4.1 Methodology in a Nutshell

In this section, we provide a specification of the model we use to indicate the measure of economic inequality (in our case, the Gini index) with a set of predictors, taking into account both the hierarchical structure and panel nature of the available data.

The main indicator for evaluating income inequality is the Gini coefficient. This numerical measure examines typical deviations in income distribution, ranging from 0 (representing perfect equality) to 1 (representing perfect inequality). Renowned for its favorable characteristics, the Gini coefficient showcases mean independence, population size independence, and symmetry (Coccorese and Dell'Anno 2022).

The challenge of computing the Gini index for data grouped into income classes, such as income or tax statistics grouped for confidentiality, is a persistent concern in empirical research (Abounoori and McCloughan 2003). Previous studies have emphasized the downward bias introduced by grouping income into limited classes. To address this issue, researchers have proposed two main approaches. The first involves fitting parametric functions to average incomes within each group, which would align with the properties of a theoretical Lorenz curve. This method, favored by applied researchers, utilizes estimated parameters to calculate the Gini coefficient. The second approach establishes nonparametric bounds on the Gini index, thus avoiding assumptions about the shape of the Lorenz curve but requiring information on the lower and upper limits of each group. This approach illustrates scenarios of uniformity as well as maximum inequality within the groups. Both approaches contribute to overcoming the challenge of Gini index computation in grouped data analysis (Van Ourti and Clarke 2011).

Given that the Gini index can be considered a continuous random variable in the interval $(0,1)$, one of the possible distributions used to interpret this variable with limited support is the Beta distribution. Considering the nature of our data, we adopted an extended version of the Beta regression model, often called the Beta Mixed Model or Generalized Beta Model with Mixed Effects (Beta GLMM).5 This model accounts for random effects in a classical Beta regression model, thus resolving the problem of dependence within clusters. In studies that collect repeated measures on each subject or cluster subjects into groups, observations associated with the same statistical unit are usually correlated, implying a violation of the assumptions associated with regression models (Bonat, Ribeiro, and Zeviani 2015). Consequently, this class of models is suitable for analyzing longitudinal and multilevel, hierarchically-structured data.

4.2 Model Specification

We highlight that the linear predictor includes the key variable of our analysis, INNER AREA, which is a dummy variable taking the value one if the municipal has the characteristic of an inner area with respect to the centers; SOUTH and CENTER dummies control for the Italian regional gap; the interaction term between INNER AREA and SOUTH/CENTER test the changing effect of INNER AREA on income inequality across Italian macro areas.

In additional columns, we report the estimations of full models in which we include the vectors of control variables not considered in the main model. These estimations act as robustness checks to account for relevant contextual features at municipal and regional levels.

First, according to Kuznets's influential hypothesis (Kuznets 1955; Rajan and Zingales 2003), we test whether income inequality follows an Inverse-U shape by controlling for the level of economic growth measured on the regional basis by inserting the variable REGIONAL GDP PER CAPITA and its square in the model. Second, in line with literature investigating the determinants of income inequality at the national level, we consider different groups of determinants (Furceri and Ostry 2019; Nolan, Richiardi, and Valenzuela 2019). Specifically, we include TAX REVENUE and a set of variables capturing mayoral characteristics (MAYOR AGE, MAYOR BACHELOR, MAYOR FEMALE) to account for the institutional context, as institutions such as municipal governance significantly influence income distribution (Stiglitz 2012; Acemoglu and Robinson 2020; Zhang, Zhou, and Fan 2020). The preferences of local administrators shape redistribution efforts and, consequently, impact income inequality. Mayors may address local income inequality through financial and social support programs (Einstein and Glick 2018; Nitschke and Roesel 2023). Moreover, as a proxy of gender (GENDER) – an important determinant of income inequality as seen in the previous literature (e.g., among others, Dang and Viet Nguyen 2021) – we have introduced into the model an index defined as the ratio between the share of female employees and the municipality's population. The variable EDUCATION includes a control for the level of education in each municipality, namely the share of permanent employees holding the minimum of a bachelor's degree. The pivotal role of education in income inequality is widely recognized (see Abdullah, Doucouliagos, and Manning 2015), as it enables upward mobility and informed decision-making, potentially reducing income gaps (World Bank 2002). At the same time, employers who favor highly educated individuals can also exacerbate inequality and widen wage disparities. Overall, higher education levels tend to equalize income distribution, but disparities in educational achievement can heighten income inequality (Thorbecke and Charumilind 2002; Rodríguez-Pose and Tselios 2009).

