Age patterns of net migration and urbanisation dynamics across European municipalities

Across the European Union (EU) Local Administrative Units (LAUs), populations are experiencing persisting differences in their age structures that can only be interpreted accounting for migration and mobility components. Yet, in the absence of census data, migration patterns of local populations are not available from EU ‐ official statistics. To fill the gaps, we firstly combine census data with statistics available from the National Statistical Institutes of the EU ‐ Member Sates in a harmonised database on age ‐ specific population structures, covering all EU ‐ LAUs for the period 2011 − 2019. Secondly, we apply model life tables to assess changes by cohort over the intercensal period and provide estimates of age ‐ specific net migration rates at LAU levels. The analysis reveals how migration dynamics vary along demographic patterns and to what extent differences are related to the degree of urbanisation and territorial characteristics (distance from city centres, remoteness, population change, GDP per ‐ capita and poverty level) across the EU municipalities.


| INTRODUCTION
The assumption that the European Union (EU) countries are converging from a demographic perspective is one of the main underlying hypotheses of the demographic projections released by EUROSTAT (2020a). However, when looking at a finer territorial classification, persisting territorial and demographic differences become evident across EU regions (Goujon et al., 2021;Kashnitsky et al., 2020). Beside the impacts of increased longevity and lesser fertility, the key-role of international migration and internal mobility in demographic changes has been assessed both in theoretical and empirical analyses. Authors have argued that the earlier stages of urban transition were driven by internal rural to urban mobility (Davis, 1965;De Vries, 2013;Dyson, 2011;Rowe et al., 2019), while more recent counter-urbanisation trends have been characterised by urban to rural reverse movements. Although van den Berg et al. (1982) have described three consecutive stages of urbanisation, suburbanisation and counter-urbanisation and a hypothetical fourth stage of reurbanisation strictly following a sequential order, recent dynamics of urbanisation outline a more stratified picture of the EU, with the coexistence of shrinking and expanding cities due to suburbanisation and reurbanisation processes (Kabisch & Haase, 2011).
Studies have revealed the plurality of net migration age-specific profiles across subregions, which are mostly explained by the economic attractiveness of places and the availability of services Popul. Space Place. 2022;e99.
wileyonlinelibrary.com/journal/psp and amenities (Goujon et al., 2021). As confirmed by the recent EU initiatives, like the Long-Term Vision for Rural Areas (EC, 2020), these dynamics have important implications, not only for the depopulation trends of rural areas and economic development of urban places, but also for political and social cohesion at the local level.
To explore the role played by territorial characteristics, empirical analyses should consider differences in age structure at municipality or finer local levels (Gutiérrez Posada et al., 2018;Sabater et al., 2017). pandemic has dramatically demonstrated, climate change and globalisation have altered ecological systems and increased inequalities in urban life (Benton, 2020). To make EU municipalities more resilient in the future, the integration of policy areas 1 has been suggested for a sustainable and well-managed development of territories.
By adopting LAUs as the territorial level of analysis, we seek to complement previous studies that have recognised (subnational) regional governance as key to addressing EU cohesion policies (de Beer et al., 2012, Groenewold andde Beer, 2014 (Champion, 1989;Fielding, 1989).
Regularities in age patterns of migration have been recognised by Rogers and Castro (1983). Accounting for heterogeneous area definitions and limitations in reliability of local data, authors have calculated regional variations in age-specific internal migration rates for a large sample of countries and modelled the age profile of migration (Rogers & Castro, 1983). Pursuing a similar approach, Rowe et al. (2019) defined the index of net migration impacts. Aiming to assess the role of internal mobility on population distribution, authors concluded that cross-national differences were driven by interactions between the intensity of migration and its effectiveness on spatial settlements, which varied systematically with urbanisation (following Ravenstein's classic conceptualisation of rural vs. urban mobility) to more recent counter urbanisation trends. Rees and Kupiszewski (1999) disentangled demographic patterns of regional net migration from urbanisation using population density as a proxy to differentiate urban from rural areas. addition to studies highlighting the role of migration as one of the determinants of population redistribution, the authors focused on economic development to understand the age-specific characteristics of rural and urban populations. For instance, Lewis (1954) provided the first conceptual framework of population-development interactions through the modelling of two closed economic sectors, the industrial sector with unlimited labour supply and the agricultural sector based on family labour, which explained the mobility from rural to urban areas. Scholars have argued the incompleteness of Lewis' model to interpret the general equilibrium of modern societies, which is restricted to the supply side of structural changes and sectoral compositions (Chenery, 1960(Chenery, , 1979. For instance, the socalled structural change paradigm (Islam, 2014) described how urbanisation could be originated from the changes of fertility and mortality in rural areas, without a substantial contribution from migration as suggested by Lewis' classic conceptualisation of development.
Currently, European countries experience the advanced phases of the demographic and migration transition (de Haas, 2010), but relative differences in the speed of the process remain across regions (de Beer et al., 2012). In European countries where ageing is one of the main demographic trends, the dynamics of urbanisation in the short and medium term are shaped by age differences in net migration: a higher proportion of older age groups tends to move from urban to rural areas, whereas urban areas retain their attractiveness mainly to younger populations (Goujon et al., 2021).  The resulting data set contains yearly information on the population size at LAU level according to the following variables: Country, year, NUTS-3 code, LAU code, age (in single years) for the period 2011−2019.
To measure the accuracy of our estimates and to check for potential anomalies in the age structure, we conducted a data validation using the mean absolute percent error. LAU data by age were aggregated to the NUTS-3 level and compared to the official data (EUROSTAT, 2021c) for the same reference year (Supporting Information: Figure A1 in the Appendix). In the majority of EU MS, the index varies in the acceptable range from 0% to +4%, except for Greece Latvia and Ireland, where it reaches +6%.

