Isolating Neighborhood Components of Regional Inequality

Abstract

Regional disparities have been measured mainly using a variety of concentration statistics applied to spatial data. This article modifies a factor decomposition of the Theil index of inequality allowing to assess which part of regional income inequalities could be due to neighborhood features. The proposal is illustrated for the case of the Spanish peninsular provinces during the period 1981–2011. It is shown that the comparison of inequality among neighborhood and specific provincial factors open a new manner of analysis that can shed light on the terms of policy recommendations, specially on those identified as place-based oriented, by introducing a new perspective about what is the relevant place on which the policy has to be set in order to achieve regional inequalities reductions.

Keywords

inequality decomposition interregional inequality

Measuring regional inequalities is an important issue both for policy and economic research (see, among others, European Commission 2010; Alexiadis, Eleftheriou, and Nijkamp 2013; Tan and Zeng 2014). Analyses of regional inequalities and their links with the regional economic convergence processes have become a debated topic in the last two decades (e.g., Geppert and Stephan 2008; and Castells-Quintana, Ramos, and Royuela 2015). Researchers have proposed many measures to reflect the level of regional inequality, mainly using a variety of concentration statistics applied to spatial data (see, among others, Krugman 1991; Brülhart and Traeger 2005). Within these concentration statistics, it is necessary to remark the notable usage of inequality indices as the Theil entropy indices (Theil 1967) in a number of studies that measure regional income inequality. At the same time, this interest in regional inequalities has been generating a proliferation of studies elaborating new tools to assess and measure regional inequalities (see, among others, Akita 2003; Rey and Sastré-Gutiérrez 2010; Bickenbach, Bode, and Krieger-Boden 2012). Even though these new measures have important spatial connotations, to the best of our knowledge, there are not contributions that isolate neighborhood components within a measure of regional income inequality.

Regional analysts are well aware of the need to account for interconnections between regional economies.¹ Therefore, it is not surprising that the last three decades have seen major theoretical and methodological developments in incorporating spatial effects into mainstream economics (Anselin 2010). Clustering of economic performance in space has generated considerable research on the spillovers and linkages among geographical neighbors. It is well known that economic activities can spill over from a region to others, crossing the boundaries of regional economies. Accordingly, socioeconomic activity in adjacent regions generates an interplay between agglomeration and dispersion forces that, in turn, influence economic growth dynamics and inequality across domestic regions (Castells-Quintana and Royuela 2014). Understanding how regional economic activities may spread to neighbors or may hinder their economic performance is critical for policy design (Beenstock and Felsenstein 2008). In this context, regional neighborhood provides a wider landscape of social and economic characteristics that can influence spatial inequalities. Nevertheless, whereas this type of spatial analysis has been standard for Econometrics and Statistics in different fields (see, e.g., Ramajo et al. 2008; Basile, Capello, and Caragliu 2012; Anselin and Arribas-Bel 2013), the counterpart for measures of regional disparities is much less developed.

In the last decades, spatial effects have been incorporated into inequality indices. Shorrocks and Wan (2005) present a review of the theory and application of inequality decomposition techniques into the spatial and regional context. These authors show that different inequality decompositions by income sources and by population subgroups have been developed to decompose inequality. Following the current literature as regards inequality, different papers attempt to combine a-spatial and spatial measures in order to reflect the proper localization of each spatial geographical unit (see, among others, Arbia 2001; Lafourcade and Mion 2007). Effectively, various studies have emphasized the role of spatial effects in the empirical analysis of regional concentration,² proposing new spatial concentration measures (see, e.g., Arbia and Piras 2009), and showing strong evidence of spatial dependence in the dynamics of inequality (Rey 2015). On the other hand, works like Reardon and O’Sullivan (2004) and Bickenbach and Bode (2008) provide measures of geographic concentration that incorporate information from nearby regions. However, although it is possible to find recent contributions related to neighborhood aspects of regional inequality, a relevant question still remains: which part of regional inequalities could be assigned to socioeconomic activity in neighboring regions? This article attempts to fill this gap in the literature by incorporating neighborhood into a specific Theil index for measuring regional income inequality.

