Despite the large attention given to regional disparities, a conceptual framework simultaneously linking the inter- and intra-regional development processes over time is still missing. A vast set of empirical analyses on their trends indeed exists. In most cases, it witnesses the presence of the famous Williamson’s inverted U-shaped relation between GDP per capita and regional income inequalities, and of its augmented shape where the inverted U turns upward again at later stages of development. The paper has the aim to present a conceptual framework on the interlinkages between inter- and intra-regional disparity trends, highlighting the influence that one exerts over the other. It does so claiming that their joint analysis can provide an explanation of situations “against conventional wisdom” and can overcome the simplistic idea that if inter-regional convergence occurs, social equity is achieved. Empirical evidence is provided in the case of European regions. The paper has a normative value, in that an interpretation of the concurrent inequality trends at different levels can lead to more efficient normative interventions, avoiding misallocation of financial resources at sub-regional level.
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1 Introduction
The trends and causes of regional income inequalities have long been of great interest to economic researchers and policy makers, as witnessed by the large literature existing in the field and by the interest of international institutions like the European Union, the OECD and the United Nations in advocating for inclusive development (Castells-Quintana et al. 2015). An excessive level of disparities has in fact been seen as an obstacle to growth, calling for specific analyses of their trends (e.g. Barro 2000, Persson and Tabellini 1994, Castells-Quintana and Royuela 2017, Camagni 2024).
Since Williamson’s famous inverted U-shaped curve (Williamson 1965), a large set of studies has been developed with the aim to provide empirical evidence of such a trend that suggests at regional level the Kuznets’ increasing path of personal inequalities within countries in early stages of economic development and decreasing in later stages (Kuznets 1955). However, the results on the existence of the bell relationship are still controversial.1 Recently, the literature suggested a notion of a Williamson wave or cycle, where an alternative shape of an augmented Williamson’s curve taking the form of an N- or a sideways S-curve was proposed (Conceicao and Galbraith 2000, Milanovic 2016; Castells-Quintana 2018; Breau and Lee 2023). The inverted U, in fact, is found to go upward again for the countries with the highest level of development, in line with the debate on the Kuznets curve (Ram 1997; List and Gallet 1999; Breau and Lee 2023).2
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Additional related literature has investigated whether convergence or divergence trends prevail. On the theoretical ground, the New Economic Geography contributed to the interpretation of regional disparity trends by elegantly introducing the relevance of centripetal and centrifugal forces pushing activities in space, and demonstrating that multiple equilibria—convergent or divergent, explosive or implosive, stable or unstable growth paths—may exist according to the values of the parameters of the structural relations of development (Krugman 1991; Krugman and Venables 1996; Venables 1996). On the empirical ground, neoclassical approaches focused on the existence of “conditional convergence” such as those conducted by Barro and Sala-i-Martin (1991 and 1992), who measure a moderate convergence rate at levels of 2% per annum. In contrast, other studies find either no convergence or even divergence (Cuadrado-Roura 2001; Lopez-Bazo et al. 1999; Magrini 1999; Puga 2002; Rodríguez-Pose 1999; Petrakos et al. 2005).
Even if to a much lower extent, attempts to understand inequality trends have been made at the intra-regional level. They mainly focused on whether a Williamson’s type of relationship between per capita GDP and regional income inequalities existed within regions, achieving what have been defined as results “against conventional wisdom” (Artelaris and Petrakos 2016, p. 291; Amos 1988). In particular, Artelaris and Petrakos (2016) find a U-shaped curve, rather than an inverted U-shaped one, claiming that this raises doubts about the adequacy and interpretative power of the Williamson’s hypothesis. In his study, instead, Amos (1988) asserts that an interesting issue is what happens at the end of the curve, i.e. in the later stages of development—when the curve unexpectedly shows divergence instead of convergence among intra-regional per capita GDP. This calls for more in-depth analysis.
Despite the interest in the validity of the inverted U-shaped curve, we agree with the researchers who claim that the attention in the literature on regional disparities trends has been on empirically testing Williamson’s law rather than on formulating a theory of regional income inequality (Fisch 1984; Fan and Casetti 1994). Instead, some reflections still need to be carried out on the way the path of development takes place. In a memorable presidential address at the Los Angeles Regional Science Association meeting in 1979, Alonso proposed the “five bell shapes in development,” based on the notion of unbalanced growth in the early stages of development, followed by progressive social, economic and geographical integration in the later stages. The five bells—namely development stages, social inequality, regional inequality, geographical concentration and demographic transition—are concurrent in development, but their interactions have not been studied enough (Alonso 1980).
In this paper, we take up the challenge launched by Alonso and present first reflections on the concurrent evolution of regional inequality and spatial polarisation/diffusion, which could lead to the formulation of a theory on the interlinkages between inter- and intra-regional disparity trends. We are indeed convinced that their joint analysis can provide an explanation of situations “against conventional wisdom” and overcome the simplistic idea that if inter-regional convergence occurs, social equity is achieved. Instead, the later stages of development, when the Williamson’s curve shows convergence, can be associated with high-income polarisation trends within regions, a situation which is far from reflecting social equity. Moreover, the analysis of the concurrent evolution of disparity trends at different geographical level can help more efficient normative interventions. Indeed, as mentioned by the literature (Gagliardi and Percoco 2017; López-Villuendas and del Campo 2024), a misallocation of financial resources can easily take place at the sub-regional level.
