1 Introduction

Thanks to the spread of Geographic Information Systems (GIS) and the ever-increasing availability of georeferenced data, the development of spatial approaches within population studies has accelerated, particularly since the early 2000s (Matthews, 2016; Matthews & Parker, 2013; Matthews et al., 2021). The impact of this change has been so significant as to lead some scholars to broaden the definition of demography by recognizing its intrinsically spatial nature (Voss, 2007; Weeks, 2016) as well as to re-evaluate its importance as a tool capable of supporting the establishment of policies based on different territorial scales of intervention (De Castro, 2007). The latter is not an entirely new topic if we consider that, almost 40 years ago, Willekens and Heide (1985) published the pioneering work “Demographic research and spatial policy: A progress report”, in which they emphasised the relevance of demographic research as a useful (and necessary) tool to facilitate the adoption of spatially appropriate and, therefore, territorially targeted policies. A fundamental and distinctive feature of this approach is that territories are no longer treated as simple classification variables in the observed processes but have, on the contrary, become the statistical units on which to conduct quantitative analyses using specific spatial approaches (Matthews & Parker, 2013). The basic idea, as Champion and Hugo (2004) remind us, is that the characteristics and spatial location of the contexts in which people live can represent a relevant factor in explaining demographic behaviour.

With reference to Italy, especially in recent years, several papers have appeared that approach demographic processes as spatial phenomena and, therefore, directly consider the spatial dimension in the measurement and interpretation of such processes (Benassi & Carella, 2023; Mazza & Punzo, 2016; Reynaud et al., 2018; Salvati et al., 2020; Vitali & Billari, 2017). Some of these contributions have focused in particular on the study of the factors that influence population change on a local scale (Benassi et al., 2022, 2023a, b), some with reference to the depopulation process (Reynaud et al., 2020). These studies have highlighted that (1) demographic change is an intrinsically spatial process that does not manifest itself in space in a uniform or even random way (Benassi et al., 2022) and (2) the drivers of population change are also affected by space (Benassi et al., 2023a, b; Reynaud et al., 2020). These contributions have made extensive use of both globalFootnote 1 and local multiscaleFootnote 2 spatial regression models, but they have done so with reference to the entire national context, that is to say, considering all Italian municipalities, and they have focused mainly on the study of the determinants of the phenomenon, rather than the geographical dimension of these determinants for the purposes of regional planning on a local scale. This last aspect, although important and highly topical in Italy, does not yet seem to have received specific treatment in the field of applied demography studies. Nonetheless, the adoption of place-based policies seems essential to govern highly heterogeneous and fragmented demographic processes efficiently and effectively. This is a need of which the relevance and urgency have also been highlighted by a recent research project promoted by the Max Planck Institute for Demographic Research and the Population Europe network on the topic of European regional demography, the main results of which are contained in Muti (2023).

There is no doubt that to adopt this type of policy it is necessary to reflect on how best to construct and identify the areas in which to intervene. This contribution is based on the idea that this construction and identification can, contrary to current trends, be based on local estimation tools and, in particular, on geographically weighted regression (GWR) models. The case study concerns the region of Molise, a context that is particularly affected by persistent population decline and unusual within the Italian regional demographic framework (Del Panta & Detti, 2019; Lallo et al., 2023). Molise stands out as the region experiencing the most significant population decline in Italy, coupled with one of the most fragile economic and socio-demographic profiles (Istat 2020, 2023). It is noteworthy that in 2002, the Italian National Institute of Statistics (Istat) estimated Molise's population to be around 320 thousand, which decreased to 294 thousand by 2021, indicating a negative annual growth rate of -4.4‰. This rate starkly contrasts with Italy's overall growth rate for the same period, which stood at around 1.8‰. From 2014 to 2021, Italy's population decreased by about 1 million, translating to an annual decline of roughly -3‰, while Molise's population decreased by approximately 19 thousand people during the same period, which is three times more than the national average (-9‰). Furthermore, the average Total Fertility Rate for the period 2017–2021 was 1.12 in Molise compared to 1.28 in Italy. Similarly, the Net Migration Rate during this period was -4‰ in Molise and 0.7‰ in Italy. Thus, from a demographic perspective, Molise serves as a significant case study for understanding processes such as demographic decline and depopulation. This demographic decline in Molise is not a recent phenomenon. Del Panta and Detti (2019) highlighted Molise's historical uniqueness in their study on Italian depopulation. They revealed that Molise was the sole Italian region to consistently record a negative average annual rate of population change from 1871 to 1971, a period when many regions, even in Southern Italy, were experiencing robust growth, including neighbouring regions like Abruzzo and Basilicata.

Through the adoption of an empirical approach at a local scale, taking as a study variable the average annual rate of population change in Molise’s municipalities in the period 2011–2019, the contribution aims to answer the following research questions:

  • Which factors influenced the population change observed in the municipalities of Molise in the period considered? (RQ1);

  • Was the influence of each factor spatially stable? (RQ2);

  • If this influence was not spatially stable, where did it act locally and how? (RQ3).

Answering these questions will allow us to show how these types of local estimation approaches can represent valid tools for the construction of territorial areas of intervention based on the geographies of the determinants of the processes to which they aim to respond. This constitutes an alternative to the more widespread top-down approach, typically aimed at defining areas of intervention on a national scale. The ultimate aim of this contribution is, therefore, to show how local approaches (in particular those using GWR models) to the study of demographic processes can provide important information to facilitate efficient regional-scale planning that is territorially targeted and specific.

The paper is structured as follows: Sect. 2 presents a critical analysis of local-scale demography, territorial models of development and place-based policies in the context of population studies along with some general considerations on the topic, particularly in light of the most recent literature; in Sect. 3, the data and methods are presented; while in Sect. 4, the results obtained are described. Finally, Sect. 5 is dedicated to a brief discussion of the results and some final considerations. The contribution concludes with an appendix presenting Italian administrative geography at different scales (macro-regional, regional and local) to help orient readers in understanding the case study.