Although capturing the complex relationships between a regional economy and its neighborhood is difficult, our article tries to measure the relevance of neighborhood factors on inequality presenting a simple Neighborhood Theil index and its associated decomposition. Therefore, information about the relevance of regional neighborhood on the origin of regional inequality is provided by our decomposition of the Theil index of inequality over per capita incomes. The main contribution of this article is to present an approach that let us decompose regional inequality into neighborhood and specific local components. To address this issue, it is explicitly incorporated neighborhood in a Theil index since, as Dietz (2002, 542) affirms, “ … indeed, the spatial array of neighborhoods within an urban area may generate additional information for the researcher.” So, a Neighborhood Theil index is proposed, identifying the neighborhood extent of income inequality. The Neighborhood Theil index is based on the concept of “pure neighboring count”, where it is only considered information in the neighboring units without considering information from the regional reference unit. Later, to measure local-specific factors, the proposed Neighborhood Theil index is subtracted from the Theil index used as reference. As a result, within the measure of regional inequality, we distinguish between neighborhood and local-level components. The local-level components can be added to integrate a specific local index. The approach presented here may improve our understanding regarding policy issues related to regional inequality.

To illustrate the proposed approach, the factor decomposition of the Theil inequality index presented by Goerlich-Gisbert (2001) is used. The Goerlich-Gisbert Theil index (GG Theil index) decomposes inequality into the unweighted sum of the inequality indices due to four factors related to labor markets. Specifically, these factors are productivity per employed worker, employment rate, active population over working-age population rate, and working-age population over total population rate. Our article provides the methodology to isolate neighborhood components within this factorial decomposition of inequality. Our empirical exercise will focus on the forty-seven Spanish peninsular provinces during the period 1981–2011. The main purpose is to isolate neighborhood and specific local components of income inequality within this Spanish regional economic system. The decomposition of the GG Theil index, its corresponding Neighborhood Theil index, and the four local-specific indices will be calculated.

Our results evidence that, at the Spanish provincial level, the neighborhood context shapes an important share of provincial inequality. Besides, our approach would let us evaluate the obtained local-specific indices, facilitating the use of this information in decision-making. As neighborhood matters and shapes regional inequality, inequality policies should make a distinction between place-based policies at both neighborhood and specific local levels. These place-based interventions (Barca, McCann, and Rodríguez-Pose 2012) would take into consideration the different factors that are affecting regional inequality.

The rest of the article is organized as follows. The second section introduces the Theil index. In the third section, a decomposition of regional inequality by isolating neighborhood factors is presented. The fourth section contains an empirical illustration of the proposal. Finally, some concluding remarks are given in the fifth section.

The Theil Index

Let x_i be the per capita income of region i, that is, $x_{i} = X_{i} / N_{i}$ , where X_i is a regional measure of income (gross domestic product [GDP] or value added), and N_i is total population for the region. Let p_i stands for the share of region i in the aggregate population for the regional economic system (nation) $p_{i} = N_{i} / N$ ; and μ for the national average per capita income $μ = X / N = \sum_{i = 1}^{n} p_{i} x_{i}$ , X and N being the corresponding national aggregate values. The Theil (1967) index is expressed as:

T (x, p) = \sum_{i} p_{i} l o g (\frac{x_{i}}{μ}) .

From the standard economic literature, the Theil index can be decomposed in two ways: into the contribution to total inequality of variation in mean incomes (as it is used in our work) and into between and within components (see Fishlow 1972). It is well known that the between (or across) component compares regional average income of the regional groups to the regional economic system average income, while the within component compares regional income to the regional average income of the regional groups. There is a large empirical literature about inequality that are using Theil and its well-known property of additive decomposition to evaluate how different subgroups are contributing to the level of total inequality. However, when those groups are defined in terms of spatial location, several new considerations emerge. Shorrocks and Wang (2005) offer an exhaustive discussion about this issue. In their work, they remark the theoretical properties involved in this type of geographical decomposition and they also offer evidence drawn for a great number of countries. It can be found contributions that analyzed the regional level, (see, among others, Novotný 2007; Paredes, Iturra, and Lufin 2014). Different authors used the Theil index and its decompositions to analyze inequality in terms of income distribution among the European regions (e.g., Doran and Jordan 2013) and among the Spanish regions (e.g., Garrido-Yserte and Mancha-Navarro 2010; Martínez-Galarraga, Rosés, and Tirado 2015).

