**2. Theoretical Background**

Uneven population growth between the core and ring, this paper's main subject, has been extensively studied and modeled, giving rise to the stages defined by the urban development model [23–26]. In short, the model claims that urban areas go through a series of successive stages depending on whether cores or rings grow and on whether the entire urban area increases or decreases. Therefore, the following four stages are extracted from the model: (1) urbanization or centralization; (2) suburbanization or decentralization, (3) desurbanization or counterurbanization, and (4) reurbanization. These four phases are also cyclical, returning to the first phase after the end of the fourth. This cyclical model also helps to explain internal migration between urban centers and peripheries, as core– periphery interactions are reconfigured at each urban population growth phase [27,28]. However, this model has been heavily criticized because empirical research has shown that it presents some major drawbacks [29–32]. For example, many urban areas show non-linear trajectories [29]; that is to say, the four phases do not always follow one another in the order that the model indicates [30]. Moreover, in a given country, some urban areas can be in the suburbanization phase while others are reurbanizing [31]. Simultaneously, it can include instances of both urban growth and shrinkage [32,33]. This diversity among urban areas, which is not explained by the model, can also be found within urban areas, as many suburban towns grow while the populations in their urban cores recover. This simultaneous suburbanization and recentralization may be caused by peripheries receiving inhabitants from city cores, which, in turn, are growing because of immigration from

outside the urban area. These external flows are not adequately captured by the theoretical model of cyclical urban growth, which treats urban regions as closed systems. However, international migrants are not the only ones attracted to urban cores. Other groups, such as young adults, non-family households, and some parts of the middle to upper classes, have also shown a preference for living in city centers in the last decades, whereas young couples with children still tend to move to suburban peripheries. The residential behaviors of families explain why population growth is still higher in the suburbs than in the city cores in most urban areas [30].

Therefore, patterns of population growth and decline in different urban areas and within major metropolitan areas (in cores versus rings) cannot be explained by a cyclical urbanization model but rather by a series of external factors acting on urban areas. For example, economic development and, more specifically, economic cycle phases (expansion, crisis, recession, and recovery) influence urban growth and decline in multiple ways. They act directly through their influence on natural growth [34,35] and, above all, on internal and external migratory growth [21,22]. However, they also have an indirect effect on other mechanisms, such as the housing market, the labor market, family transformations, and changes in socio-residential patterns.

Starting with the housing market, urban development in general and residential and international migration flows in particular are highly dependent on the institutional factors affecting the way that housing market mechanisms function [36], including mortgage access [37] and public housing policies [38,39]. In fact, they are all conditioned by the current economic cycle phase of the country. For example, in Spain, as in other European Mediterranean countries, it is considerably difficult for young people, as well as certain immigrant groups, to afford housing [40]. These difficulties worsened when the economic crisis subsided because of rising purchase and rental prices, particularly in large cities [41]. Although household construction slightly picked up and it was easier to get a mortgage during the post-crisis period, these changes were not able to compensate for this housing affordability problem. On the contrary, financial globalization has favored a rise in prices since housing has become an attractive investment option for small investors and particularly for large funds, rather than satisfying a basic need [42,43]. In some large city neighborhoods, the transformation of dwellings into a financial asset has intensified gentrification [44]. Tourist pressure or "touristification" has also become an additional constraint [45–48] that causes that part of the housing stock is no longer used for residential purposes but rather for tourism demands, thereby reducing the housing supply. All of these processes linked to the housing market have led to a price rise, especially in large cities, resulting in increased residential mobility. Indeed, the growing problems related to housing accessibility and affordability in urban centers have displaced some of their residents, especially in the most attractive neighborhoods. This could be a possible explanation, at least in part, for the renewed native and immigrant population suburbanization flows that occurred during the post-crisis period. For example, after recentralizing during the economic crisis years, Latin American immigrants decentralized once again during the recovery years [49].

