipality of Montreal is the central city, while the rest of the MMC compose the suburb (78 municipalities). Map 1 spatially illustrates the municipalities under study and shows their grouping into regional county municipality (RCM)³, a spatial aggregation used for some variables in the analysis.

Figure 1

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Our dynamic time-based microsimulation model is called LDS (Local Demographic Simulations) and is built using SAS Software. The starting population is extracted from the 2006 Census and the projection’s horizon is 2031. The 20% microdata file of the 2006 Canadian Census⁴ provides a large database (682 000 respondents in the MMC territory) with all the individual characteristics necessary for our model. It makes up our starting population. Its large sample size is useful to ensure robust estimates of relatively rare events and to reduce the Monte Carlo error inherent to microsimulation. The following characteristics are extracted from the database:

1. Age (0 to 119);

2. Sex (male or female);

3. Municipality of residence (79 municipalities of the Montreal Metropolitan Community);

4. Place of birth (in Canada, foreign-born);

5. Year of arrival in Canada (specific to foreign-born);

6. Language spoken at home (English, French or other).

   From these variables, we derive four other variables that will be used in different modules:

7. Age at immigration (specific to foreign-born);

8. Number of years since arrival (specific to foreign-born);

9. Regional county municipality of residence;

10. Type of municipality (central municipality or suburb).

To account for the net census undercount (2.07% in Quebec), we reweighted the population using the 2006 population estimate by age groups and municipalities (Institut de la statistique du Québec 2013). Each individual weight is corrected using an age group-municipality-specific factor.

Modeled events are represented schematically in Table 1, with the independent variables where appropriate:

Characteristics at the beginning of the period are used to estimate the likelihood of each event. For example, a 20 year old woman living in a given municipality at the beginning of the year who migrates to another municipality during the year has the probability of giving birth of women aged 20 living in the initial municipality for all the period. Only in the following year, when she will be 21 at the beginning of the year, will her probability of giving birth change.

Our projection starts with the 2006 population, but we have age-municipality specific population estimates for 2011. Therefore, we are using the period 2006–2011 to validate and calibrate the parameters of the model prior to the 2011–2031 projection.

Once the 2011 population resulting from the simulation is calibrated with the 2011 population estimates, we can run the 2011–2031 population projection. Results from this simulation are presented in the column 6 of annex 1. Map 2 presents population growth rates by municipality and Table 8 presents a synthesis of the results.

Figure 2

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The projected growth between 2006 and 2031 for the whole MMC is 27.5%, which is consistent with the official population projection (Institut de la statistique du Québec 2010). The projected growth varies widely between municipalities from −38.1% to 82.9%. Municipalities that will have the fastest expected relative growth are located on the North Shore, mostly those which are at the limit of the MMC. These municipalities are new suburbs where the development potential is the largest according to urban plans. Our model predicts low growth for most municipalities on the island of Montreal (RCM66, see Map 1) and in oldest suburbs (RCM58, RCM72 and RCM73), where housing potential development are much lower because the land is already occupied. This shows the importance of this variable in small area population projections. Urban sprawl, however, could be limited by protecting agricultural land and increasing residential density in other parts of the MMC to absorb projected population growth, but this would necessitate major policy changes, which are clearly not in the assumptions of the authors of the urban plans.

As for the rest of the country, an important population aging is expected in the MMC. Our results show that the proportion of people aged 65 and over will grow from 13.2% in 2006 to 19.2% in 2031. Overall, this age group will increase from about 475,000 people to 893,000 people, or by 88.1%. However, population aging won’t affect all municipalities in the same way. Map 3 displays the projected growth of the population aged 65 and over by municipality and clearly shows rapid population aging in several suburban municipalities. Actually, municipalities that currently or in the near future show fast population growth and are attractive to young families, will see faster population aging. In the future, parents of these families will age in place, while their children will more likely migrate to the central municipalities or elsewhere. As a result, the population aged 65 and over can quadruple in some of them between 2006 and 2031. At the opposite end, because this process of aging-in-place and migration of the youths is already much completed in the central municipality and in the oldest suburbs of the inner ring, the future growth of the elderly population will be relatively much smaller.

Figure 3

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The main advantage of microsimulation is that it can generate results along several dimensions, such as linguistic characteristics in this case. In the Montreal context, where the spatial distribution of population by language groups is the subject of constant debates (Termote, Payeur et al. 2011), it should be of interest to look at projected results by language.

Table 9 presents the distribution of municipalities according to the relative rate of change in the proportion of francophones from 2006 to 2031. Overall, for the whole MMC, the proportion of francophones declines from 69.7% in 2006 to 63.8% in 2031, a loss of 6 percentage points, which is consistent with a similar projection for the Montreal metropolitan area (Termote, Payeur et al. 2011). The range of the variation varies from −28.3 to 17.1 percentage points. Our results show that the proportion of francophones will decline in 65 of the 79 municipalities. This is mainly caused by the low fertility of Canadian-born population and high immigration of non-francophones. At the opposite, our projection predicts an increase of the proportion of francophones in 14 municipalities.

Small area population projections are subject to particular challenges. One of them is to take into account local conditions that may affect future population growth, particularly through residential moblity. In this study, we present a dynamic time-based microsimulation model, called LDS, that includes, among others variables, the planned number of new houses and the distance from downtown as determinants of residential location for internal and external migrants to project the population of the Montreal Metropolitan Community’s municipalities. Furthermore, it takes into account the particular context of Montreal as the only metropolis in North America that is the home of a large francophone community and is receiving a large influx of immigrants from diverse origins and languages. We thus add to our model differential behaviors according to linguistic groups for mobility, residential location and reproduction, so the model can also project population at a local level by language groups.

Many small area projection models exist, but the one developed in this paper innovates in its treatment of mobility. We used conditional logistic regressions to estimate parameters used as assumptions of the residential location module. The method allowed for the implementation of the effect of contextual variables such as planned new housings from urban development plans, socio-demographic composition and of geographical location as determinants of future residential location process. Moreover, concerning the socio-demographic composition of the population, we develop LDS with a specific interest to linguistic variable which is an important issue in the Montreal metropolitan area context, but its methodology could be transposed to other variables, such as family composition, race or ethnicity which are also parameters that determinate mobility.

Like all models, our model has some limits. The parameters used to model residential location performs generally well, but for some municipalities, the discrepancy can be important and parameters were subject to some calibration. Another limit concerns the geographic scale. For a large city like Montreal, projections at the neighbourhood level might be useful, but the Census question on place of residence one year ago does not allow the analysis of mobility at a finer geographical scale than the municipality.

This small area population projection model reveals some trends that could challenge public policies. One of them is the continuous urban sprawl implied mostly by the urban development plans used as assumptions. Municipalities with the fastest expected growth are located far from the core, where farm and forest lands still exist. The second challenge concerns the investment in local infrastructure to face the aging of the population. Municipalities where the elderly population is expected to grow the fastest are those that nowadays attract young families. In the next decades, their infrastructure might need to be adapted for this changing population. Another result from our projections which can be of concern to policy-makers is the relative decline of the French community, which will be generalized in most of the MMC. As the language most commonly spoken in the neighbourhood is an important determinant of linguistic integration of allophones (Carpentier 2004), the relative decline of French in most municipalities could therefore be an obstacle to the adoption of French by the fast-growing foreign-born population.

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Author details

1. Guillaume Marois

   INRS – Centre Urbanisation Culture Société, Canada

   For correspondence

   Guillaume_marois@ucs.inrs.ca

2. Alain Bélanger

   INRS – Centre Urbanisation Culture Société, Canada

   For correspondence

   Alain_belanger@ucs.inrs.ca