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While the paper does not intend to build a full-fledged theory of regional income inequality, it has the aim to elaborate a conceptual framework able to lead towards the formulation of a theory on the interlinkages between inter- and intra-regional disparity trends and on the influence that one exerts over the other.
An approach like this calls for the merging of two blocks of theories: regional growth theories, able to explain why growth happens in one region and not in others, on the one hand, and location theory, and particularly the growth centre literature discussed, among others, by Perroux (1955), Hansen (1967), Lasuen (1962), Lewis and Prescott (1972), on the other. This latter can explain through the location choices of economic activities how development (growth) diffuses over space. Such theories provide a ready pool of knowledge that, once appropriately applied, can supply a possible interpretative framework of the double bell in regional dynamic income inequality, giving a logic explanation to the results that at present seem to go against “conventional wisdom.” The purpose of the empirical analysis is to verify our suggested approach.
In order to address the topics highlighted above, the paper is organised as follows. The next section (Sect. 2) explains our theory on the evolution of inter- and intra-regional disparities. Subsequently, the operational identification of different groups of countries is illustrated (Sect. 3) and an empirical verification of the conceptual framework over time is reported (Sect. 4). Finally, concluding reflections are put forward (Sect. 5).
2 A double bell interpretation of regional disparity trends
2.1 Conceptual assumptions
As we mentioned above, the aim of this work is to provide an integrated framework of the way regional disparities evolve at different spatial levels. The Williamson’s theory (Williamson 1965) is the main reference in this respect. It analyses the evolution of the country starting from early stages of development through an inverted U-shaped relationship between disparities and regional development.
Once one wants to verify the Williamson’s law in the real world, one has to take into consideration that divergence and convergence trends heavily depend on the choice of a time period (Petrakos et al. 2005). In this respect, our model is conceptualised starting from an exogenous expansionary shock that hits the regional and local economic systems and aims at describing the expected spatial growth trends and their regional disparities, irrespective of the development stage of a country.
Intra-country regional disparities deal with differences in per capita GDP among regions belonging to the same country, and their evolution is therefore explained by the reasons for GDP growth to occur in one region or another.3 Intra-regional income inequalities, instead, are explained by the way in which, once a region starts growing, development spreads around. They are therefore associated with the spatial development processes, governed by the changes in the presence of attractive (repulsive) locational factors, giving rise to a core or peripheral development.
The attractive location factors are represented by the availability in an area of economic resources, in the form of production factors and growth assets in general. They are especially present in core areas, i.e. cities. In a geographical perspective, indeed, a city is a locus where growth assets—e.g. human capital, private and public services, accessibility and knowledge accumulation—are concentrated. In a territorial perspective, a city is a source of growth (Camagni 2004), producing increasing returns in the form of agglomeration economies for the firms there located (Alonso 1971; Duranton and Puga 2004). The periphery, made of middle and small cities or rural areas, according to the settlement structure of the region, has instead a limited endowment of growth assets.
Our theoretical model is built with the idea to conceptually link inter- and intra-regional disparity trends within the same country. The model is based on the following assumptions:
1.
Two countries exist, each characterised by a poor and a rich region;
2.
Regions have either a spatially uneven distribution of economic resources (urban–rural structure) or a spatially even one (urban polycentric structure);
3.
Each country is characterised by one of the two types of settlement structure;
4.
The propagation speed of growth and development is different in the two countries, as it depends on the presence of economic resources in possible alternative locations than the one where growth insists. In the country with a spatially uneven distribution of resources, the fastest growth transmission channels are the inter-regional ones, and growth opportunities spread firstly horizontally between cities of the same hierarchical level within the national urban system, as suggested by the city network theory (Camagni and Salone 1993). Cooperation among actors in this case takes place through long-distance linkages among actors located in faraway cities where the necessary economic resources are available. Instead, in the country with a spatially even distribution of resources, the quickest growth transmission channels are the intra-regional ones. Growth opportunities first emerge through the regional urban system in close by areas where the necessary growth assets are available, as spatial spillover effects;
5.
Technological progress and the evolution of knowledge take place over time, relaunching a new growth cycle. Technological progress has inevitably an urban nature, taking place in the core city irrespective of the settlement structure of a region. This is especially the case during the incubation or invention phase, related to the take-off of a new technology. Its effects are assumed to be first noticed in the largest and most central metropolitan areas, irrespective of which settlement context they are in, as largely highlighted by the spatial innovation diffusion theory (Hägerstrand 1967; Davelaar 1991).
This is graphically presented in Fig. 1. Each country is characterised by either an even or an uneven distribution of resources and by the presence of a rich and a poor region. In the first case, the first spatial transmission of growth occurs between regions, followed by a within regional diffusion. In the second case, the homogenous spatial distribution of resources allows the transmission of growth to take place first within the region and then between regions.