In our article, regional inequality is focused on the distribution of per capita income across the regional economic system and it is measured using the Theil index. For a region, it is possible to calculate the contribution of this region to the overall income inequality. This regional contribution to the income inequality may be explained not only by the specific local factors in its own income but by contextual factors related to its neighbors’ incomes. To isolate the contributions derived from these factors clearly bear the advantage of comprehension about the sheer neighborhood and local-level factors that may affect the regional inequality. Nevertheless, to our knowledge, there are not contributions assessing sheer neighborhood components in measures of regional economic inequalities. At this point, it is important to underline a remark in the context of the decomposition of inequality (by population groups, income sources, or other dimensions), where the between (or across) and the within components of the distribution of the variable of interest are provided. Effectively, the between or among neighborhood effects are not spillovers but spatial pattern of variables. Thus, the question of whether the regions differ in their incomes because of their neighborhood factors is minimally explored by this type of literature (De Dominicis 2014).

Which part of regional inequalities is due to neighborhood features? As explained previously, this issue has received little attention in the vast literature on spatial inequality. There would be two main ways of development: first, it would be to analyze how the spatial array of neighborhoods could generate relevant information for the measures of regional economic inequalities and second, it would be to understand how the new measures will affect the economic policy recommendations relative to regional disparities. In the next section, we develop an empirical approach at the regional level to find the main components (neighborhood and local specific) behind the evolution of regional income inequality. The results obtained from this approach call for a reflection on the adoption of regional policies related to inequality within a regional economic system.

Decomposition of Regional Inequality by Neighborhood Factors

Taking as point of departure the Theil (1967) index of inequality over per capita incomes, Duro and Esteban (1998) presented a decomposition of the Theil index of inequality into the unweighted sum of the inequality indices due to productivity per employed worker (y), employment rate (e), active over working-age population rate (a), and working-age over total population rate (r). In this decomposition, these authors use the country shares of aggregate population as weights. Goerlich-Gisbert (2001) extends the decomposition of Duro and Esteban (1998) to another Theil index of inequality where instead of the country shares of aggregate population, the country shares of aggregate income are used. Although other expressions could be considered, we limit our attention to the article of Goerlich-Gisbert (2001),³ and this is the measure of regional income inequality which will be modified.

Let E_i, A_i, and R_i be region i’s total employment, active (labor force), and working-age populations, respectively, and let E, A, and R be the national aggregate values of those variables. We shall then denote regional productivity as $y_{i} = X_{i} / E_{i}$ , the employment rate as $e_{i} = E_{i} / A_{i}$ , the regional active over working-age population rate as $a_{i} = A_{i} / R_{i}$ , and the working-age population over total population rate as $r_{i} = R_{i} / N_{i}$ . It is clear that $x_{i} = y_{i} e_{i} a_{i} r_{i}$ and μ = year where $y_{} = X / E_{}$ , $e_{} = E / A$ , $a = A / R$ , and $r = R / N$ are the average values of these variables.

Let us consider the Goerlich-Gisbert (2001, 305) index, where q_i stands for the share of region i in the aggregate income $q_{i} = X_{i} / X$ :

T (x, q) = \sum_{i} q_{i} l o g (\frac{x_{i}}{μ}) = \sum_{i} q_{i} l o g (\frac{y_{i}}{y}) + \sum_{i} q_{i} l o g (\frac{e_{i}}{e}) + \sum_{i} q_{i} l o g (\frac{a_{i}}{a}) + \sum_{i} q_{i} l o g (\frac{r_{i}}{r}) .

The expression of this GG decomposition of the Theil index would become:

T (x, q) = \sum_{i} q_{i} \log (\frac{x_{i}}{μ}) = \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{X_{i}}{E_{i}}}{\frac{X}{E}}) + \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{E_{i}}{A_{i}}}{\frac{E}{A}}) + \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{A_{i}}{R_{i}}}{\frac{A}{R}}) + \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{R_{i}}{N_{i}}}{\frac{R}{N}}) .

It is necessary to highlight that, according to Shorrocks (1982) and Goerlich-Gisbert (2001), unless the factors are not correlated, these contributions could be negative. As in this case the different factors are correlated, every component does not measure the contribution of a source of income differences to inequality of total incomes. Nevertheless, even if it is not clear what is the quantitative role of every factor, it will be possible to obtain a qualitative evaluation.