2 Local-Scale Demography, Territorial Development Models and Place-Based Policies

The territorial scale at which to interpret demographic processes is a dimension that cannot be ignored if we wish to establish efficient and effective policies in this area. What occurs on a regional or supra-regional scale is often the result of profoundly different if not, as is often the case, strictly opposite local dynamics (Benassi & Naccarato, 2017; Benassi et al., 2022; Strozza et al., 2016). Population change dynamics in Italy are a valid example of this since growing local centres (typically the urban areas of Central and Northern Italy) form a contrast with areas subject to systematic demographic contraction, which become progressively weaker and more marginal (Benassi et al., 2021). The result of this dual process is a weakening of the national system from both a socioeconomic and an environmental point of view and, consequently, an increase in its susceptibility to exogenous shocks (De Lucia et al., 2020).

For many years, usually identified with the period of the economic and demographic boom, in Italy, as in many other European countries, the logic of competitive territorial development models prevailed. This is one of the reasons why, at least in terms of public policy, not much attention was given to territories that were already experiencing systematic demographic decreases in those years despite the fact that, especially in Italy, these were already numerically significant (Del Panta & Detti, 2019; Sonnino, 1975, 1978, 1979). The fairly widespread consensus was that the growth, both in economic and demographic terms, of cities would also guarantee the development of other territorial contexts, both through the expansion of urban functions fuelled by suburbanization processes and through classic spillover processes. This anticipated dynamic would eventually create city–regions in which even local units of smaller demographic size would grow in a balanced and harmonious way (Beel & Jones, 2021). The reality, however, was very different if not—in cases such as the Italian one—diametrically opposite to what was expected. The city–region dynamics, as well highlighted by Cardoso (2022), generate socioeconomic and development effects that manifest themselves in space in a non-uniform way. The persistence of intra-regional imbalances, net of what may be caused by demographic and economic dimensional differences in the various local contexts, proves the presence of negative externalities due to the effects of urban agglomeration, which cause the progressive emptying of small and medium-sized cities and rural contexts in terms of population, jobs and services. These polarization effects, typical of competitive rather than redistributive models, exacerbate intra-regional inequalities and limit the cooperation of local authorities, which frequently find themselves competing against one another. All of this creates a generally unfavourable context for smaller and non-urban units, resulting, in the long term, in an overall loss for the regional and national systems (Barca, 2019; Cardoso, 2022).

Territorial development inequalities are a deep-rooted and persistent phenomenon in Italy. The issue has, over time, attracted the attention of many scholars of varying disciplines, who have produced several studies on the topic. Among the most recent and relevant, we include the work of Viesti (2021) regarding the territorial gaps in socioeconomic development in Europe and Italy—especially the South—and the polarization processes that accompany these; we also include that of Sbrana (2023), who, referring more specifically to the Italian case and making use of largely unpublished documentation, reconstructs the genesis of the fracture between North and South and narrates its historical evolution. Even in population studies, attention to territorial disparities in demographic development has been growing, particularly in recent years, as highlighted in the 2021 report of the Italian Association of Population Studies, in which a specific chapter is dedicated to “inequalities between territories” (AISP, 2021).

It is in this context of renewed (and forced, given the losses to the overall system) attention to the local that scholars and political authorities began to consider how to set policies for and about different territories. Over time, and lately thanks to the availability of new technologies such as GIS, it has been increasingly understood that intervention through active policies concerning macro-processes, such as attempts to counteract demographic decline and its most extreme form (i.e., depopulation), cannot be pursued without attention being paid to studies based on local approaches, which by their very nature guarantee less loss of information. The adoption of population policies aimed at specific territories requires the construction of territorial areas of intervention that allow place-based policies to be adopted and their effects to be monitored over time. This construction is, in essence, nothing more than the functional classification of territories. Starting, almost always, from elementary administrative geographies (for example that of municipalities), scholars attempt, using various techniques based on multivariate statistical approaches of synthesis and classification, to construct new functional partitions of space, which may or may not respect supra-local administrative boundaries and which should serve specific objectives.

The operational logics adopted for the construction of these areas are multiple. However, they can be traced back in a somewhat crude but perhaps effective way to two main categories, which are the same as those found in statistical clustering approaches: from top to bottom (top–down) and from bottom to top (bottom–up). When we move from top to bottom, classification rules are defined a priori and in a standardized way, for example on a national basis, and then applied to the different local contexts. The result is that partitions are established using common criteria and therefore allow for national “direction”, where the defined partitions serve, for example, for the implementation of policies that are specific but attributable to a common national framework. The downside is that classifying space in this way can imply relatively high information loss where local contexts are characterized by marked heterogeneity, especially of an intra-regional nature. The second logic moves from bottom to top, that is, from local to global (or from micro- to macro-, to put it another way). In this case, therefore, the act of partition considers local differences even if it still classifies all local units in one or more global clusters (since the sum of the units that make up the clusters constitutes the entire population of territories), thus granting them a supra-local nature. Even in this second case, therefore, problems of internal heterogeneity may arise. In both cases, then, unless we place spatial contiguity constraints, we can obtain territories (for example municipalities) that belong to the same clusters but are located in different supra-local (for example regional) divisions, and this can create problems for management purposes.

As previously mentioned, one of the most interesting uses of these functional areas is that relating to the adoption of place-based policies. In the view of Neumark and Simpson (2015), these are policies which attempt to reduce the gaps between particular territories in disadvantaged conditions and those in better conditions, thereby increasing the former’s economic competitiveness and overall level of well-being. From a more purely demographic point of view, interest lies in a particular subcategory of these policies, namely those defined by Ladd (1994) as place-based people strategies, which remain territorially targeted but are oriented towards directly supporting the populations who reside in those territories (we might consider particularly fragile populations such as the elderly or particular ethnic minorities). In a European context characterised by persistent differences in regional populations (Rees et al., 2012,) the relevance of spatially oriented policies has recently been recalled: “European regions are heterogenous, and demographic changes require place-based solutions” (Muti, 2023: 7).