Fig. 1
Growth propagation speed in two different country archetypes.
Legend: arrows = the transmission of growth, numbers = order of the move
×
The model explains what happens once an expansionary shock to the national economy takes place. The theory suggests that inter-regional disparities start to increase and then to decrease, following the inverted U-shaped curve à la Williamson. Whatever the settlement structure archetype of the country, growth starts where there is an availability of productive assets, i.e. in the core region. Therefore, inter-regional disparities grow due to the well-known “crowding-out” effects which favour the strong economy over the weak one. The rich area does not exert pull effects on the poor one because capital flows, the availability of infrastructures, services and a potential market, better environmental conditions for firms and allocation of a larger share of public investments to strong areas make the wealthier region still more attractive and competitive. Emigration of skilled labour from the weak area to the strong one worsens the situation. Over time, the processes exacerbating regional disparities within a country continue until mechanisms working in the opposite direction begin to operate, leading to a decrease in inter-regional disparities.
Associated with such an inter-regional trend we expect an intra-regional curve changing its shape according to the settlement structure archetype prevailing in the country. In a situation of uneven spatial distribution of resources, the expansionary push takes place in cities, representing the natural loci of high-quality production factors, knowledge and innovative capacity, and attracting new productive activities thanks to agglomeration economies, of both static and dynamic nature widening the gap between urban and peripheral areas in the core regions. When the cities in the core region reach congestion effects, more peripheral but also more convenient locations are chosen, thanks to their availability of production factors (especially labour and land) close to the core of the large city, which still offers, thanks to its physical proximity and accessibility, all its advanced services to population and business activities. Instead, in a situation of even spatial distribution of resources, the effects of the expansionary shock spread simultaneously along the regional urban hierarchy within the region (Camagni 1993), with the consequence of decreasing intra-regional inequalities.
The literature is vague as to when the reverse points occur in the inter- and intra-regional curves. According to Alonso, this is something that can only be proved empirically (Alonso 1980). Instead, given our assumptions, we expect the inverted intra-regional U-shaped curve to achieve its peak, or its polarisation reverse as Richardson called it (Richardson 1980), after the inter-regional one, when we are in the archetype of spatially unevenly distribution of resources. The opposite holds in the other archetype of spatially evenly distribution of resources, as explained in depth in the next section.
2.2 The spatially uneven resource country archetype: The concentration diffusion trend
The concurrent trends in inter- and intra-regional disparities in the spatially uneven resource country archetype are presented in Fig. 2, where four clear conceptual phases of spatial development are depicted.
Fig. 2
Double bell in regional disparities: phases of development in a spatially uneven resource country archetype
×
2.2.1 The concentration phase
The starting of growth is determined by initial location advantages, in the form of resource endowment, accessibility and attractiveness, of the strong region. Within it, location advantages are concentrated, in this country archetype, in the large city. The first expansionary shock is followed by a cumulative, self-reinforcing process, driven by increasing returns to scale and by the crowding out effects, which favours the strong region over the weak one. The expected high returns attract public and private investments that once again reinforce the positive effects, as suggested by Williamson (1965).
In the first phase, therefore, growth is concentrated in the rich region, with a spatial concentration of economic activities in the large city. As a result, a core–periphery model of development is established, both between and within regions, with the strong region consisting of a primate city that dominates over the rest of the space that depends on it, à la Christaller (1933) and Losch (1940) (Table 1). This leads to a concentration phase, characterised by an increase in both inter- and intra-regional disparities (Fig. 2).
Table 1
Development phases and the reasons for their sequentiality: the spatially uneven resource country archetype
In italics: reasons for the inversion of the trend
2.2.2 The concentrated diffusion phase
Over time, growth filters through horizontal linkages from the large city of the strong region to the large city of the weak one. Thanks to strong economic, social and physical interconnections among large cities, in fact, the geographical, historical and cultural specificities of each individual city in the country provide a broad and diversified range of possible urban locations for firms and households (Alonso 1980; Fan and Casetti 1994).
Williamson (1965) highlights specific mechanisms working in the direction of inter-regional dispersion. New activities and jobs are created in less developed regions, stemming from market saturations and physical congestion of rich regions. The diffusion of growth in less developed areas, however, takes place unevenly. Less developed regions attract new activities in selected, large urban centres, offering agglomeration economies and economies of scale. The consequence is that most of the growth insists on the large city of the weak area, giving rise to a worsening of intra-regional disparities (Table 1). A concentrated diffusion phase takes place, in which the inter-regional convergence comes at the expenses of an increase in intra-regional income disparities (Fig. 2).
2.2.3 The diffused concentration phase
While time passes, the centripetal forces emerge again, relaunched by technological progress, social changes and the evolution of knowledge. The inter-regional inequality trends abandon what is seen as a natural, deterministic and universal market law by neoclassical economists, and start growing again, thanks also to a spatial transformation that begins to occur within the strong region. It is in fact difficult to claim that the inverted U-shaped form of the inter-regional disparities remains fixed. The above-mentioned factors may indeed give the advanced region the capacity to shift the frontier of decreasing returns on investment at higher level of development.