Now, the regional neighborhood (the neighbors of the region of reference) will be considered as the unit of enquiry, rather than the individual region. Although different works examined the extent to which income inequality is related to income variation across neighborhoods (see, e.g., Wheeler 2006), our proposal will depart from the standard analyses, since the quantification of our Neighborhood Theil index does not incorporate information from the individual region (a “pure” concept of neighborhood is used). Thus, to the best of our knowledge, our article is the first attempt to adapt a Theil index to account for the distribution of neighbors in the estimation of regional inequalities measures. Our work presents some similarities to different works on spatial segregation measures,⁴ such as Morrill (1991) and Wong (1993). Nevertheless, while this literature assumes that the population counts mixes information in the areal unit of reference and information in all surrounding units (Wong 1998), our proposal is only focused on the information from the neighbors. (We do not consider information from the individual region of reference.) Effectively, these spatial segregation indices (Wong 2005) are based on the concept of “composite population count,” that considers both information in the reference region and information in the neighboring regions (as if in the reference region). Summarizing, this method considers the observation with its neighbors when computing spatial segregation. Nevertheless, our approach is different, since it only includes the neighbors of an observation.⁵ Consequently, this article uses the concept of “pure neighboring count,” and the Neighborhood Theil index is built upon this concept. For a regional unit, the Theil index will measure the contribution of the region with respect to the distribution of per capita income across all the regional units. On the other hand, the Neighborhood Theil index is calculated for a regional unit (the reference region), and the corresponding information will focus on the contribution of the region’s neighbors to the inequality across all the pure neighboring counts.

Assuming that a “pure neighboring count” (regional neighborhood) can be denoted as a spatial lag, let Wz _i be the spatial lag for variable z in region i, where W represents the first-order spatial lag operator $W z_{i} = \sum_{j} w_{i j} z_{j}$ . In matrix notation, W is a n × n weighting matrix with elements w_ij.·Wz_i is a weighted measure of z_i in all regions except the ith (because by convention, w_ii = 0). In that manner, the Neighborhood Theil index will be,⁶

N T (x, s q) = \sum_{i} s q_{i} \log (\frac{W x_{i}}{s μ}) = \sum_{i} s q_{i} \log (\frac{W X_{i} / W E_{i}}{\frac{\sum_{i} W X_{i}}{\sum_{i} W E_{i}}}) + \sum_{i} s q_{i} \log (\frac{W E_{i} / W A_{i}}{\frac{\sum_{i} W E_{i}}{\sum_{i} W A_{i}}}) + \sum_{i} s q_{i} \log (\frac{W A_{i} / W R_{i}}{\frac{\sum_{i} W A_{i}}{\sum_{i} W R_{i}}}) + \sum_{i} s q_{i} \log (\frac{W R_{i} / W N_{i}}{\frac{\sum_{i} W R_{i}}{\sum_{i} W N_{i}}}),

where sq_i stands for the share of regional neighborhood i in the aggregate regional neighborhoods $s q_{i} = W X_{i} / \sum_{i} W X_{i}$ and sμ for the share of neighboring average per capita income $s μ = \sum_{i} W X_{i} / \sum_{i} W N_{i}$ .

Equation (4) could be used as a standalone measure, quantifying inequality across all the pure neighboring counts, and showing a decomposition about the qualitative importance of the different factors (productivity per employed worker, employment rate, active over working-age population rate, and working-age population over total population rate). The analysis of the four components can show the relevance of each factor in the increase or decrease of the inequality in terms of per capita income across all the pure neighboring counts.

Regional economies are not isolated entities; they are influenced by both specific local factors and neighborhood factors that determine their contributions to regional inequalities. Thus, it would be useful to know the relative importance of these two types of factors. As every “pure neighboring count” has its corresponding reference region, it would be interesting to subtract the Neighborhood Theil index from the GG Theil index. Consequently, subtracting from the GG Theil index (2) the Neighborhood Theil index (4),

T (x, q) - N T (x, s q) = \sum_{i} q_{i} \log (\frac{x_{i}}{μ}) - \sum_{i} s q_{i} \log (\frac{W x_{i}}{s μ}) .