We also utilize a proxy for innovation to account for the effect of technological improvements. More specifically, we include the dummy UNIVERSITY, which is equal to one if a university is located within the municipality and 0 if not. The hypothesis that the presence of a university positively contributes to knowledge spillover is well documented in the literature (Bonaccorsi et al. 2014; Muhamad et al. 2022; Rukanyangira and Oidu 2021).

We also include some sociodemographic characteristics such as SENIOR INDEX and MERGED MUNICIPALITY. These control variables allow us to account for the redistributive effects of pensions among an older population as well as the merger of municipalities in the period under consideration. Finally, TIME TREND captures the effect of time on the Gini index.

The descriptive statistics shown in Table 2 influenced the choice of determinants for dispersion models, as they evidence the fact that the variation ranges of the Gini index signal strong variability. Likewise, Table 3 shows that our key regressors affect the variability of the inequality measure (e.g. inner area categories and geographic localization).

Moreover, we replicated the analysis with a greater degree of disaggregation by substituting our main variable – INNER AREA – with INTERMEDIATE, PERIPHERAL, and ULTRA-PERIPHERAL. It is worth noting that in our analysis, both the INNER AREA dummy and the NSIA classes INTERMEDIATE, PERIPHERAL, and ULTRA-PERIPHERAL are defined in such a way as to carry out the comparison with all categories comprising centers (e.g., poles, inter-poles, outlying cities).

5.1 Data and Sample

We accessed several sources to retrieve our data. We drew fiscal declarations by municipality for 2012–2018 from the website of the Ministry of Economy and Finance (MEF – Department of Finance).8 The latter provides information on the income and stock of taxpayers across consistent income brackets and for each municipality. This data is derived from tax returns spanning the period under consideration. The uniformity of income intervals is maintained over time and across municipalities to ensure comparability. We calculated the Gini index using municipality-specific tabulated data on declared gross income, which is classified into seven income intervals. Specifically, the income intervals are (in thousands of euros): (i) 0–10,000; (ii) 10,000–15,000; (iii) 15,000–26,000; (iv) 26,000–55,000; (v) 55,000–75,000; (vi) 75,000–120,000; and (vii) greater than 120,000.9

Tax returns for each municipality comprise all sources of income including labor, pensions, property, self-employment, and business income. Property income is calculated based on cadastral rent and encompasses all forms of property income including land as well as owned and rented residential and commercial buildings. In other words, registration of a previously unregistered building is reflected in the tax base as imputed rent (Rubolino 2023).

We gathered information on Italian inner areas, as classified by the National Strategy for Inner Areas (NSIA), from the website of the National Agency for Territorial Cohesion.10

Data on personnel indicators, demographic characteristics and other local features of the municipalities were obtained from the Italian National Institute of Statistics (ISTAT).11 We also consulted the Bureau van Dijk's Aida PA to retrieve financial data on local public authorities.12 Lastly, we gathered information on municipal administrators from the website of the Italian Ministry of the Interior.13

5.2 Descriptive Statistics

Table 2 reports the descriptive statistics referring to our dependent variable, the Gini index, for each year included in the analysed period. Figure 1 displays the trend of the Gini index for Italy and the three macro-areas of the north, center, and south. Even if the trends are quite similar and slightly increasing with a peak in 2015, the presence of differences among areas is evident. The southern regions show the highest concentration while northern Italy demonstrates the lowest values of the Gini index.

Table 3 presents the Gini coefficient for 2018 categorized by NSIA classifications in Italy.14 The national average Gini index is approximately 0.38, with southern Italy recording the highest average at 0.39 and the north exhibiting the lowest value at 0.37. Central regions display an average Gini index of 0.38. It is notable that both nationally and within the three macro areas, inner areas generally have lower average Gini index values compared to non-inner areas. Upon further analysis, cities classified as poles consistently show higher Gini coefficients. Ultra-peripheral, peripheral, and intermediate areas in the north demonstrate lower Gini coefficients, as do ultra-peripheral municipalities in southern regions. Conversely, in the central region, poles and ultra-peripheral municipalities report the highest Gini index values. The data in Table 3 reveal significant variability in the Gini index, with ranges and coefficients of variation consistently higher in inner areas compared to centers. These descriptive measures suggest the presence of heteroskedasticity in the dependent variable, prompting the adoption of a dispersion model that utilizes Beta regression for further investigation.