The labor market and, more specifically, the impact of economic cycles on the levels of labor insertion of foreign immigrants and native workers have also influenced changes in urban population via international and internal mobility [33]. There are two opposing hypotheses on this issue. The first, based on the "buffer theory" [50–52], claims that foreigners act as buffers that absorb labor market tensions. Therefore, during economic growth phases, the number of immigrants rises as a response to an increasing demand for workers. However, in deep economic crisis periods, they are expelled from the labor market in greater numbers than native workers. By contrast, the second hypothesis [53], based on a "new migration model" [54], maintains that, in developed countries, labor markets constantly need foreign workers to fill low-wage and unstable jobs. With this hypothesis, these immigrants, mainly from developing countries, replace national workers, even during recession periods. This is especially the case in countries with highly dual labor markets [55], such as those of Southern Europe in general [56] and Spain in particular [57,58], where foreign immigrants have filled occupational niches in low-added-value economic sectors, such as construction, tourism, intensive agriculture, and the care of elderly people.

Which hypothesis best explains foreign immigrants' behavior in Spain during the 2008 economic crisis? Evidence shows that migrants behaved differently depending on their origin. On the one hand, Africans and Asians seem to have responded better to the "new migratory model," as they have barely left Spain: Quite to the contrary, their numbers increased during that period. On the other hand, the "buffer theory" seems to better explain the behavior of Europeans and, particularly, Latin Americans [59]. The latter immigrant group left Spain in the greatest numbers during the economic crisis, either returning to their homeland or moving to a third country [60]. Similarly, Latin Americans are also the origin group for which the number of entries to Spain increased the most during the post-crisis period. This shows their great capacity to adapt to economic cycles and, therefore, to impact population growth and decline in Spanish urban areas, where they tend to concentrate.

In addition, due to their greater labor and housing instability, foreign immigrants, who have lower rates of home ownership, have higher internal migration rates compared to natives [61,62]. Indeed, due to the economic recession, many foreigners either changed their places of residence inside the country, migrating to provinces that suffered less from the economic crisis, or moved from one metropolitan municipality to another. Research carried out in the metropolitan areas of Barcelona and Madrid has shown that there was a recentralization of foreign migrants, particularly Latin Americans, as urban cores had more rental housing stocks, better public transport, and more jobs than peripheral municipalities. These features also explain the increasing attractiveness of urban cores and the reduced suburbanization flows among Spaniards during the recession period. The end of the economic crisis stimulated new suburbanization flows by these groups, which had already been moving to peripheries during the years of economic expansion before 2008 [4,5,49].

Nevertheless, residential mobility does not only respond to temporary fluctuations in the economic cycle. On the contrary, it varies for different reasons, some of which are more structural in nature. This is the case, for instance, of residential moves related to biographical events, that is, address changes caused by life course transitions, such as leaving parental homes, couple formation, birth of a new child, or retirement [63,64]. Another example is household and family transformations linked to the Second Demographic Transition model [65]. The increasing numbers of union break-ups [66] and of more unstable household types, such as single-parent and one-person households [67], among other changes, influence people's residential mobility decisions. Classical contributions, such as Frey and Kobrin [68] or Buzar et al. [69], have provided in-depth knowledge on such issues. Finally, other authors have underlined that family relations, called *entourage* by Bonvalet and Lelièvre [70], also have an impact on migration. This would be the case for residential movements seeking family support.

These two connected factors—the increasing numbers of life cycle transitions and of more unstable household types compared to previous decades—could lead to the hypothesis that residential mobility has increased around the world. However, this is not the case for all types of mobility or for all geographical contexts [71]. For example, in some developed countries, residential mobility rates are presently lower than before [72]. In Spain, residential mobility levels have traditionally been lower than those of other European countries, and they decreased even more during the recession years, largely because fewer foreign immigrants (who change addresses more frequently than Spaniards) were arriving in Spain and fewer natives were leaving their parental homes and forming new families. The latter was caused by the "empty" cohorts—those born in the decades of low fertility (1980s and 1990s)—reaching adulthood [62].