| EMPIRICAL STRATEGY
We adopt model life tables 4 by single-year of age period-cohort in order to derive net-migration. Due to heterogeneity in the dates of the 2011 population census across EU MS (for instance, Germany the probability that individuals of the same birth theoretical cohort will still attain older ages (or be alive one or several years later).
Due to the lack of mortality data at LAU level, we used the information about mortality at NUTS-3 level. We therefore assume that people living in neighbouring LAUs, within the same NUTS-3 territory, are exposed to similar mortality regimes. We use the model life tables developed by Coale and Demeny (1966)  We adopt the survival ratio method (UNDESA, 1970) to formalise the computation of theoretical cohorts as follows: where, i represents the LAU unit.
a corresponds to the age and period interval.
x corresponds to the age group in 2011. The difference between the theoretical cohorts and observed cohorts in t + a is the estimated net migration during the period t to t + a: It should be noted that the reference period of analysis consists of 8-year interval, which differs from the conventional age-group interval (or its multiple) commonly applied to aggregate population structures. This constraint motivates our methodological choice to stratify population data by annual age groups. 6 We apply a synthetic indication of 1-year age/period as whole, rather than notations of exact age and specific point in time. 7 In model life tables, the function reflects the age composition of a population which experiences a constant replacement by 100,000 births and a mortality regime as observed during the reference period. This population is described as stationary, with a zero growth rate for all age groups. We compute the annual theoretical cohort net migration rate as the proportion of the estimated annual theoretical cohort net migration in people exposed to the risk of migration, meaning the average cohorts between age x and x + a. Doing so, we provide the crude annual period-cohort net migration rate of the (x + a/2) age theoretical cohorts of surviving individuals during the mid-period (t + a/2). The model algorithms were implemented in R language within the GNU R computing environment (R Core Team, 2020).