In Italy, for almost a decade now, the efforts made in this regard have contributed to the ongoing formulation of the National Strategy for Inner Areas (SNAI).Footnote 3 This initiative, promoted by the Agency for Territorial Cohesion and the former Minister for Territorial Cohesion, Fabrizio Barca, aims to revitalize the most disadvantaged areas of the country by implementing active policies capable of removing obstacles to socioeconomic development, thus counteracting demographic decline and geographical marginalization. It represents a completely original operational system for Italy, based precisely on the concept of place-based policies, as described by Carrosio and Barca (2020). The origins of the SNAI lie in the seminal work of Barca (2009) in ideas that were subsequently developed further by Barca et al. (2012). Within this strategy, the so-called inner areas constitute the set of municipalities in which intervention is made through targeted active policies. It is not our intention here to go into detail about these geographies but rather to underline at least two relevant aspects. The first is that the inner areas are defined through a complex process which is based essentially on accessibility but adopts a top–down classification system of the various local contexts. The second is illustrated by Fig. 1, which shows, on the left, the municipalities experiencing systematic population loss from 1981 to 2019 and, on the right, the geography of the inner areas as defined in 2020.

Fig. 1
figure 1

a Systematic depopulation in Italian municipalities from 1981 to 2019; red polygons represent affected municipalities (b) 2020 inner areas as defined by the National Strategy for Inner Areas (SNAI); yellow polygons represent municipalities classified as “intermediate”, orange polygons “peripheral” and red polygons “ultraperipheral”. (a) Recreated from Benassi et al., (2023a)

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The municipalities classified as inner areas (which include three types: “intermediate”, “peripheral” and “ultraperipheral”) are significant in number, totalling 3,834. The municipalities that have suffered systematic depopulation across the period 1981–2019 number 1884, a figure very close to the sum of the two categories of most disadvantaged municipalities in the SNAI classification, the “peripheral” and the “ultraperipheral”, 1906. However, it should be noted that some municipalities that fall within the SNAI classification were not affected by systematic demographic decline and that some municipalities that were affected by a systematic decline in population do not fall within the SNAI classification. This opens up interesting opportunities for reflection, in our opinion, on how best to classify territories for the purposes of setting active intervention policies, especially in relation to combating demographic decline. In what follows, we focus exactly on this point, using an approach based on local regressions and referring to the Molise region as an emblematic case study. The aim of the work is to reflect on the drivers of the demographic change that occurred in the municipalities of Molise in the period 2011–2019 (prior to the disturbing effects of Covid-19) using a local estimation approach. The average annual rate of demographic change for the period 2011–2019 in each municipality is placed in relation to four indicators measured in 2011, relating to aspects (namely attractiveness, labour market and the ageing process) closely related to the demographic performance of a territory: foreign population, female participation in the labour market, youth employment rate and the (potential) need for assistance of households. The analysis logic followed is of a “pseudo-causal” type and is similar to that adopted by Benassi et al., (2023a). What manifested itself in a given period of time (2011–2019) on a given set of statistical units (the municipalities of Molise) is placed in relation to the initial condition (in 2011), measured according to specific indicators, of those same statistical units. The originality of this approach lies in reconstructing the geographical variability of the predictors at a local level in order to highlight any spatial patterns that may represent natural areas for intervention based on the real dynamics of the observed phenomena and their determinants.

3 Data and Methods

The data used in the study were sourced from Istat (the Italian National Institute of Statistics). The geographical level to which they refer is the municipal one. For the calculation of the dependent variable (y), the average annual rate of population change across the period 2011–2019, the inter-census reconstruction of the population was used. These are official estimations produced and disseminated by Istat. The four indices used as independent variables were computed using data from the 2011 census and are available on the public portal “8mila census” (https://ottomilacensus.istat.it/). The municipal geographical data (shape files) were also taken from Istat sources. The thematic maps were created using QGIS 3.20.2 while the regression models were estimated using MGWR2.2 (Oshan et al., 2019).

3.1 Dependent Variable and Independent Variables

The dependent variable (y) is represented by the average annual rate of population change (r) expressed per thousand. For each municipality (i) it is defined as:

$$r={\text{ln}}\frac{{P}_{t}}{{P}_{0}}\times \frac{1}{t}\times 1000$$
(1)

where ln is the natural logarithm, P0 is the resident population of the municipality in 2011 and Pt is the resident population of the municipality in 2019. The four independent variables represent dimensions relevant to the growth or decline of a population in a given territory, namely the territory’s attractiveness to international migrants, the role of women in the local labour market, the level of youth employment and households’ potential need for assistance. As is usual in work with data relating to territories, these dimensions were measured indirectly through indicators that represent proxies. In this specific case, the indicators used were as follows:

  • Share of foreign population in per cent (x1) indicates how much the foreign population constitutes of the total resident population in each municipality. Comparatively high values of the indicator should indicate attractive territories (at least to the foreign population) with the same denominator. It must be considered that, as has been widely demonstrated, the foreign population has much greater territorial mobility than the citizen population (Casacchia et al., 2022), and it has often been argued that the former can contribute more to population growth than the latter overall since it has a younger average age structure and, usually, a higher propensity to have children (Strozza et al., 2007).

  • Female participation in the labour market in per cent (x2) measures the active participation in the labour market of the female population in each municipality. The indicator, also known as the activity rate of the female population, represents the percentage share of women who belong to the labour force (forming an ‘active population’ because they are employed or looking for work) out of the total female population of the appropriate age range. In essence, this figure represents the current offering of the job market and the propensity of the female population to carry out or want to carry out work activities capable of generating income. This is a crucial aspect that negatively characterizes Italian society as a whole (where female activity rates are notoriously low). Furthermore, it is a phenomenon closely connected to birth rate, even if the relationship between activity rates and fertility is, especially in Italy, complex and elusive (Bratti, 2003; Del Boca, 2002; Mencarini & Vignoli, 2018; Vignoli et al., 2020). Indeed, higher activity rates indicate greater autonomy for women and potentially more options for reproductive choices. At the same time, lack of parental support policies and rigid rules in the labour market, lead to the renounce or postponement of having children.