Along with changes in housing and labor markets and family transformations, urban mobility has also been influenced by socio-residential pattern modifications. This relationship works in both directions since residential changes between (or within) cores

and rings also modify the demographic and social composition of the different parts of urban areas [73]. In addition to population growth and decline (this paper's main subject), mobility flows cause changes in age structure (rejuvenation or aging [74]) and have an impact on socioeconomic spatial distribution patterns, which can be measured by social class, income, or education level.

Several studies show the existing interaction between residential mobility and the spatial distribution patterns of the urban population by the socioeconomic characteristics of residents. In other words, it is a determinant of segregation and polarization processes in urban areas [75–77]. The literature analyzing urban socio-residential segregation in Spain's metropolitan areas is relatively extensive. Several recent studies focused on the cases of Barcelona and Madrid (either the cities or the whole metropolitan areas) [39,78–82] or analyzed the case of Catalonia [83]. However, few have related socio-residential restructuration dynamics to residential mobility patterns [84,85], and most of them have focused on specific case studies: Madrid [17], Barcelona [86,87], Paris [88], or Buenos Aires [89], among others.

Similar to segregation, socio-spatial polarization is also produced by socioeconomic inequality. This polarization is related to urban space through mechanisms and structures, such as the way that the productive system works, existing social structure tensions, wealth distribution policies, and, as already mentioned, real estate market characteristics and housing policies [90]. In this sense, certain authors have claimed that rising socio-spatial polarization has produced a process called "the suburbanization of poverty," leading to increased wealth in urban cores to the detriment of peripheries [73]. Some researchers have analyzed it as an independent phenomenon [91,92], while others have related it to gentrification [76,93]. This issue is not addressed in this paper. However, if the suburbanization of poverty is confirmed, the resulting greater spatial polarization could be related, as both a cause and a consequence, to growing intra-metropolitan residential mobility levels in the post-crisis period, to which the COVID-19 health crisis put an end.

## **3. Data and Methodology**

The main aim of this paper is to study the demographic reconfiguration of Spanish urban regions during the post-crisis period from a municipal perspective. To this end, current population dynamics are compared to those of the previous economic crisis phase, focusing on the population growth or decline in the metropolitan city core and periphery. The criterion used to define the spatial units analyzed in this paper is that of functional urban areas (FUA) set by the Spanish National Institute of Statistics (INE, Madrid, Spain) and Eurostat. A functional urban area is a group of municipalities around a city, linked to it by commuting. The delimitation of FUAs considers the main city and its area of influence, or hinterland, as an integrated labor market and consumption area. Commuting between a city and its neighboring municipalities has been used to set the limits of the area of influence. The main selection criterion for a municipality is that at least 15% of its residents move daily to the city to work or study. There are exceptions to the general rule for very small municipalities. Though commuting remains the main criterion, others, such as contiguity, are also taken into account. The number of FUAs with more than 100,000 inhabitants has increased in Spain, from 45 in 2011 to 69 in 2019, which are analyzed in this paper. The advantage of using this definition is that it allows comparisons with the rest of the European urban areas [94].

The present research used microdata from the Padrón Continuo, an administrative population register that records each municipality's residents, as its main data source. The National Institute of Statistics (INE) coordinates the collection and depuration of local data and publishes official population figures on 1 January every year. It also offers basic population data on the age, sex, place of birth, and nationality for all Spanish municipalities.

Cumulative annual growth rates (CAGRs) were calculated for both periods discussed in this paper. The first, ranging from 1 January 2011 (the highest population figures around the beginning of the economic crisis) to 1 January 2015 (the lowest population figures around the end of the crisis), is called the "crisis phase" in this paper; the second, lasting from 1 January 2015 to 1 January 2019 (the last official data available at the time of writing the paper), is the "post-crisis" phase.

The following formula was used to calculate the cumulative annual growth rates:

$$r = \left(\sqrt[n]{\frac{P\_{i+n}}{P\_i}} - 1\right) \* 100\tag{1}$$

where *n* represents the number of years, *Pi* is the initial population, and *Pi+n* is the final population of the area under study.