| Method validation
To control and when possible, partially reduce the bias, an adjustment strategy is designed based on the alternative method of reverse survival ratios, which consists in the use of the reciprocals of the survival ratios to calculate the expected cohorts that would have been x years old at the beginning of the reference period. The rationale is that the cohorts at the time t are composed by the survivors at the end of the reference period (time t + a), plus the migrants and deaths that occurred during the interval.
The application of two methods provides different estimates of the cohort-period net migration, following opposed timing of migration and mortality events (concentrated at the beginning and at the end of the period). To compensate errors in the scheduling of cohort events, that should be rather distributed over the interval, we calculate the adjusted cohort-period net migration rates, as the average of two different estimates, referring to migration events that occurred in the middle of the interval for the mean age (x + a/2) cohorts of survivals. To assess the appropriateness of our model specifications, we compare adjusted net migration rates (net migration rates obtained from survival ratios and reverse survival ratios) with the population growth. This check gives an indication of the coherence and consistency of the demographic components across age groups. Theoretically, when appropriate life tables are available and cohort population data sets are accurate, the estimated net migration rates should approximate migration tendencies by cohort along the population lifetime.
We verify the consistency of estimated net migration rates with the rates derived from the official demographic projection (baseline scenario) data sets provided by Eurostat at NUTS-3 level (EUROSTAT, 2021d) for the period from 2019 to 2027 (8-year interval). In the Supporting Information: Figure A2 in appendix, we show an example of a validation for the municipality of Torino in Italy (the results for all EU NUTS-3 are available upon request). We compare the Eurostat annual period-cohort net migration rates with:-estimates of annual period-cohort net migration rates derived from the application of the prospective survival probability method;-estimates of annual period-cohort net migration rates derived from the application of the reverse prospective survival probability method;-estimates of the adjusted annual period-cohort net migration rates;-the annual exponential population growth.
In general, estimated and projected migration trends are similar; estimated net migration diverges from the population growth from age 40+, mirroring the increase of mortality along age-groups. Likely, mortality regimes at older ages motivate deviations when the reverse survival probability method is applied (Supporting Information: Figure A2 in the Appendix, light blue line). As expected, the method generates results in line with the demographic projection trends.
We extend our method operability by its generalisation at NUTS-1 levels using Eurostat statistics on immigration and emigration from 2011 to 2019 (EUROSTAT, 2021e). Supporting Information: Figure A3 in the Appendix exemplifies the validation for Austria.
The method fits well the generalisation at NUTS-1 for all cohorts, with some few exceptions for young adults and older cohorts.
Specifically, higher estimated rates derive from under-enumeration of mortality levels for cohorts aged 18−24, whereas lower ones are a consequence of over-representation of mortality severity among cohorts aged 66−72.
As additional implementation, we apply the method to LAU data sets on populations and internal and international migration made available by the Austrian Institute of Statistics' data sets (2021) from 2011 to 2019. Supporting Information: Figure A4 in the Appendix compares population growth rates and estimated annual migration rates across pooled Austrian LAUs for the 2011−2019 period. When comparing estimates of annual migration rates with annual periodcohort rates derived from official statistics, discrepancies are not higher than standard error levels (4%). Thus, we can conclude that the method seems to be satisfactory in profiling age-specific migration rates at LAU levels. Nevertheless, it remains clear that the method's goodness-of-fit depends on the accuracy of population data sets and life table applied in the method.

| Territorial characteristics
We apply the estimated age-specific net-migration rates to investigate differences by degree of urbanisation, using the Eurostat categorisation of LAUs into cities, towns and rural areas (EUROSTAT, 2020b(EUROSTAT, , 2021a, which distinguishes three categories or degrees of urbanisation: (a) urban, areas where more than 80% of the population lives in urban agglomerations; (b) rural, areas where at least 50% of the population lives in rural agglomerations; (c) intermediate, areas where more than 50% and up to 80% of the population lives in urban agglomerations. Furthermore, we select five variables corresponding to the most frequently used criteria in EU regional strategies: distance from city centres, remoteness, population change, GDP per capita and poverty level. Even though the distance from city centres partly overlaps the degree of urbanisation, each category gives a slightly different perspective in terms of territorial characteristics.
These different perspectives have a fundamental role in highlighting some features in the dynamics of urbanisation and counterurbanisation which could be unnoticed, when referring to the simpler dichotomy between rural and urban areas and conducting analyses at higher levels of geographical units. Supporting Information: Figure A5 in the Appendix visualises the application of criteria by the mapping of German municipalities.

| RESULTS
We divide EU municipalities into discrete classes reflecting the above-described territorial characteristics to present differences in population structure and age-specific net migration.

| Age-specific populations by spatial pattern
The age-specific populations in 2011 (the starting year for the analysis) are displayed in Figure 1 by single year of age and according to the territorial characteristics of the LAUs.

| Degrees of urbanisation/distance from cities/remoteness
The share of population up to 45 years tend to be underrepresented in rural areas and towns, in LAUs more distant from city centres, in remote areas and in LAUs experiencing moderate or severe depopulation. Older people, on the contrary, become increasingly overrepresented in towns and rural areas, distant places and depopulating areas. The largest gap between rural areas and cities is recorded for ages from 60 to 64 years, whose share is 0.2 percentage points higher in rural areas than in cities. The share of the population between the age of 15 and 35 years is 0.2 percentage points lower in LAUs that are more than 20 km far from city centres than in city centres. Consistent with the classification by degree of urbanisation, the share of middle-aged adults (with ages between 40 and 44 years) is higher in cities and in suburban centres at a distance between 5 and 20 km from city centres. The same pattern is visible for those between 10 and 19 years of age, which correspond most-likely to the children of those middle-aged adults.