The economic relaunch of the strong region has a negative impact on its intra-regional inequalities, since the large city of the rich region starts growing again (Table 1, case a). At the same time, in the weak region, the large city may achieve its peak. In this case, all congestion effects and increasing land values exert a pull effect of activities and population towards the periphery of the weak region that move towards either satellite (medium and small) cities when they exist, or towards rural areas, close to the primary city (Table 1, case b). The new locations allow to enjoy the agglomeration benefits of the large city, as suggested by the “borrowed size” theory developed by Alonso (1973). This leads to a spatially homogeneous development within the weak area.
The overall (national) effect on intra-regional disparities depends on what prevails: if the growth of the large city in the rich region or the spatial diffusion of growth in the weak one. If the latter prevails, a diffused concentration takes place characterised by increasing inter-regional income inequalities and decreasing intra-regional ones (Fig. 2).
2.2.4 The diffusion phase
After the diffused concentration phase, one could expect a diffusion phase (Fig. 2). In fact, once the large city of the strong area achieves saturation levels, growth moves towards the large city of the weak area leading to a diffusion at the inter-regional level, while intra-regional disparities continue their decreasing trend (Table 1). However, it is difficult to find clear conceptual explanations for this trend to continue, since once the diffusion occurs at the inter-regional level, this should be expected to go at detriment of an intra-regional diffusion.
We leave to empirical evidence the proof of the existence of this phase.
2.3 The spatially even resource country archetype: The diffused concentration—concentrated diffusion trend
The development of the four phases depicted in the previous section assumes that, once the expansionary shock occurs, growth concentrates in the core region, where most of growth assets are located, with the consequence that inter-regional disparities worsen. This is also the case of a country with spatially even resources, since it is largely implausible that growth starts in peripheral regions, leading to a decrease of inter-regional disparities.
In this country archetype, however, the core region is characterised by a diffused urban settlement structure, made of individual cities, well connected and integrated, that shape a regional urban system, and develop in a harmonious and balanced manner. A structure like this makes a difference with respect to a national urban network typical of the previous case. A regional urban system, in fact, makes it possible to exploit the geographical, historical and cultural specificities of each regional individual city, to provide a broad and diversified range of possible close by locations for firms and households, and to avoid the hyper-concentration of production and residential activities in a few large-sized cities (Capello 2016).
Also in this case, four phases of spatial development can occur (Fig. 3).
Fig. 3
Double bell in regional disparities: phases of development in a spatially even resource country archetype
×
2.3.1 The diffused concentration phase
When an expansionary shock takes place, the core region grows, worsening inter-regional disparities. However, in this settlement structure country archetype, growth does not insist only on the large city, but expands to all the regional urban system. This allows each individual city of the core region to take growth advantages, leading to an overall decrease of intra-regional disparities (Table 2).
Table 2
Development phases and the reasons for their sequentiality: the spatially even resource country archetype
In italics: reasons for the inversion of the trend
If this occurs, the first step of the development is therefore a diffused concentration, characterised by increasing inter-regional disparities and decreasing intra-regional ones, as depicted in Fig. 3.
2.3.2 The concentration phase
Over time, technological progress takes place, because of an incubation phase typically related to the core city, representing the node of the regional urban network. The core city goes through a process of economic relaunch, generating an increase in intra-regional disparities (Table 2). As a result, a phase of concentration emerges (Fig. 3).
2.3.3 The diffusion phase
In principle, after a certain time span, the market saturations and physical congestion are expected to appear at both regional and urban level in the rich region. If this is the case, the growth diseconomies taking place in the core regional and urban areas lead towards a pure diffusion phase (Fig. 3; Table 2).
2.3.4 The concentrated diffusion phase
The natural trends presented in Fig. 3 would bring us to expect a concentrated diffusion phase to occur, through a decrease in inter-regional disparities, accompanied by an increase in intra-regional ones. However, this would mean that the source of rebound, i.e. a technological upgrading, takes place at the same time in strong and weak regions, a difficult situation to be expected in the real world.
The unsatisfactory interpretation of the two last phases leads us to suppose that the spatially even resource country archetype shows exclusively the diffused concentration and the concentration phases. After these two, it is difficult to theoretically envisage any sort of logical trend. This is why the following parts of the curves are dotted in Fig. 3.
Interestingly enough, if our conceptual framework applied to the spatially even country archetype holds, then the counterintuitive results obtained by Artelaris and Petrakos (2016) and by Amos (1988) would be fully consistent with what is presented in Fig. 3. The U-shaped form and the divergence obtained at the end of the curve find in fact a clear explanation in our approach.
Our theory deserves empirical verification. Although we expect the trend in inter-regional disparities to move faster with respect to that in intra-regional ones in countries where resources are unevenly distributed across space, and the opposite to occur in countries with more evenly distributed resources, the shapes and slopes of the curves need to be empirically confirmed.