Figure 2 shows maps of the Gini index for Italian municipalities in 2018 alongside the inner area classification. The figure reveals a gap between the northern and southern regions in terms of income distribution and inner area classification. Northern municipalities, which are mostly classified as centers, exhibit lower levels of income concentration compared to those in southern regions, which consist mainly of inner municipalities with higher income inequality. In central Italy, where the Apennines define the presence of inner areas,15 most Gini index figures fall within the low to medium range except for those areas surrounding the capital city of Rome, where intermediate and peripheral municipalities exhibit higher income inequality.

Lastly, while Table 4 offers a description and main summary statistics of the variables employed in the econometric analysis, Table 5 shows the correlation matrix between them.

6.1 Estimations for the Beta Regression: The Role of Inner Areas

Table 6 reports estimates of different specifications for the mean and the dispersion model. In particular, the first block refers to the equations in mean. Based on the discussion of evidence on aggregated inner areas, the different specifications displayed in the table vary according to the progressive inclusion of the covariates.

In Columns 1 and 2, we find strong evidence that income inequality in inner areas is smaller than in non-inner areas. For both models, the estimated parameters of INNER AREA are negative and strongly significant (−0.045). However, the following comments refer to the estimations shown in Column 3 of Table 6, which reports the results of the best specification from a statistical perspective; indeed, it produces the lowest AIC value.17 In this model, we exploit the territorial dimension of the Gini index by including the interaction between INNER AREA and the geographic location of the municipalities. We find that municipalities classified as inner areas have lower income inequality compared to non-inner areas, across all geographic localizations. However, the magnitude of these effects shows enough divergence to justify a more detailed inspection of the phenomenon. We shed light on this subject by analyzing potential factors influencing differences in inequality between southern, central, and northern regions among inner area municipalities.

In northern Italy, we find a clear difference between inner areas and non-inner areas. Indeed, the estimated coefficient associated with INNER AREA should be interpreted only for the control group for the geographical location, which is NORTH. The estimated parameter is equal to −0.028 (as reported in Column 3), meaning that the inner municipalities register a lower inequality index. Observing INNER AREA*SOUTH, we find notable differences between inner and non-inner areas in the southern regions as well. In these regions, the odds of the average concentration being an inner area is about 6% lower than the odds ratio for non-inner areas located in southern Italy [exp(−0.02808–0.03250) = exp(−0.06058) = 0.9412; 0.9412–1 = −0.06].18 Moreover, when considering the interaction INNER AREA*CENTER, the odds of the average concentration being an inner area is about 4% lower than the odds ratio for non-inner areas in the central regions of the country.19 Essentially, increased job opportunities in the centers do not always translate into dignified living conditions for the population, given the high levels of income inequality.

These findings further explore the initial investigation in Acciari and Mocetti (2013), which also provides a map of income inequality across different regions. Indeed, while Acciari and Mocetti (2013) find the existence of regional disparities in Italy, our study goes much deeper by investigating the influential role of inner-area versus non-inner area municipalities within these regions. Our results are also in line with Mastronardi and Cavallo (2020) who, by estimating linear regression models, find a higher Gini index for hub municipalities when compared to income concentration in inner areas. In this case, as well, we move beyond the previous authors' findings by verifying the relationship between inner areas and income inequality in the various geographical regions, as discussed above.

To better explain the economic impact of inner area status for municipalities located in different regions of the country, Figure 3 reports the marginal effects and the relative percentage change between non-inner and inner areas, referring to Model 3 of Table 6. Here we find that location matters. Indeed, the impact of inner area status differs by macro-region. In the north of the country, inner areas register a 1.75% lower Gini index as compared to non-inner areas.20 The reduction is even greater for central regions in Italy, where the marginal effect is equal to −3.19%. Finally, inner area status in southern Italy decreases the Gini index by the highest percentage (−3.82%).