| Population change/economic dimensions
We observe that youth aged between 20 and 24 years are not necessarily underrepresented in areas experiencing population decline. Similarly, differences in the share of age-groups below 35 years seem not to be influenced by the two economic dimensions, the level of GPD per capita of the region and the poverty level. By contrast, these dimensions are related to positive differentials among adults aged between 40 and 55 years, and negative for those between 55 and 65 years. Youths are overrepresented in poor regions while ages from 50 to 55 years are underrepresented.
In 2011, the largest rural-urban differentials were recorded for youth aged from 20 to 24 and from 75 to 79 years. For the former, the gap is −0.24 percentage points between the share of urban versus rural, and for the latter it is +0.26 percentage points. Figure 2 displays the age-specific rural-urban differentials by single year of age and over time, comparing 2011 with 2019.
In 2019, while the proportion of youth population remained higher in urban than in rural areas, the gaps between the proportion of rural and urban population narrowed, becoming more evenly distributed across ages. More specifically, the rural-urban differential was less marked for ages from 20 to 24 years (narrowing to −0.14 percentage points from percentage points in 2011), whereas it increased for the ages from 50 to 64 years. This reveals a potential trend in resettlement between urban and rural areas: in 2019, a greater proportion of the adult population preferred rural municipalities than in 2011. If this counterurbanisation trend was to continue in the future, it might be able to mitigate or slow down the speed of ageing, which mainly affects rural municipalities in the EU (Goujon et al., 2021).

| Age-specific net-migration by spatial pattern
We present the smoothed age profiles of net migration for the selected territorial characteristics, obtained by averaging the estimated net migration at LAU level (Figure 3).

| Degree of urbanisation
There is a positive net migration (more in-flows than out-flows) of youths in cities, which corresponds to a negative net migration in

| Distance from cities
We observe a tendency of adults aged between 35 and 39 years to move far away from urban municipalities (both classes of distance, 5−20 km and 20+ km). As expected, this propensity is reflected in the youngest age-groups, while older population (65+ years) are more likely to move close to city centres (reporting a negative net migration for all three classes of distance). Consistently with previous findings, youths are likely to move towards cities.

| Remoteness
These profiles do not provide additional insights in terms of net migration, besides a slightly higher tendency of young people to leave more remotely located areas in comparison with other areas. 27% of EU territories benefitted from positive net migration to counterbalance the deficit in the working-age population due to cohort turnover.

| Economic dimensions
Three main patterns become evident when looking at GDP per capita: a negative net migration for ages between 20 and 24 years in low and medium GDP per-capita municipalities, a positive net migration for ages from 35 to 39 years in all municipalities, and a negative net migration for population above 40 years of age in high GDP per capita municipalities. Whether the low income operates as a push factor for younger population, it becomes a pull factor for older population. High GDP per capita seems to be an additional pull factor for ages from 35 to 39 years, doubling up the rates recorded in lowincome areas. The poverty dimension does not reveal relevant differences in terms of net migration across territories. As for GDP per capita, low poverty areas show relatively higher positive net migration rates among those aged between 35 and 39 years.
The age-patterns of net migration exhibit strong variations across EU municipalities. Figure 4 illustrates the case of the 20−24 cohorts.
F I G U R E 4 Net migration rates of the 20−24 age-groups across EU municipalities. EU, European Union.
The majority of EU municipalities (53%) experience net negative migration rates for these young cohorts, while only 36% exhibit positive net migration rates among the 20−24 cohorts 11 . As expected, the vast majority (85%) of EU municipalities recording a negative net migration are classified as rural.
Yet, spatial patterns are dissimilar across countries. For instance, in Germany, two parallel dynamics are evident: immigration (positive net migration) of young people towards large cities; emigration (negative net migration) of young people from Eastern to Western and Southern municipalities. By contrast, in Southern EU countries like Italy, the net migration of the 20−24 age-group exhibit a more uniformed pattern, negative in the South and positive in the North municipalities, pointing at internal mobility. The intensity is lesser 12 than what was observed in Germany and with a larger spread across territories. Similar tendencies are observable in France, where, beside a vast majority of Eastern and Southern municipalities exhibiting negative net migration rates, a few municipalities in the same regions seem to be attracting these youth cohorts. In Bulgaria, the dominance of negative net migration rates may be an indication that young people are moving outside of the country. These dynamics are less evident in the EU Northern countries, where there seems to be a (in-out movement) compensation within the countries.
With the aim to reduce the uncertainties in the net migration outcomes, we measure the impact of our empirical strategy by excluding LAUs with imputed population values from the analysis.
Supporting Information: Figure A6 in the Appendix shows the netmigration rates for the 20−24 cohorts limited to the countries where input data were derived from official data available through the NSIs.
The proportion of EU municipalities reporting a negative net migration rate for the young cohorts remains around 52%, with a prevalence (82%) of rural municipalities. This implies that our findings are robust and not impacted by the imputed values.