That is,

T (x, q) - N T (x, s q) = \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{X_{i}}{E_{i}}}{\frac{X}{E}}) + \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{E_{i}}{A_{i}}}{\frac{E}{A}}) + \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{A_{i}}{R_{i}}}{\frac{A}{R}}) + \sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{R_{i}}{N_{i}}}{\frac{R}{N}}) - \sum_{i} s q_{i} \log (\frac{W X_{i} / W E_{i}}{\frac{\sum_{i} W X_{i}}{\sum_{i} W E_{i}}}) - \sum_{i} s q_{i} \log (\frac{W E_{i} / W A_{i}}{\frac{\sum_{i} W E_{i}}{\sum_{i} W A_{i}}}) - \sum_{i} s q_{i} \log (\frac{W A_{i} / W R_{i}}{\frac{\sum_{i} W A_{i}}{\sum_{i} W R_{i}}}) - \sum_{i} s q_{i} \log (\frac{W R_{i} / W N_{i}}{\frac{\sum_{i} W R_{i}}{\sum_{i} W N_{i}}}) .

Substituting sq_i by $W X_{i} / \sum_{i} W X_{i}$ , and making a few manipulations, a new Theil index decomposition is obtained:

T (x, q) = N T (x, s q) + (\sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{X_{i}}{E_{i}}}{\frac{X}{E}}) - \sum_{i} (W X_{i} / \sum_{i} W X_{i}) \log (\frac{W X_{i} / W E_{i}}{\frac{\sum_{i} W X_{i}}{\sum_{i} W E_{i}}})) + (\sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{E_{i}}{A_{i}}}{\frac{E}{A}}) - \sum_{i} (W X_{i} / \sum_{i} W X_{i}) \log (\frac{W E_{i} / W A_{i}}{\frac{\sum_{i} W E_{i}}{\sum_{i} W A_{i}}})) + (\sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{A_{i}}{R_{i}}}{\frac{A}{R}}) - \sum_{i} (W X_{i} / \sum_{i} W X_{i}) \log (\frac{W A_{i} / W R_{i}}{\frac{\sum_{i} W A_{i}}{\sum_{i} W R_{i}}})) + (\sum_{i} \frac{X_{i}}{X} \log (\frac{\frac{R_{i}}{N_{i}}}{\frac{R}{N}}) - \sum_{i} (W X_{i} / \sum_{i} W X_{i}) \log (\frac{W R_{i} / W N_{i}}{\frac{\sum_{i} W R_{i}}{\sum_{i} W N_{i}}})) .

Denoting the new terms as follows, it is obtained:

T (x, q) = N T (x, s q) + L T (y, s q) + L T (e, s q) + L T (a, s q) + L T (r, s q) .

Expressions (7) and (8) show a new decomposition of the Theil index obtained from expression (2), assessing which part of income inequality is related to neighborhood factors (measured by the component NT(x, sq), that isolates the neighborhood component), and which part is explained by specific local factors; that is, components LT(y, sq), LT(e, sq). LT(a, sq), and LT(r, sq). These specific local indices are associated with local factors related to local productivity per employed worker, local employment, local labor force population, and local working-age population.

Expression (7) let us combine the global dimension of concentration embedded in the Theil index and the neighborhood dimension from our Neighborhood Theil index. The level of concentration, evaluated by the Theil index, is decomposed into two parts. The first part, Neighborhood Theil index, to account for the concentration explained by neighborhood factors and the second part, integrated by the four specific local components. These four specific local components can be combined into a single index (specific local index, LT(x, sq)), that is,

L T (x, s q) = L T (y, s q) + L T (e, s q) + L T (a, s q) + L T (r, s q) .

And so,

T (x, q) = N T (x, s q) + L T (x, s q) .

The logic of expression (10) is as follows: if the specific local index does not show a relevant role (through their relative importance within the global dimension in the Theil index), there are limited opportunities to consider only specific local factors in order to reduce regional inequalities, because regional concentration is being mainly determined by factors at neighboring level (neighborhood factors). Additionally, if a meaningful analysis of regional inequality at local level is desired, the focus should be on the four specific local indices, where the specific local determinants of regional inequality are isolated.

These specific local components are associated with local factors related to productivity per employed worker (LT(y, sq)), employment rate (LT(e, sq)), active (labor force) population rate (LT(a, sq)), and working-age population rate (LT(r, sq)). Specific components try to measure the contribution of each individual factor at local level to measure aggregate inequality over per capita incomes.