  • Youth employment rate in per cent (x3) indicates the employment level of young people (15–29 years old) in each municipality. In this case, as in the previous case, the relationship between this indicator and population change cannot be defined a priori. Theoretically, higher levels of the indicator could correspond to more dynamic territories in terms of the labour market, though a higher value of this indicator could, in the same way, indicate territories with less human capital, which are therefore potentially more exposed to emigration processes in the medium term [that analysed here; Staniscia and Benassi (2018)].

  • Share of households with a potential need for assistance in per cent (x4) indicates the share of total households with at least two members with all members aged 65 or over and at least one member aged 80 or over. The indicator measures the incidence of families made up only of elderly people and, therefore, potentially at risk of encountering difficulties in the case of the most elderly member(s) requiring care. In consideration of the high risk of chronic diseases and functional limitations in daily activities linked to advanced age, the indicator expresses an implicit demand for assistance and measures potential social vulnerability.

Of course, many other variables could be used. However, the overall goal is less to produce an efficient estimate of y than to define the spatial variability of the regressors. In fact, the general intent is to show how territorial classifications developed upstream on a national scale may not work when placed in peculiar local contexts because the local drivers of demographic change have their own specific geography, which may not coincide with taxonomies established from above. Given that the independent variables chosen are policy-responsive and that they are often described (even at the level of public debate) as relevant to demographic processes (Benassi et al., 2022, 2023a), the selection appears reasonable, as well as useful for the purposes of the overall analysis.

3.2 Local Regression Models

The estimated local regression models refer to GWR models (Fotheringham et al., 2003). The fundamental difference that exists between GWR models and traditional global regression models (ordinary least square [OLS] models) is that in the former, the spatial stationarity of the relationships between the dependent variable and the independent variables is not assumed a priori, as is implicitly—and often unconsciously—done when we apply OLS models to variable case matrices in which the statistical cases are territories (municipalities, provinces, etc.). This assumption represents a significant logical (as well as mathematical–statistical) forcing because it is akin to asserting that the processes we measure through our variables (y and x) manifest themselves in space in a uniform way. That assumption can easily be refuted by observing simple thematic maps and, in any case, it must be ascertained through specific statistical tests. In local estimation approaches, on the contrary, we are interested precisely in detecting the spatial non-stationarity of the regression coefficients. To this end, we therefore resort to the estimation of specific models, that is, GWR models, after using a Monte Carlo test to verify the existence of spatial variability (Li & Fotheringham, 2020). It follows that, if this test gives a negative result (i.e., there is no spatial variability for any independent variable), then it is not necessary to estimate a local model but would be sufficient to estimate a simple OLS. To summarize, OLS models are global, non-spatial models, while GWR models are local and spatial models. Following Oshan et al. (2019) for a generic GWR model, the linear regression model can be formalized as follows: assuming that there are n observations (i.e., n statistical units), for the observation \(i\in \left\{\mathrm{1,2},\dots ,n\right\}\) at location \(\left({u}_{i},{v}_{i}\right)\),

$${y}_{i}= {B}_{0}\left({u}_{i},{v}_{i}\right)+ {\sum }_{j}{B}_{j}\left({u}_{i},{v}_{i}\right){x}_{ij}+{\varepsilon }_{i}$$
(2)

where \({B}_{0}\left({u}_{i},{v}_{i}\right)\) is the intercept, \({x}_{ij}\) is the jth predictor variable, \({B}_{j}\left({u}_{i},{v}_{i}\right)\) is the jth coefficient, \({\varepsilon }_{i}\) is the error term and \({y}_{i}\) is the response (or dependent) variable. The dependent variable (y) can take different forms, which influence the type of GWR model chosen. In our case it was necessary to estimate a Gaussian GWR model. The model was estimated using a Golden Section algorithm (to identify the best bandwidth, i.e., the number of municipalities on which the different local models are estimated) and a spatial kernel of the adaptive bi-square type for the process of model weighting in the calibration phase. This type of kernel is appropriate when the distribution of statistical units (centroid) is not uniform (as in our case; see Fig. 2). As the optimization criterion, we used the corrected Akaike criterion (AICc) (Burnham & Anderson, 2004). These parameters and criterion are normally adopted in these types of models, which have also been applied in the Italian case, for example in relation to the potential economic distress of households (Benassi & Naccarato, 2017), the factors that affect the share of resident foreign workers in Italian provinces (Benassi & Naccarato, 2018) and, more recently, the analysis of Sri Lankan settlement models in major Italian urban areas (Bitonti et al., 2023).

Fig. 2
figure 2

a Municipalities of molise b centroids of the municipalities

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In the regression analysis, as is usual in this type of study, we first estimated an OLS (global and non-spatial) model. This model and its results served as a benchmark in evaluating the performance of the GWR model. The evaluation of the two models was conducted according to the classic parameters relating to the explanatory capacity (R2), the overall performance of the model (AICc) and the level of spatial clustering of the residuals (Moran’s I). The statistical significance of the regression coefficients and the overall consistency of the results were also compared and considered. From a purely spatial point of view, prior to the analysis, it was necessary to transform the polygons (the 136 municipalities of Molise; Fig. 2, Panel a) into points (of which we must know the geographical coordinates, as clearly shown in Eq. 2). To this end, we computed the centroids (or geographical centres of gravity) of each municipality. This step was necessary since the GWR model estimation is based on point geographies (Sachdeva & Fotheringham, 2020).