| DISCUSSION AND CONCLUSIONS
There have been multiple conceptualisations of the role of rural to urban dynamics in shaping population structures at territorial levels. (Davis, 1965;Rees & Kupiszewski, 1999;Rees et al., 2017). However, we lack knowledge about the nuances and changes in migration at local level due to missing data. In this study, we undertook two major efforts. Firstly, we created a data set of population by age at LAU levels for the entire EU, handling the large coverage and variations in the data coming from different national sources. Doing so, we complement the figures available from the 2011 population census with the latest statistics available from NSIs, anticipating the release of the 2021 gridded population census statistics foreseen for 2023.
Secondly, we use these data sets to derive age-specific net migration rates at LAU level using the survival method. Finally, we explore how territorial characteristics interplay with net migration by age-group, across EU municipalities. Results by different categorisation of LAUs show heterogeneity over the EU that cannot simply stem from the rural-urban dichotomy. The combination of spatial and demographic factors plays a more central role in explaining these territorial divergences. As main outputs, we assess age-specific net migration differentials across the selected geographical and economic characteristics. Although young people (aged from 20 to 24 years) tend to move towards urban areas to reside close to city centres, their mobility seems less affected by the contextual level of GDP per capita and poverty levels. A tentative explanation is that the movements towards cities at these ages may be mostly associated with the undertaking of tertiary education and career development.
Because these migrations are linked to the transition to adulthood, they may translate in (un)stable settlements. Young adults (of ages from 30 to 34 years) exhibit a preference toward rural areas rather than cities, but they also live at intermediate distances from city centres. The mobility behaviours among this age group, clearly mirrored by similar patterns in children, are likely linked to family formation. The need for bigger housing arrangements and access to green spaces may be among the fundamental drivers for these movements. Finally, elderly would be less discouraged by low economic conditions and tend to move more toward rural areas in respect to younger generations. In this case, adding distance from the city centres to the rural-urban characteristics provides additional insights by showing that, in parallel to a preference for rural areas, some population groups prefer living in city centres.
Although further analyses would be needed, especially along a longer time horizon and disaggregating in-and out-flows, we outline a stratified picture by age over the EU. Youths experience high rates of rural to urban mobility, happening at national level (internal migration) or intra-EU level (international migration) affecting particularly Eastern EU territories. By contrast and overall, young parents and children are more likely to be attracted by towns and rural areas contributing to and potentially leading the counterurbanisation tendencies. Those have been further fuelled by the COVID-19 pandemic that has led to the increase of remote work practices (Stawarz et al., 2022). By revealing how the age structure and net migration patterns vary greatly across EU municipalities, findings confirm the relevance of the link between urbanisation and demographic dynamics. These patterns are evident not only through the rural-urban dichotomy, but also accounting for changes in the attractiveness of places over the life course. Consequently, the deepening of territorial differences in the EU should not be merely analysed using the simplistic paradigm of rural-urban migration. Large movements across EU municipalities respond to residential preferences which change over the lifetime of individuals. The presence of services, like universities and health-care structures, should be considered essential in policy planning to contrast territorial economic and demographic divergences within the EU. By targeting territorial patterns, our analysis would serve the planning of these 11 The remaining share of municipalities experiences net migration rates closed to zero. 12 Migration behaviours of young cohorts may reflect and be also a consequence of their transition to adulthood. For instance, the observed lower migration effects may result from the fact that Italian young adults used to leave the family home only at a later age (Billari and Liefbroer, 2010). GHIO ET AL. | 11 of 13 social cohesion initiatives, aimed at improving the accessibility of services, the revamping of local economies and the attractiveness of depopulated areas. Yet, the successful implementation of these policy actions requires better structural coordination among the EU and local stakeholders.