In the next section, we will carry out an empirical analysis testing the configurations of the inter- and intra-regional inequality curves and investigating which of the two curves achieves the peak more quickly after a shock in the economy. The empirical analysis will be based on an econometric exercise whose goal is rather to describe the evolution of inter- and intra-regional inequalities over time than to interpret their causes.
3 From theory to empirics: Identification of the time span and of groups of countries
3.1 The choice of time zero
As explained in the introductory part, divergence and convergence trends depend heavily upon the choice of the time period (Petrakos et al. 2005), since in the same moment countries may find themselves at different stages of development. Our approach consists therefore in identifying a shock that has affected growth opportunities for European countries, and since that particular moment (time 0 in our empirical approach) in calculating the reaction of each country in terms of growth and therefore disparities.
The expansionary shock we identified in the history of the EU members is the entry into force of the single market. Officially in place from 1993, it allows four types of free movements (goods, services, capital and labour), besides the removal of nontariff barriers, the integration of the labour market and the mutual recognition of education degrees.
Generally, economic integration decreases the costs associated with participating in and coordinating activities across space, the so-called spatial transaction costs (McCann 2008), enhancing regional growth opportunities. Thus, the advent of the single market can of course be considered as favourable for the overall progress and development of the European countries and regions. However, we should not forget that the result of integration inevitably affects spatial disparities (Camagni and Capello 2011; Capello and Dellisanti 2024). In particular, we should consider the risk of potential (internal) divergence due to more advanced urban areas capitalising the advantage of the single market, because of widest shares of investments in services (e.g. finance, insurance and commerce) and greater concentration of a highly qualified workforce (Camagni et al. 2020). These elements could clearly contribute to the enlarging of the gap with small and medium cities and regions and rural areas, especially if reinforced by the new Information and Communications Technologies (ICTs) paradigm that started in those years, displaying its centripetal forces. At that time, in fact, cities became the principal loci of higher-quality ICTs networks and services, obtaining strategic advantages from new technologies.
After identifying the single market as an appropriate shock to look at for our purposes, a further consideration is due on the evolution of the situation over time. One of the original contributions of this work, in fact, is that time is considered as country-specific. This means that time 0 corresponds to 1993 (the year of the official start of the single market reform) for all the countries that were already members of the EU at that time, while it corresponds to the respective accession year for the countries that joined the EU later. In this way, we avoid business cycles as much as possible (Petrakos et al. 2005)4 and concentrate on the period following the initial shock (whatever the year).
3.2 The choice of groups of countries
The empirical analysis calls for a grouping of EU countries able to reflect the two archetypes described before. To achieve such a goal in empirics, we reverse the reasoning with respect to the conceptual part. We first group the countries according to the inter-regional and intra-regional disparity trends, and then, we check whether this distinction is consistent with other theoretical assumptions concerning the spatial distribution of resources. Regions are identified through the NUTS2 level of the European geographical disaggregation, further disentangled at NUTS3 level for what concerns the intra-regional level of analysis.
The inter-regional and intra-regional disparities are measured through a traditional Theil index, considering NUTS3 level data on GDP in Purchasing Power Standards (PPS) and population provided by the European Commission (ARDECO database) (Table 3). The Theil index is chosen since it is easily decomposable in between and within regional components and therefore allows to explore the different levels of disparities.
Table 3
Data for the empirical analysis and their sources
Variable
Source
Period
Geographical level
GDP (PPS)
ARDECO
1993-2019
NUTS3
Population
ARDECO
1993-2019
NUTS3
Area
Eurostat
1993-2019
NUTS3
Employment in industry
ARDECO
1993-2019
NUTS3
Total employment
ARDECO
1993-2019
NUTS3
Not every EU country is included in our analysis, though. More specifically, the countries administratively organised in less than three NUTS2 regions were disregarded, since a computation of the Theil index on those countries would provide volatile and unreliable results.5 Germany was also excluded because the integration between the Eastern and Western parts of the country just at the beginning of the 1990s generated an atypical situation, while Ireland was withdrawn from the sample due to the “jump” in its GDP data between 2014 and 2015.6
The Theil indices are displayed in Table 4, where the levels of the between and of the within components are compared in each country between time 0 and time 5. The choice of time 5 is made based on the need to look at a short-term reaction to the shock. Considering more than 5 years, in fact, would imply dealing with medium- to long-term trends.7
Table 4
Identification of groups of countries
Country
Theil between NUTS2 time 0
Theil between NUTS2 time 5
Theil within NUTS2 time 0
Theil within NUTS2 time 5
Increasing between and within Theil indices over the first 5 years: concentration
Bulgaria
0.014113
0.014573
0.045466
0.053562
Czechia
0.052769
0.060123
0.000409
0.001091
Denmark
0.007363
0.009043
0.013550
0.017128
Finland
0.009233
0.014529
0.003769
0.005267
Hungary
0.055217
0.071303
0.005146
0.007223
Netherlands
0.008147
0.009649
0.016898
0.016901
Poland
0.020254
0.024339
0.040339
0.042210
Portugal*
0.015342
0.017609
.01466406*
0.016061
Romania
0.038029
0.044711
0.024700
0.027269
Sweden
0.007273
0.007865
0.000852
0.001656
Slovakia
0.089644
0.124916
0.004391
0.005177
Increasing between Theil index and decreasing within Theil index over the first 5 years: diffused concentration
Belgium
0.028689
0.030034
0.015864
0.015369
Croatia
0.035746
0.037901
0.013312
0.010046
France
0.021640
0.024131
0.022896
0.021369
Greece
0.026708
0.027476
0.021854
0.019516
Italy
0.023263
0.028855
0.006899
0.006712
Spain
0.013215
0.016008
0.009883
0.008021
Decreasing between Theil index and increasing within Theil index over the first 5 years: concentrated diffusion
Austria
0.017162
0.011646
0.022798
0.024868
*For Portugal, the value reported for the within component at time 0 is the one of time 1, since in this case the overall trend is definitely a concentration one, although starting from time 1 instead of time 0
Looking at Table 4, a first interesting result is that, with the only exception of Austria8, countries fall indeed only in two conditions: a situation of pure concentration or a situation of inter-regional concentration and intra-regional dispersion.