Additionally, this decomposition could provide a classification of regions according to their contribution to the inequality taking into account both neighborhood and specific local components.

Empirical Illustration: The Case of the Spanish Provinces

In order to illustrate the proposal of the third section, data from the forty-seven Spanish peninsular provinces are used. From the nomenclature of territorial units for statistics (NUTS) developed by the European Union, the Spanish provinces are classified as NUTS-3, that is, small regions for specific diagnoses. Our main purpose is to isolate neighborhood and local-level components of income inequality within this Spanish regional economic system.

With respect to the statistical sources, homogeneous series were obtained from the Valencian Institute of Economic Research (IVIE) database for the period 1981–2011. This database linked different series, obtaining data of annual GDP for the Spanish provinces at constant euros of year 2008⁷ and of provincial total population.⁸ In addition, the time series for provincial employed population (in thousands of employed persons), active—labor force—population (in thousands of persons), working-age population (in thousands of persons), and provincial total population (in thousands of persons) have been taken from the IVIE database.

The evolution of the GG Theil index expressed in equation (2) for the provincial per capita income, as well as for the four components mentioned above, is plotted in Figure 1. In the Appendix, Table A1 offers the quantification of the Theil index and its decomposition. This decomposition allows us to assess which part of income inequality is due to provincial productivity per employed worker (productivity rate), to provincial employment rate (employment rate), to provincial active population over working-age population rate (activity rate), and to provincial working-age population over total population rate (population rate).

Figure 1.

Goerlich-Gisbert decomposition of the Theil index. From expression (2), THEIL denotes Theil index, while the other indices are its corresponding components, relative to the provincial productivity per employed worker (PROD), to the employment per active population rate (EMP), to the active-population of working-age rate (ACT), and to working-age population over total population ratio (POP).

From Figure 1 and Table A1, it is possible to say that overall inequality in the Spanish peninsular provinces has been relatively stable over thirty years, but its components have not. This way, from 1981 to 2000, Spanish provincial income inequality is mainly due to the differences in provincial productivity per employed worker. From 2001 to 2007, provincial income inequality was mainly caused by differences regarding the population of working-age over population ratio. From 2008 onward, the labor force over working-age population rate increases its relevance, being the main factor in the last year. Finally, it is clear that factors related to the provincial working-age population over total population rate (population rate) are not important when explaining this regional inequality. Nevertheless, from this analysis it is not possible to assess which part of the Spanish provincial income inequality is due to specific local (provincial) factors and which part could be explained by neighborhood factors.

On the other hand, with respect to the matrix W in equations (3) and (4) reflecting the spatial connectivity structure between provinces necessary to build the spatially lagged variables used in the Neighborhood Theil index, this spatial weights matrix is based on a pure geographical criterion (physical distance), a standard first-order contiguity scheme, this being defined by the existence of a common border between each two regions. Then, a binary neighborhood-based spatial weights matrix is built defining nonnormalized weights $w_{i j}^{*}$ as (by convention, self-neighbors are excluded, so $w_{i i}^{*} = 0$ ):

w_{i j}^{*} = {\begin{matrix} 1 if provinces i and j are geographical neighbors \\ 0 otherwise \end{matrix},

and next a $W_{geog} = (w_{i j})$ row-standardized weights matrix is defined as $w_{i j} = w_{i j}^{*} / \sum_{j} w_{i j}^{*}$ .

For each province, the provincial weights w_ij form a row-standardized N × N connectivity matrix W with elements known a priori satisfying w_ij = 0 and $\sum_{j = 1}^{N} w_{i j} = 1$ . Then, a spatially lagged variable summarizes the state of the variable of interest in the neighboring provinces.

Figure 2 provides a clearer view of the global spatial autocorrelation for the Spanish provincial per capita income in the different years through the Moran’s I statistic (Cliff and Ord 1981). As can be seen, there is evidence of the existence of a strong positive and statistically significant degree of spatial dependence in the distribution of the provincial per capita income over the 1981–2011 period (p values are, for all the cases, under .0001). Figure 2 corroborates the idea that there is a significant geographical pattern in the provincial inequality in Spain, revealing that the potentially underlying positive spatial dependence is time changing, and raising the necessity to explore the contribution of this spatial dependence on the measurement of regional inequality. Hence, although the evolution of the Moran’s I measures the level of polarization (Arbia 2001), it does not provide information about which part of the inequality could be associated with neighborhood factors.