The variables (dependent and independent) were, prior to the regression analysis, standardized into a Z distribution so that each of them had a zero mean and a standard deviation of 1. This choice was also made to facilitate efficient computation, favouring interactions and therefore enabling faster fitting of the model itself (Oshan et al., 2019). Before moving on to the presentation and discussion of the results of the empirical analysis, we take this opportunity to note that a sensitivity and robustness check was conducted on the local estimates; this is available upon request to the authors. In fact, it is usually recommended to use at least 300 observations (Oshan et al., 2019). Molise is a very small region, both in terms of overall demographic size and number of municipalities—just 136. This obviously amounts to a number of observations smaller than 300. The analysis was therefore repeated, taking the municipalities of Molise and Abruzzo jointly as reference (for a total of over 440 municipalities). The two regions, which border one another geographically and which for many years formed a single region, have characteristics that are not overly dissimilar, granting the exercise, in addition to its usefulness in testing the robustness of the estimates made previously, an interpretative value of its own. The results, which are available from the authors on request, are consistent with those relating only to the Molise municipalities, thereby presenting no problems of instability and/or lack of robustness in the estimation procedure.

4 Results

In the presentation and discussion of the results, we first offer some descriptive statistics for the dependent and independent variables used in the regression analysis. We subsequently move to the results of the global and local regression models.

4.1 Some Descriptive Features of the Dependent and Independent Variables

In the municipalities of Molise, the average annual rate of population change in the period 2011− 2019, as shown in Table 1, has a negative mean value (− 8.9‰) and a particularly low minimum value (− 34.6‰). The four indicators, which represent the explanatory variables included in the regression models and were measured in 2011, also describe a peculiar regional context in which, among other points, there is a non-negligible share of households in potential need of assistance. This is a characteristic closely related to demographic ageing, which, in turn, is usually associated with shrinking populations (Reynaud & Miccoli, 2018).

Table 1 Summary statistics of the variables used in the regression analysis
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The parameters reported in Table 1 constitute syntheses of different geographical patterns. The territorial distribution of each indicator (Fig. 3) in fact represents a fairly heterogeneous regional context, albeit characterized by significantly widespread demographic fragility. As we can appreciate from Fig. 3, particularly low values of population change characterize many municipalities that are spatially contiguous to the coastal ones, but these are still far from being the most significant municipalities from a demographic and administrative point of view (such as Isernia and Campobasso, the two capital municipalities of the two provinces of the same names; see Appendix). The municipalities that recorded positive rates of population change in the period considered number only 16 (12% of the total) and they are mostly concentrated in the coastal area of the region. The other indicators also highlight a critical situation strongly reminiscent of the concept of “demographic malaise”, long since coined by Golini et al. (2000) precisely in reference to contexts similar to that observed here. The region’s demographic fragility is long-standing and, as shown by recent contributions on the topic (Reynaud et al., 2020), is prone to deepen over time as a self-propelled and spreading phenomenon.

Fig. 3
figure 3

Quantile maps of the dependent variable and independent variables

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The relatively low values of the share of foreign population show a widespread lack of attractiveness of these territories for international migration or internal migration by foreign populations. In fact, the value of the indicator for Italy as a whole in 2011 was approximately 7%. Below this value, we find 127 municipalities, that is to say, almost all of Molise’s municipalities. It seems worthwhile to observe that the areas with the greatest foreign resident presence are, as highlighted by the map, only in some cases those with the greatest demographic dynamism (as, for example, in the case of the coastal municipalities), demonstrating that, as previously anticipated in the discussion of this indicator, comparatively high values of the indicator may in some cases signify contexts with a small overall population (they are those municipalities which in fact recorded significant negative values for average annual growth rate). In these contexts, the foreign resident presence, although not capable of reversing the process of demographic contraction that has been underway for some time, has at least guaranteed strong resistance, thus avoiding total demographic collapse and effectively keeping alive territories otherwise struggling in terms of generational change. Similar situations pertain to the other indicators. The geography of women’s participation in the labour market outlines a region “spatially broken” between, on the one hand, municipalities located on the coast and in areas adjacent to it and municipalities located around the two provincial capitals (Campobasso and Isernia), which record comparatively high values of the indicator (though these are still low compared to the national average of 41.8%), and on the other hand, a spatially compact area of municipalities in which the indicator values are very low. The youth employment rate and the index of households in potential need of assistance similarly show a heterogeneous regional territory with strong differences between municipalities. Furthermore, the local situation with regard to these two indicators is also far from the national average, which in 2011 was 34.7% for the first indicator and 3.0% for the second. This large intra-regional local heterogeneity underscores the empirical (as well as theoretical, which we have already discussed here) need for locally calibrated intervention areas as well as areas defined on a national scale (using top-down logic).

4.2 Regression Models

The OLS model, the results of which are contained in Table 2, shows good explanatory capacity (just under half of the variance of y is “explained” by the model). The AICc index is equal to 318.862. The Moran’s I index (Moran, 1948) highlights the absence of spatial autocorrelation in the geographical distribution of the residuals. The model, based on the tolerance, variance inflation factor and multicollinearity condition number parameters, does not appear to be affected by multicollinearity problems. In fact, the variance inflation factor is relatively low for each variable (< 10), and although on average it is slightly greater than 1 (1.30), the average tolerance is not less than 0.2 (0.81); therefore, we can exclude problems of collinearity (Goss-Sampson, 2019). At a global level, this is confirmed by the value of the last parameter (multicollinearity condition number), which, being lower than 30 (26.11), excludes the existence of multicollinearity (Anselin & Rey, 2014). This is, naturally, at the level of global estimates; for the local estimates, we calculated a specific local test since the local regression models are subject, at least theoretically, to problems of collinearity in the local estimates (Wheeler & Tiefelsdorf, 2005). These problems, however, now seem to be resolved (Fotheringham & Oshan, 2016); we will return to this issue shortly.