In order to verify the consistency of our grouping with the conceptual assumptions, we need to check the distribution of resources within the two groups of countries. For this aim, we look for a statistical association between the intra-regional income distribution and the distribution of economic resources. A simple ANOVA does not fit our purpose given the huge national specificities that accompany both urban population density and the share of employment in industry.9 To overcome such an issue, we run two sets of regressions, separately for the two groups. Time fixed effects are also included. They are fundamental to control for the national heterogeneity in economic development stages affecting regional disparity levels.
The intra-regional concentration of wealth is measured as the within component of the Theil index in the first five years after the expansionary shock. For the spatial distribution of economic resources, we resort to two proxies capturing the spatial concentration of growth assets. Particularly, we use the intra-regional concentration of population, computed as the within component of a Theil index made on population density, for the urban settlement structure, and the intra-regional concentration of the share of employment in industry for the productive structure (Table 3). In order to make the results more intuitive, in the spatially even resource country archetype, we turn the Theil index into an index of diffusion.10
The outcome of these analyses is reported in Table 5. As can be seen from the table, in the spatially uneven resource country archetype there is a clear association between the intra-regional concentration of per capita GDP and the intra-regional concentration of both population (column 1) and productive resources (column 2). The results are perfectly consistent with our conceptual expectations.
Table 5
Association between spatial distribution of resources and intra-regional disparities
The results for the spatially even resource country archetype are also in line with the conceptual expectations. In this case, in fact, the decreasing trend in intra-regional disparities is associated with a greater diffusion of the population (column 3) and of productive resources (column 4).
All this preparatory work allows us to verify the shapes of the inter- and intra-regional disparity curves and their respective peaks, representing the relative speed of the trends of disparities at the two geographical levels. Results are presented in the next section.
4 An empirical test of the double bell conceptual framework
In the literature, the shape of the Williamson’s (or Kuznets’) curve is empirically investigated by regressing disparities over per capita GDP and its square.11 Our work does not aim at explaining causally the existence and causes of regional disparities, but it rather focuses on their evolution over time. In this sense, the model does not estimate a causal relationship, but it describes the temporal trends.
More specifically, in order to check the shape of the curves, we regress the between and within components of the Theil index over time and its square and cube terms, as in the following equations:
where Theil between GDP pcct and Theil within GDP pcct are computed as the between (among NUTS2 of a country) and within (within NUTS2 of a country) component of a Theil index based on NUTS3 GDP PPS per capita in country c at a specific time t. The evolution over the long run starts from time 0 and continues up to 2019, which is the last year included in the analysis and corresponds to year 26 for the countries that were already members of the EU in 1993.
Country fixed effects (δc) are included. They are particularly important since they control for the national heterogeneity in: (i) macroeconomic trends, (ii) economic development stages and (iii) level of intra-country regional disparities. In addition, the estimations are carried out separately for the two groups of countries to highlight the different trends.
Table 6 displays the results of the specifications run for the spatially uneven resource country archetype. The outcomes are also graphically presented in Fig. 4, where panel (a) and panel (b) report the trend in inter- and intra-regional inequalities, respectively.
Table 6
Evolution of inter- and intra-regional disparities in the spatially uneven resource country archetype
Robust standard errors in parentheses. Significance levels as follows: *** 1%, ** 5%, * 10%
Fig. 4
Empirical double bell in the spatially uneven resource group of countries
×
The results are impressive. The trend in inter-regional disparity perfectly mirrors the conceptual expectations. In the long run, the inverted U-shaped curve is followed by a U-shaped curve, once again proving the “N” or “S” shape of the curve suggested by the literature (Conceicao and Galbraith 2000, Milanovic 2016; Castells-Quintana 2018; Breau and Lee 2023). The trend in intra-regional disparities is also rather consistent with the expectations, detaching from them in the intensity with which the diffusion processes take place.