Our investigation provides further contributions with respect to the previous literature in terms of the modeling of its dispersion model, reported in the second block of Table 6, which highlights significant differences in the variability of the Gini index between the different geographic regions. In particular, according to Column 3 of Table 6, there is an increase in the variability of income inequality for inner areas in all Italian macro-regions. The negative sign of INNER AREA signifies a reduction in the estimation of the precision parameter and, therefore, an increase in the variability of the Gini index. By contrast, when the dummy INNER AREA is equal to 0, an increase in the estimation of the precision parameter associated with SOUTH and CENTER suggests a lower variability of income inequality in pole municipalities.

6.2 The Role of Controlling Variables

From an economic standpoint, several factors can influence income concentration. Taking this fact into account, Columns 4 and 5 of Table 6 offer robustness checks of the results for our key variables with the addition of a set of control variables.

First of all, we estimate a concave quadratic relationship between higher regional income per capita and the logit of income inequality. Indeed, the signs of the estimated coefficients are negative for the quadratic terms and positive linear terms of REGIONAL GDP PER CAPITA. This result implies that the link between income inequality and regional GDP per capita displays an inverse U-shaped pattern over the period under scrutiny. However, the quadratic component of GDP is weakly significant, and thus we cannot draw firm conclusions regarding Kuznets's and Piketty's theories.

Interestingly, as also highlighted in the previous literature (Furceri and Ostry 2019), we found a puzzling scenario when considering institutional factors. The inclusion of these controls at a municipal level represents a strong contribution to the previous literature on income inequality. Indeed, this group of variables accounts for the institutional context of the local governments under consideration in our analysis. Specifically, we find that higher tax revenues translate to higher income disparities (the sign of TAX REVENUE is positive). The investigation by Asawasakulkrai (2022) studies the effect of tax revenues on income inequality at the national level (measured through the Gini index). Even if the broader scope of observation differs from our more targeted analysis at a municipal level, the underlying result is the same: a higher degree of tax revenue does not necessarily result in a reduction of income inequality. Iosifidi and Mylonidis (2017) also find a positive relationship between tax revenue and income inequality; they suggest that the government's reliance on personal income taxation results in more of a burden than a support for the average income earner, leading to a higher level of income inequality.

The same sign is estimated for the variables MAYOR AGE and MAYOR BACHELOR, which capture details about the municipality's political context. Our evidence shows that municipalities governed by elderly mayors and/or those with a bachelor's degree or higher register an increased level of Gini index. The first result may be due to career concerns, whereby younger politicians behave more strategically in response to electoral incentives (Alesina, Cassidy, and Troiano 2019), thus leading them to prioritize the well-being of their constituents more often than older mayors might do. Conversely, we find that when the mayor of the municipality is female, income is distributed more equally (the sign of MAYOR FEMALE is negative, meaning a reduction of Gini). The recent study of Ermini, Santolini, and Ciommi (2023) confirms this interesting result, demonstrating that greater representation of women in municipal, executive, and council leadership has significant associations with improved municipal well-being.

In the same line of reasoning, we found a strong negative impact of the share of female employees on income inequality (GENDER). One possible explanation of this evidence theorizes a negative association between gender equality and income inequality through various channels (Gonzales et al. 2015). First, gender gaps in wage and labor force participation rates directly contribute to income inequality, leading to inequality in earnings between men and women. Thus, as women increase their access to the labor market, they effectuate a rise in household income and a decline in poverty and, thus, in income inequality. Gender inequality in education also yields economic inefficiency, as restricting women from educational achievements limits the supply of skilled workers, leading to lower employment and wage levels which are primary causes of income inequality. Finally, gender gap inequalities limit women's participation in productive employment and better-suited jobs, reducing the value of output and the potential economic growth dividend, thereby influencing income distribution (Baloch et al. 2018).

Our results also suggest that income inequality increases along with education levels, which we demonstrate with the variable EDUCATION. This correlation is well documented in the literature. A larger share of highly educated workers in a given municipality may signal a larger earnings differential between highly educated and less educated workers, thus leading to higher income inequalities (Rodríguez-Pose and Tselios 2009; Shahabadi, Nemati, and Hosseinidoust 2018).