Figure 2.

Global spatial autocorrelation for the Spanish provincial per capita income: Moran’s I.

Isolating Neighborhood and Specific Local Components

Figure 3 shows the results obtained for the Neighborhood Theil index and its decomposition (from expression 3). Thereby, as previously, overall inequality in the Spanish peninsular provinces for the case of the pure neighboring counts has been relatively stable along the period. Nevertheless, as in the case of the Theil index, its components have not been stable.

Figure 3.

Neighborhood Theil index and its decomposition. NTHEIL denotes the neighborhood Theil index. The other indices are its components, and they are related to the provincial productivity per employed worker (NPROD), the employment per active population rate (NEMP), the active population over working-age population rate (NACT), and the working-age population over total population ratio (NPOP).

Figures 1 and 3 show that the decomposition for both indices (Theil index and Neighborhood Theil index) is qualitatively similar. Similar information is obtained from both decompositions. The main difference is that the relevance of the provincial productivity per employed worker as the main factor explaining inequality for the Theil index was during the subperiod 1981–2000, while in the neighborhood Theil case, the relevance of this factor was reduced to the period 1981–1996.

Nevertheless, intuition suggests that while the role of neighborhood in explaining the provincial inequality in per capita income should be similar as at global level, specific local factors could have different behaviors. This intuition is tested through the use of the neighboring decomposition of the Theil index. Figure 4 offers the neighboring decomposition of provincial inequality in per capita GDP according to expression (4). These results are reported in the Appendix, Table A2.

Figure 4.

Neighboring decomposition of Theil index. This figure displays the Theil index (THEIL) and its decomposition from expression (4) in five indices: the neighborhood Theil index (NTHEIL) and the four specific local indices. LPROD denotes the specific local index related to provincial productivity per employed worker; LEMP denotes the specific local index related to provincial employment rate; LACT denotes the specific local index related to provincial active population over working-age population rate; LPOP denotes the specific local index related to provincial working-age population over total population rate.

In Figure 4 (and the corresponding information in Table A2), the Spanish provincial aggregate inequality over per capita incomes (shown in the Theil index) was decomposed in both the neighborhood component (represented by the Neighborhood Theil index) and the four specific local indices. Focusing on the provincial specific local indices, the qualitative and quantitative information in Figure 4 and Table 1 show important differences in their respective evolutions with respect to the diagnosis obtained from the previous decompositions using the Theil index (see Figure 1) and the Neighborhood Theil index (see Figure 3).

Table 1.

Share of Specific Local Indices on Theil Index.

Year	1981	1985	1990	1995	2000	2005	2010	2011
LPROD (%)	36.86	36.08	24.72	15.09	11.71	9.74	8.97	9.51
LEMP (%)	−2.91	−6.23	0.74	0.63	1.34	1.72	4.59	5.42
LACT (%)	6.82	6.23	8.89	7.95	11.00	13.29	10.57	9.90
LPOP (%)	−6.24	−8.54	−9.63	−2.77	−0.47	−1.52	−2.19	−1.90

Note: LPROD denotes the specific local index related to provincial productivity per employed worker; LEMP denotes the specific local index related to provincial employment rate; LACT denotes the specific local index related to provincial active population over working-age population rate; LPOP denotes the specific local index related to provincial working-age population over total population rate.

Table 1 is revealing that the shares of the specific local indices are changing during the period. Isolating neighborhood components, it is clear that the main factors behind the evolution of provincial inequalities are not related to the specific local index related to provincial employment rate; thus, the conclusions are different that those obtained from Figures 1 and 3 (and their corresponding Tables A1 and A2). Effectively, both, the specific local index related to provincial active population over working-age population rate and the specific local index related to provincial productivity per employed worker indicate that factors related to “active rate” and the “productivity rate” have remained as main local factors explaining the behavior of provincial inequalities. In other words, our decomposition shows that the analyses derived from Figure 1 (Theil index) were clearly conditioned by neighboring factors. For example, in the case of the last year (year 2011), the most important factors explaining inequality at global and neighborhood level would be related to (1) employment rate, (2) productivity rate, (3) active rate, and (4) working-age rate. Nevertheless, on the other hand, for the same year 2011, the most important factors explaining inequality at specific local level would be related to (1) active rate, (2) productivity rate, (3) employment rate, and (4) working-age rate. The relative importance of the causal factors is not the same. Besides, the negative contributions to inequality of the specific local index related to provincial working-age population over total population rate during all the years indicate that provincial factors related to working-age are reducing provincial inequalities.