Table 2 Global regression results (ordinary least squares model)
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The two explanatory variables whose regression coefficients (betas), at a global level, are statistically significant (p < 0.05) are female participation in the labour market (x2), with β equal to 0.384, and the share of households in potential need of assistance (x4), with β equal to − 0.369. In relation to the first variable, the results show that in local contexts where the level of participation in the labour market of women was higher (as of 2011), population growth in the subsequent period was, other conditions being equal, greater. Conversely, the index of households in potential need of assistance (as of 2011) has a negative correlation (again at a global level) with the population change observed in the period 2011–2019. This second variable is, by construction (as described in Sect. 3 above), an indicator of the age structure of the population: it essentially measures the municipality’s share of “elderly” households, which may, as a consequence of members’ ages, be in need of assistance. The model therefore shows that the territories with the greatest share of elderly households and hence the greatest potential need for assistance (in 2011) were those contexts in which, other conditions being equal, the change in the population in the subsequent period was (more strongly) negative, thus confirming the relationship between ageing and demographic decline on a local scale (Reynaud & Miccoli, 2018) but also highlighting the idea of the vicious circle of marginality/fragility (De Lucia et al., 2020). The results of the global OLS model also indicate that the share of foreign population (as of 2011) and the youth employment rate (as of 2011) do not qualify, for the time period observed here and following a global regression logic, as drivers of population change in Molise’s municipalities, as their regression coefficients are not statistically significant.

Obviously, what has been said above is valid “on average”, that is, assuming that the estimated regression equation (which is singular in this case and does not include any spatial dimension) is representative of all local relations. This is a point always worth ascertaining when the statistical units are, as in our case, territories and when, as in our case, the geographical variability of the indicators appears evident (Matthews & Yang, 2012). Before continuing with the local estimates, therefore, it is necessary to statistically ascertain the existence (or nonexistence) of spatial variability of the independent variables that we intend to include in the model. The results of the Monte Carlo test are reported in Table 3. As we can see, net of the intercept, the only variable that shows statistically significant spatial variability (p < 0.05) is x2, female participation in the labour market. It is no coincidence that this same variable demonstrated the greatest impact, in the OLS model, on y.

Table 3 Monte Carlo test for spatial variability
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The results of the Monte Carlo test tell us at least two things: it is incorrect to estimate a completely global effects model (such as OLS); and from a strictly statistical point of view, the local effects should be estimated only for the variable x2. In this work, we thus naturally focus in particular on the local estimates of x2; however, for purely illustrative purposes, we also report the results of the local estimates of the other explanatory variables included in the GWR model. Those results, to which we will return shortly, are therefore those relating to a GWR model estimated with only local effects (as if all the variables inserted in the model itself varied spatially) as indicated in Eq. (1). Before presenting the results of the local regressions analytically, it is appropriate to observe (see Table 4) that the GWR model, on an overall level, is statistically preferable to the global one. The former model’s explanatory capacity is higher (R2 is now 0.61, significantly higher than before), while the AICc index is lower (303.7), thus highlighting a better fitting. In both cases, the residuals are not clustered, but it is useful to observe that the value of Moran’s I is even closer to zero in the case of the GWR model.

Table 4 Comparison between OLS and GWR models
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Figure 4 shows two maps. The first (Panel a) reports the values of the local R2 obtained using the estimated GWR model. The second (Panel b) reports the values of the local condition number, which inform us about the possible presence of local collinearity problems inherent to the estimates obtained. The overall R2 of the GWR model was 0.61, but as is evident (see Fig. 3, Panel a), this “global” value is not actually stable in space; on the contrary, it presents a marked variability indicating rather a clear geographical pattern. The map, constructed using the natural breaks method, highlights how, as one moves from the coast towards the interior, the explanatory capacity of the model, though remaining relatively high (especially in comparison to that of the OLS model), decreases significantly. The map relating to the local condition number (Fig. 4, Panel b) provides reassurance because, consistently with what has already been observed at a global level, it clearly highlights that there are no problems of local multicollinearity of the estimates (as the values are well below 10).

Fig. 4
figure 4

a Local R2 b local condition number

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We can thus move on to comment on the local estimates in both aggregate form (Table 5) and analytical form (Figs. 5 and 6). The summary statistics of the local estimates show that there is variability in these estimates, therefore indicating that these have peculiar geographical distributions, not visible in the global estimation processes, that must be mapped and analysed.

Table 5 Summary statistics of local regression (geographically weighted regression model)
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Fig. 5
figure 5

Local parameter estimates of female participation in the labour market (x2)

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Fig. 6
figure 6

Local parameter estimates of the independent variables with non-significant spatial variability

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To better understand and analyse the variability of the local estimates, it is useful to map them, thus creating thematic maps that allow us to evaluate where these estimates are significant (and where not) and observe possible variations in intensity and sign of the local coefficients in comparison with the global one obtained using the OLS model. As highlighted by Matthews and Yang (2012), this is the distinctive feature and added value of using local regression models. Figure 5 shows the local parameter estimates of the only variable that was not spatially stable based on the results of the Monte Carlo test (see Table 3). The results, especially when compared with the global result, are of interest for the purposes of our study.

At a global level, the impact of x2 was positive, with β equal to 0.384. The local estimates highlight some interesting points in this regard: (a) the local coefficients (where significant, p < 0.05) show variable intensities that outline well-defined geographies (for example, in the area of north-eastern Molise, the impact is higher than the global one); and (b) the relationship is not significant everywhere. The implications of such empirical evidence, especially in connection with the policies to be adopted and financed, are evident. We will return to this point in the next section.

As stated above, we also report, for descriptive purposes, the local estimates of the other variables included in the model (x1, x3 and x4), whose geographies are represented in the maps of Fig. 6. We also propose an interpretation of them below, although it is worth recalling that these results must be treated with caution given the results of the Monte Carlo test.