When we refer to the inverse effect of UNIVERSITY, which accounts for the presence of a university within the municipality, we can say it is a proxy for the presence of knowledge spillover in that municipality (Bonaccorsi et al. 2014; Muhamad et al. 2022; Rukanyangira and Oidu 2021). The estimated positive coefficient indicates that the presence of a university in the municipality exacerbates inequalities in the distribution of income. To the extent that the knowledge spillover favors those with higher skills and widens the “skills gap” through the proliferation of technological developments, it adversely affects the distribution of income by reducing the demand for lower-skill jobs and increasing the premium for higher-skill employment (Acciari and Mocetti 2013; Dabla-Norris et al. 2015; Furceri and Ostry 2019). Lastly, in terms of sociodemographic characteristics, the senior index has a negative impact on the Gini index, suggesting that income distribution appears more balanced where the population contains a higher number of elderly residents. As Mastronardi and Cavallo (2020) have argued, in municipalities with a higher number of elderly residents, the distribution of income is more balanced because of the equalizing effects of the pension system. This result is also in line with Acciari and Mocetti (2013), who estimate a significant negative coefficient associated with the presence of a higher share of retired people within the population.

Similarly, income inequality is lower in merged municipalities than in non-merged ones. The idea that the consolidation of municipalities results in administrative efficiency and the well-being of residents is controversial (Goto 2023). Our finding can be explained in terms of gains obtained by merged governments, such as (i) reorganization of institutional structures in the territory and (ii) an increase in the quality and variety of services offered in the new municipal aggregation (Aiello, Mercuri, and Bonanno 2017). With a higher probability, both these aspects can foster equal opportunities among residents (and, thus, lower income inequalities) compared to non-merged municipalities.

Finally, we estimate a positive coefficient for the TIME TREND, signaling a slightly positive trend in the Gini index over time (the estimated coefficient is equal to 0.005). Figure 4 shows the link between the Gini index and the time trend for all 20 regions. The slopes of the functions are the same because we do not assume a random slope in the multilevel specification of our models. However, based on the graphs, we can capture differences in terms of a shift in the inequality index among the various regions. The red line represents the overall estimated mean of the Gini index (${\omega }_{00}$).

6.3 Further Analysis: Inner Area Disaggregation

After disaggregating inner areas, we find that the AIC statistics reported in Table 7 show that the best specification is Model 3, from which it emerges that the importance of inner areas in terms of income inequality is heterogeneous. The variables of interest are INTERMEDIATE, PERIPHERAL, and ULTRA-PERIPHERAL. According to Column 3, we observe a noteworthy difference from our earlier results. In northern Italy, we find strong differences between all inner area subcategories (intermediate, peripheral, and ultra-peripheral municipalities) and centers. The odds ratios for classification as intermediate, peripheral and ultra-peripheral are approximately 2, 4% and 5% lower than the odds ratio for non-inner areas.21

In southern and central Italy, we also find noticeable differences between inner areas and center zones. Beginning with the interaction between SOUTH and INTERMEDIATE, we estimate a negative parameter, meaning that the odds ratio of the average concentration for intermediate municipalities in southern Italy is about 4% lower than the odds ratio of the average concentration of non-inner areas.22 With regard to the interaction PERIPHERAL*SOUTH, the odds ratio of the average concentration for PERIPHERAL is about 6.7% lower than the odds ratio of the average concentration for centers.23 The coefficient of the interaction between SOUTH and ULTRA-PERIPHERAL implies that the odds ratio of the average concentration for ULTRA-PERIPHERAL is about 10% lower than the odds ratio of the average concentration for non-inner area classification.24

As for the gap between inner and non-inner areas in the central regions, we estimated that the odds ratios of the average concentration for INTERMEDIATE and PERIPHERAL are respectively about 4% and 4.6% lower than the odds ratio of the average concentration for center zones.25 By contrast, when we look at the interaction ULTRA-PERIPHERAL*CENTER, the estimated coefficient is positive (0.139). This implies that the odds ratio of the average concentration for ULTRA-PERIPHERAL municipalities in the central regions of the country is about 9% greater than the odds ratio of the average concentration for non-inner areas.26 In light of these findings, along with those regarding inner areas, we note that while there is an abundance of job opportunities in centers, the opportunities do not consistently translate into satisfactory living standards across the population, thus contributing to notable levels of income inequality.