A second interesting result is that the peak of the inter-regional disparities appears before the intra-regional one, as expected, underlining that the speed with which growth spreads around is higher between regions rather than within them (Fig. 4).12 This determines the expected phases: concentration is followed by a concentrated diffusion.
What is missing is the phase of diffused concentration where the two expected trends of concentrated growth in large cities of the rich regions and the continuous growth in all cities of the weak regions (see Table 1) offset each other in the real world. Instead, a phase of diffusion emerges, even if contained for what concerns the intra-regional trends. This phase is hard to be achieved and to be maintained. Once the diffusion is reached in less developed regions, a new round of growth has already begun in core regions, restarting the whole spatial process, probably driven by technological progress that provide advanced regions with the capacity to start the agglomeration–dispersion process again. The cycle continues through a new concentrated diffusion phase, eventually turning again into the concentration phase (Fig. 4).
The high levels of R-squares are driven by the national fixed effects, that reflect the specificity of each country in the level of disparities, suggesting that inequalities are structural and dependent on historical factors, difficult to be reversed. In this sense, contrasting disparities is like “fighting gravity” (Camagni et al. 2020).
As for the spatially even resource country archetype, the results are shown in Table 7, clearly suggesting a U shape for the evolution over time of intra-regional disparities (Fig. 5). Instead, the trend in inter-regional disparities shows an increasing path at decreasing rates, being the coefficient of the square term not significant (column 2a, Table 7). Although slowing down their increase towards the end of the period considered, indeed, a clear decrease is not visible in our data. The specification including the cube term demonstrates that the inverted U shape does not exist, being the cube term not significant (Appendix B, Table 10).
Table 7
Evolution of inter- and intra-regional disparities in the spatially even resource country archetype
Robust standard errors in parentheses. Significance levels as follows:*** 1%, ** 5%, * 10%
Fig. 5
Empirical double bell in the spatially even resource group of countries
×
Figure 5 depicts the trends estimated in Table 7. As expected, the turning point (minimum) of the U-shaped curve of the intra-regional disparities occurs before the one of the inter-regional inequalities, witnessing a more rapid growth transmission within regions rather than between regions thanks to the even spatial distribution of resources.
These trends lead to a sequence of phases. The process starts from an initial phase characterised by “diffused concentration.” After that, a concentration phase follows, where inter-regional inequalities keep on increasing, accompanied by intra-regional disparities.
Overall, the results show that our conceptual archetypes fit the reality, with only a few interesting deviations. Firstly, in countries with spatially uneven distribution of resources, the diffused concentration does not occur. Secondly, in this group of countries, the intra-regional diffusion only marginally takes place. Finally, in the spatially even resource group of countries, with respect to the conceptual framework (Fig. 3), the reality depicts only the first two phases (Fig. 5), suggesting that either the full cycle requires a rather long time, or that it does not even exist.
As for the previous estimates, R-squares reflect the national specificities, captured through the country fixed effects.
5 Conclusions
This work aimed at putting forward a conceptual framework able to interpret simultaneously the trends of within country inter- and intra-regional disparities over time. A concurrent analysis of the two levels, in fact, was missing in the existing literature and can instead provide an interesting way to interpret regional disparity trends. A relatively vast array of empirical analyses addressing the existence of the famous Williamson’s inverted U-shaped curve is indeed present, but this mainly focuses on the inter-regional level and does not study within region processes, let alone both levels at the same time. This means that the extant research tends to look for this type of curves, without really providing a sound conceptual interpretative framework.
The present paper has tried to move the frontier of knowledge further, by claiming that the interpretation of regional disparities calls for a concurrent analysis of inter- and intra-regional inequality trends that takes into consideration the simultaneous evolution of the two geographical levels. This allows us to highlight different development phases and to interpret in a more comprehensive and complete way the geographical trends of regional inequalities, thus allowing to suggest policy makers a more effective allocation of development funds.
Our conceptual assumption of linking the regional disparities trends with types of settlement structure in the country turned out indeed to be meaningful in the interpretation of inter- and intra-regional disparities. In fact, once grouped in this way, the two blocks of countries fitted our expectations, with a few interesting deviations, that stress some policy implications. In countries with spatially uneven distribution of resources, a diffusion trend in intra-regional disparity does not take place naturally. When the Williamson’s curve shows convergence, a concentration phase starts at intra-regional level and strong income polarisation trends within regions appear, a situation which is far from reflecting an overall social equity and suggests the strategic importance of the distribution of funds also within a region.
Moreover, our results suggest that in front of spatially even resources, the diffusion phase is not reached, even in the long term. Instead, the concentration phase tends to be the norm in the long run, suggesting that development funds must “fight gravity” (Camagni et al. 2020) at all geographical levels to deviate from this natural trend.
Given these outcomes, we believe that the concurrent reading of the two (inter- and intra-regional) disparity trends represents a fruitful conceptual framework for further interpreting the evolution of the two levels of disparities. The paper is a first step towards the formulation of a full-fledged theory on the concurrent evolution of inter- and intra-regional disparities, to be expanded in future research.