At the global level, the impact of x1 was not statistically significant. Local estimates confirm (only in part) what was found on a global scale. The foreign component of the population (as of 2011) had no significant effect on the population change that occurred over the period 2011–2019 (y) in the vast majority of municipalities, but not in all. Where it played a role, it was a negative one, a seemingly counterintuitive result worth reflecting on. One interpretation could be that, as previously suggested, the foreign resident presence was relatively high in municipalities with a small population and subject to strong depopulation. In these contexts, therefore, the possibility cannot be ruled out that the foreign presence contributed to preventing demographic collapse. At the global level, the impact of x3 on y was not statistically significant. The local estimates highlight that this was not the case everywhere. Indeed, we note that there is a spatially compact set of municipalities in which the effect was significant and negative (all other conditions being equal). In these municipalities, a higher level of youth employment in 2011 produced a negative effect on the population change recorded in these same municipalities in the period 2011–2019. The result is paradoxical at first reading. In reality, however, it tells us something important: supporting the employment rate of young people is a crucial intervention, but we must reflect on what types of employment to promote, for what types of young people and in what types of territories. Poor paid and precarious jobs may in fact not allow for the minimum economic (and emotional) stability necessary (although not necessarily sufficient in itself) to have children or to not migrate. At a global level, the impact of x4 was negative, with β equal to − 0.369. The local estimates highlight that the impact was statistically significant in some areas and that, where significant, it takes on different intensities which, as in the previous cases, shape peculiar geographies. The strongest negative effects (dark brown polygons) are concentrated in a specific area of the region. The information we derive from these local estimates (and from their geographical distribution, in particular) is clear: the problem (as of 2011) of households in potential need of assistance had a negative impact on population change between 2011 and 2019. If we are to invest to counteract the phenomenon in a spatially targeted way, we should concentrate this investment where the impact has been most negative. Naturally, there is little that can be done on the demand side because the elderly population will continue to grow and what we see in the estimates is a classic age structure effect. However, the results can help us consider, with proper perspective, the best options for intervention in terms of the territorial organization of care service provision. A viable strategy could address the recruitment of carers, including through municipal public tenders, to be allocated precisely in these areas or consider the construction of accessible infrastructures used for the care of the elderly, such as assisted residential facilities, or the public acquisition of suitable privately owned apartments. At the same time, policies attractive to young people and new families could help reduce the structural demographic imbalances that, as we have seen, specifically affect some areas of Molise more than others.

5 Discussion and Conclusions

The results obtained here highlight the relevance of space in approaching demographic processes at a municipal scale or, in the words of Fotheringham and Sachdeva (2022), the “importance of thinking locally for statistics and society”. In particular, these results demonstrate the importance of local spatial approaches for providing information that allows the implementation of spatially targeted policies and that can subsequently allow for capturing the effect over time of such policies.

The fundamental idea underlying the construction of inner areas as defined within the SNAI appears to be thus confirmed as both valid and viable as well as extremely current and necessary, as has also been underlined by the most recent programmatic reporting at the European level (Muti, 2023). Nonetheless, the criteria and logic adopted for the construction of these areas, at least from our demographic point of view, could be fruitfully reconsidered and perhaps revised in light of the type of analysis we have proposed.

From this perspective, the case of Molise seems paradigmatic if not exactly unique. Two variables that are usually considered drivers of demographic growth, namely the foreign resident presence and youth employment, do not seem to have had a significant effect on population change in Molise (at least in the period considered). This shows that approaches that work for many may not always work for all, therefore indicating the need for the establishment of regional demographic observatories. Furthermore, the results related to the two variables suggest that those who are typically more geographically mobile (i.e., those who have a greater propensity to migrate), such as foreigners and young people, have probably left Molise in the period observed.

From this point of view, it is therefore necessary to invest in policies that maximise the attractiveness of areas for migrants from other Italian regions or from abroad, while at the same time trying to retain those who are already present in the territory. To this end, it is necessary to try to make the region more competitive and attractive through policies aimed at reducing the infrastructural gaps that still characterise the entire regional territory, one of the least accessible in Italy. Attractive policies can also focus on reducing taxes on the earned income of certain groups of the population (e.g. young people), or policies to encourage the purchase of housing by those who wish to settle permanently in the Molise region.

Complicating these observations, however, the results of the local estimates clearly show that what is detected at a global level can be the result of highly heterogeneous local dynamics. The case of the activity rate of the female component of the population is a clear example of this. The local estimates of the relationship existing between this variable, measured in 2011, and the population change recorded between 2011 and 2019 in fact show peculiar geographies characterized by variable intensities and large areas in which the relationship is not statistically significant, coupled with a positive and statistically significant overall estimate. What this means in terms of territorial planning is rather intuitive. To calibrate a public policy intervention on the basis of the results of the global model, in order to support demographic growth, it would be necessary to invest money and resources to support the female activity rate in all Molise municipalities (a top-down approach). In this case, therefore, the place-based policy would be of a regional type. In reality, following this approach, at least at the level of the Molise region, would waste public money and secure only modest results. The mapping of local estimates clearly indicates that for the effective investment of resources on women’s participation in the labour market in order to support demographic growth within a limited budgetary framework, these resources must be directed as a first option to the municipalities (which form a compact block) where the local relationship between women’s labour participation and demographic growth is intense and significant and only as a second option to the municipalities where the relationship is comparatively less so. Directing money, resources and interventions to municipalities where the relationship is not statistically significant would in fact imply losing money, a net cost given that the investment concerned is public and not private. As a side note and a further indication of the importance of local evidence, it would also be necessary to understand what happens in those municipalities where the relationship is not statistically significant and try to remove any obstacles that place female labour market participation and fertility in competition, thus applying a combination of differentiated and multi-scale interventions, as already described in the pioneering contribution of Willekens and Heide (1985).

The findings presented herein can serve as a useful tool, illustrating the significance of local statistical data in reinforcing regional demographic planning efforts. To support the engagement of women in the workforce, tailored policies aimed at maximising the flexibility of working hours and, at the same time, at guaranteeing access to full-time schooling so as to make the choice between work participation and family role less problematic, are needed. Moreover, accessibility of places and services that can be spread over more municipalities than those of work and/or residence becomes a relevant issue.