These results demonstrate the crucial importance of further disaggregating the NSIA classifications. After implementing a stronger disaggregation, we found evidence of a clear heterogeneity in terms of income inequality. Ultra-peripheral areas manifest the greatest difference in income disparities with respect to non-inner areas, and they do so in a heterogeneous manner. Ultra-peripheral municipalities that are more than 75 minutes away from a center show a lower income concentration than other types of municipalities in the north and south of the country, while in the same subcategory of inner areas located in the central regions, we estimated a higher Gini index than non-inner areas. Thus, it seems that ultra-peripheral areas propel the disparity between inner and non-inner areas in terms of income inequality. Our findings also demonstrate a high amount of heterogeneity for the southern and northern regions of the country: in ultra-peripheral areas with less access to essential services, the reduction of income inequalities is likely due to greater flexibility and a propensity to seize the opportunities offered by government programs. Thus, it seems that additional economic policy efforts should be implemented to promote socioeconomic inclusion in more remote country areas. Our findings are confirmed even when we change the model specification by including control variables (e.g., socioeconomic and demographic characteristics as well as time trends).

Our results stand in contrast of those reported in Gallo and Pagliacci (2020); indeed, they demonstrate marginally positive effects for the three inner subcategories compared to only one category defined in the macro-group of centers, e.g., poles. Additionally, the prior study claims that in Italy, inner areas “clearly do not matter” (Gallo and Pagliacci 2020, p. 217). Our evidence contradicts this notion and, conversely, offers an opportunity to analyze the advantages of suburbs (Viesti 2020) and to encourage economic policies that favor socioeconomic promotion in these areas. Finally, our findings are in line with De Renzis, Faggian and Urso (2022), who find that inner areas are more adaptable to the prolonged challenges associated with peripheral conditions.

In the dispersion model results reported in the second block of Table 7 (Column 3), intermediate, peripheral and ultra-peripheral municipalities show lower precision coefficients, implying an increased variability in terms of income concentration. The same categories of municipalities in southern and central Italy elicited similar findings, with the exception of peripheral municipalities in central region.

In sum, our findings demonstrate territorial differences in the variability of income concentration, and inner-area municipalities present a lower dispersion of income inequality compared to non-inner areas.

Figure 5 illustrates our calculations of the marginal effect of non-inner areas (control group) and the three subcategories of the inner areas (intermediate, peripheral or ultra-peripheral) on income concentration. These marginal effects refer to Column 3 of Table 7.

In northern Italy, all municipalities comprising the three subcategories of inner areas demonstrate reduced inequality with respect to non-inner areas. Ultra-peripheral municipalities register a high difference with respect to poles (-3.19%). In the south, intermediate areas show a decrease of income inequality by 3.56% over that of the poles. The reduction is more evident for peripheral and ultra-peripheral municipalities, which register a diminishing income concentration index of about 5.1% and 7.2%, respectively. Even in this case, the overall reduction associated with inner areas in the south (Column 3 of Table 6) is mainly driven by the results obtained for ultra-peripheral municipalities (Column 3 of Table 7).

The results for the central regions of the country are puzzling. Income inequality is slightly decreased in intermediate or peripheral municipalities, while the Gini index appears to increase in ultra-peripheral municipalities compared to non-inner areas by about 5 percentage points. To better explain our findings for central Italy, we refer to Figure 1 (Section 3.2). One explanation may involve structural and infrastructural factors. As the map shows, the territorial formation and the distribution of central inland areas are largely determined by the presence of the Apennine mountain range and by the clustering of most inner areas within Lazio, and more particularly around Rome (De Renzis, Faggian, and Urso 2022). Even if the number of inner areas classified as ultra-peripheral municipalities is very low, the estimated coefficient of the interaction term ULTRA-PERIPHERAL*CENTER (Column 3 of Table 7) is positive and statistically significant. In other words, the morphological characteristics of the central region reduce access to essential services, as the Apennines obstruct connections between the poles and the inland areas and, as a consequence, inner area municipalities show greater income inequalities as compared to those in the north and south.