An analysis like the one proposed in this paper could be useful to shed light on the effectiveness of the spatial distribution of European funds, not only between, but also within, NUTS2 regions. There are in fact suspects in the literature that the somehow limited expansionary effects of the cohesion policy at the NUTS2 level is the result of a misallocation of resources at NUTS3 level (Gagliardi and Percoco 2017; López-Villuendas and del Campo 2024). This would be an interesting reason to expand the research avenue in this field of study in the future.
Declarations
Conflict of interest
The authors do not have any conflict of interests to declare.
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With 4 years, the grouping of the countries is the same (which means the regressions are the same, since time 0 is country-specific and depends exclusively on the entry into the single market). Using less than 4 years would not catch a reaction to the expansionary shock, while more than 5 years would be a medium rather than a short term. See Table 8.
Table 8
Robustness check on the identification of the groups of country using a 4-year time span for the first phase
Country
Theil between NUTS2 time 0
Theil between NUTS2 time 4
Theil within NUTS2 time 0
Theil within NUTS2 time 4
Increasing between and within Theil indices over the first 4 years: concentration
Bulgaria
0.014113
0.016907
0.045466
0.054309
Czechia
0.052769
0.062985
0.000409
0.001101
Denmark
0.007363
0.008686
0.013550
0.016428
Finland
0.009233
0.017900
0.003769
0.005006
Hungary
0.055217
0.066635
0.005146
0.007586
Netherlands
0.008147
0.009211
0.016898
0.017000
Poland
0.020254
0.021922
0.040339
0.040610
Portugal*
0.015342
0.017284
0.014664
0.016614
Romania
0.038029
0.040866
0.024700
0.032416
Sweden**
0.007273
0.006964
0.000852
0.000900
Slovakia
0.089644
0.102988
0.004391
0.006328
Increasing between Theil index and decreasing within Theil index over the first 5 years: diffused concentration
Belgium
0.028689
0.030780
0.015864
0.015340
Croatia
0.035746
0.038690
0.013312
0.011339
France
0.021640
0.023284
0.022896
0.021678
Greece
0.026708
0.027491
0.021854
0.019974
Italy
0.023263
0.030396
0.006899
0.006747
Spain
0.013215
0.015748
0.009883
0.008256
Decreasing between Theil index and increasing within Theil index over the first 5 years: concentrated diffusion
Austria
0.017162
0.012843
0.022798
0.023011
*For Portugal, the value reported for the within component at time 0 is the one of time 1, since in this case the overall trend is definitely a concentration one, although starting from time 1 instead of time 0
**The between Theil index decreases slightly in Sweden if we consider year 4. However, even removing Sweden from the sample, the econometric results do not change
Evolution of inter- and intra-regional disparities in countries with spatially uneven resource distribution, first years of significant coefficients
Theil between: concentration 13 years
Theil between: concentration 14 years
Theil within: concentration 18 years
Theil within: concentration 19 years
Time
0.0024598***
0.0025502***
0.0009259**
0.0009456***
(0.0007541)
(0.0007091)
(0.0003626)
(0.0003428)
Time2
−0.000298**
−0.0003195***
−0.0000814*
−0.0000849 **
(0.0001275)
(0.0001186)
(0.0000457)
(0.0000407)
Time3
0.00000900
0.0000103*
0.00000223
0.00000238*
(0.00000629)
(0.00000573)
(0.00000171)
(0.00000143)
Country FEs
YES
YES
YES
YES
Constant
0.0103676 ***
0.0103082***
0.0528234***
0.0528071***
(0.0012652)
(0.0012102)
(0.0014905)
(0.0014807)
No. of obs.
152
161
185
190
R2
0.9878
0.9856
0.9810
0.9801
Robust standard errors in parentheses. Significance levels as follows: *** 1%, ** 5%, * 10%
Table 10
Evolution of inter- and intra-regional disparities in countries with spatially even resource distribution, specification including the cube term of time
In the case of the Kuznets curve, the evolution of income per capita is associated with the evolution of the manufacturing mix, shifting away from mass produced consumer goods towards more advanced and technologically intensive sectors where a disproportionately large share of workers is among top income earners (Kanbur 2017, Breau and Lee 2023).
This paper focuses on inter- and intra-regional inequalities, while it does not take into consideration any interpersonal income inequality trends that might occur at a finer geographical scale, like within a city.
The “lack of any single trend in the level and evolution of regional polarisation in the various countries” is also highlighted by Ezcurra and Pascual (2007: p. 106).
This is due to a change in national accounting and would lead to a biased interpretation of the evolution of a Theil index based on GDP per capita over time.
Differences among countries are due to specific characteristics of their administrative units (e.g. area, demographic size, number of spatial units, average size of spatial units) and governance systems (ranging from highly centralised to federal systems). Thus, international comparison is not straightforward (Eva et al. 2022).
Table 9 in Appendix B reports the econometric results for the first years in which the coefficients are fully significant, i.e. year 14 for inter-regional disparities and year 19 for intra-regional disparities.