What to do, then? The results for the case of Molise make one thing clear. We need to address two components of the population:

  • The female component (by supporting women’s participation in the labour market with territorially targeted policies in the areas identified as having a positive relationship between this and demographic growth but also with interventions aimed at making the relationship statistically significant where it was not found to be so, hence with a view to territorial diversification of interventions)

  • The elderly component, attempting to reduce the share of households in potential need of assistance (by investing in the areas where the impact on population change was strongest to increase the services available, as detailed in the previous paragraph, but also by attracting new, possibly young families, perhaps through ad hoc policies for housing and new settlements)

It is noted that the female population and the presence of elderly people are crucial and unavoidable components of the current (and past) demographic system. To support fertility, in fact, it is necessary for a population to have a significant share of women of childbearing age, a share which is progressively diminishing due to the decline in births, triggering the so-called demographic trap (Mencarini & Vignoli, 2018); it is also necessary that these women not be put in the position of having to choose between a productive and reproductive role. Simultaneously, even with health and care provision remaining static, the population ageing process, which has been underway in Italy for some time now and which is particularly widespread in Molise, will ensure that the share of households in potential need of assistance increases considerably in the years to come. It will therefore be necessary to work to increase the self-containment capacity of the Molise regional system and its various local components by diluting the factors that underlie emigration to other Italian regions or abroad and, at the same time, increase the region and its component contexts’ capacity to attract new families and new individuals both from within and abroad. All of this must be done while also supporting the processes of endogenous demographic growth, that is, supporting fertility. A fundamental consideration from this point of view, in relation to both reproductive choices (deciding to have children) and the attractiveness or self-containment capacity of territories, is undoubtedly the labour market. The local results seem to indicate, coherently with what has been found by other studies conducted on the topic of female job insecurity and reproductive choices in Italy (Modena & Sabatini, 2012; Modena et al., 2014) but also, in more general terms, on economic uncertainty and reproductive choices (Vignoli et al., 2020), that the deterrent to having children is not determined, at least in the areas where the relationship between female labour market participation and demographic growth is statistically significant, by the greater participation in the female labour market (since this causes an increase in the monetary costs associated with having children) but rather by precarious work and the instability of the working condition in general (as a result of occasional and low-paid jobs), which notoriously mainly affect the “most fragile” categories, namely women but also foreign residents (allowing, of course, that the two categories are not mutually exclusive but rather present vast areas of intersection). As is evident from the analyses conducted here, we do not currently have variables capable of directly measuring this aspect, but the combined analysis of local estimates of female activity rates, foreign presence and, above all, youth employment rates (15–34 years) seems to support these theses. Investing therefore in non-precarious, non-occasional job provision, possibly that of jobs with a high human capital content, seems an important dimension for stimulating the growth of territories. Naturally, this aspect would not only facilitate the reproductive choices of couples but also serve as a factor of attraction (for internal and international migration) and increased self-containment (reducing emigration). The crucial issue, however, seems to be the local dimension of these relationships.

We conclude this contribution with some reflections of a more general nature regarding what is currently being done in Italy, also from a future-oriented perspective. As a premise, it must first be said that the SNAI is an initiative which, although naturally open to improvement, has represented from its inception a keystone in the setting and management of active policies aimed at combating the factors underlying the lack of development of vast areas of Italy. It is a strategy which, for the first time in Italy, has put in place an operational structure that functions for the adoption of real place-based policies that, in more than a few cases, have allowed an improvement in their contexts of operation and, in a more general sense, have made it possible to measure these improvements (or even non-improvements), thus allowing an evaluation of the elements of the different contexts and policies adopted. All of this has significantly contributed to the birth and growth of a certain sensitivity to the local dimension of socioeconomic processes and to the dilution of the processes of spatial polarization in progress (Barca, 2019). As a national strategy with a direction designed and implemented at a national scale, for the definition of internal areas, the SNAI has adopted, as we have seen, a top–down logic, a choice which, especially where intra-regional heterogeneities are large, may have led to the lower effectiveness of the classification itself (Scrofani & Accordino, 2023). Nonetheless—and this is an unavoidable fact—space is a continuous variable and any classification of it, however accurate and methodologically rigorous, by definition involves a loss of information. The reason for this loss is mathematical–statistical and thus represents a caveat that must always be taken into consideration. Our contribution therefore represents a proposal for an operational logic to be understood as complementary to that which forms the basis of the SNAI, a logic which has its roots in spatial approaches to population studies. It must also be said that the classification of internal areas itself is not a static reality but is, on the contrary, to be understood as dynamic and variable over time. This is demonstrated by the new inner areas (2021–2027), which present interesting innovations compared to the previous schema from both a quantitative point of view (there are 56 new internal areas for a total of 549 municipalities and a resident population of over 2 million) and a qualitative one (for example in the “smaller islands project”), thus illustrating the process of successive approximation that characterizes any empirical experiment, even within the social sciences. In this regard, it is also necessary to underline that our “exercise” stops in 2019, that is, before the Covid-19 pandemic. This event, on the one hand, represented an exogenous shock capable of significantly altering “normal” demographic dynamics, and for this disturbing aspect it was excluded from the analysis, while on the other hand, it also stimulated the different local contexts, especially rural contexts and those with low human pressure, to adopt policies to attract new residents (so-called nomadic workers), including through the leveraging of (relatively) new forms of work such as smart working (Corazza, 2022). The future is, therefore, unwritten, and there are many potential scenarios that may emerge in front of us. It is obvious, however, that a necessary (although not sufficient) condition for the success of these policies aimed at attracting to more rural contexts prospective workers and, therefore, new families and settlements is that these contexts are, for example, connected on the digital level (Petrillo et al., 2021). To do this, it is necessary to reduce the digital divide, which is a significant phenomenon in Italy (Ruggieri et al., 2015) and which also, thanks to initiatives such as the SNAI, is the subject of territorially targeted interventions, which we hope will be able to produce positive effects for the entire national system.