Therefore, the decomposition provided in this article can shed new insights into the analysis of per capita income inequality, opening a door to neighborhood factors versus specific local factors. This distinction is important in the design of policy measures since the efficiency of the public policy to reduce provincial inequality should consider the existence of sources of provincial inequalities related to the neighborhood, and sources related to specific local provincial characteristics.

From another perspective, the neighboring decomposition of Theil index into Neighborhood Theil index and specific local index (see expression 10) reveal that the part of provincial inequality caused by neighboring factors was not uniform over time (see Figure 5). The provincial income inequality could be explained by the spatial location of the provinces (neighborhood factors) and by other provincial characteristics (specific local factors). Neighboring factors dominate the explanation of the Spanish provincial income inequality. From Figure 6, the share of explanation of neighborhood factors and specific local factors are both, different and shifting. Two general phases can be distinguished. The neighborhood component increases its relevance on the Theil index during the period 1981–1996 (starting from 65.52 percent in 1981, and reaching 79.51 percent in 1996), being around 77 percent in the last years. At the same time, the specific local component accounted around 34.48 percent in 1981, decreasing its relevance at the end of the period (about 23 percent).

Figure 5.

Neighboring decomposition of Theil index: neighborhood Theil index and specific local index.

Figure 6.

Relevance, in percentages, of neighborhood Theil index and specific local index on Theil index.

Consequently, our results provide an interesting pattern: the relevance of both neighborhood factors and specific local factors on provincial income inequalities. As shown in Figures 5 and 6, the neighboring decomposition of Theil index indicates that, for the Spanish provincial level, neighborhood factors are more important than specific local factors in the evolution of inequality. Figure 6 shows that, in general, the vast majority of a region’s destiny is the result of its neighbors. Neighborhood really matters. The quantitative contribution of this neighborhood component to the overall inequality in per capita income shows that neighborhood factors matter more than specific factors, and this should have consequences in terms of regional policy. The neighboring dimension of inequality indicates that the “amelioration” of inequality should be achieved involving all neighborhood and provincial policies but focusing mainly on neighborhood factors. Any efforts a region makes to help itself will have little impact on itself. If provinces are geographically related, it is expected that the adjacent Spanish provinces share socioeconomic factors that conditioned their inequalities at a provincial level. From this evidence, and considering as unit of analysis the provincial level (NUTS-3 level), policy makers should have to be concerned with neighboring policies. Although our findings could be showing a disempowering story for local governments, the positive spin is that provinces may need to collaborate with their neighbors so any of them can benefit.

Cross-provincial Comparison of Income Inequality: From the Standard Theil to the Neighborhood Decomposition

In this part of the fourth section, and according to expression (10), the neighboring decompositions of Theil index into Neighborhood Theil index and specific local index for each forty-seven Spanish provinces were calculated. This subsection presents the mean values of these results for each forty-seven provinces in the period 1981–2011.

Figure 7 shows the mean contribution of provinces to the income inequality index using the Theil index. The pattern is clear: provinces located in the Northeast of Spain contribute importantly to the inequality. The Moran’s I statistic (.144) shows evidence of the existence of a strong positive and statistically significant degree of spatial dependence (p value = .028) in the distribution of the mean provincial contributions to the per capita income inequality. This result is not new, because regional income inequality uses to display positive spatial correlation (Deaton and Paxson 1994; Chun-Hung, Suchandra, and Ching-Po 2015; Rey 2015).

Figure 7.

Mean contribution of the Spanish provinces to the income inequality index using the standard Theil index. ST_CONT denotes the mean contribution of provinces to the income inequality index using the Theil index.

Figure 8 displays the mean provincial contributions by provinces using the Neighborhood Theil index proposed in this article. The pattern shows that provinces located in the Northeast of Spain have an important role on inequality among pure neighboring counts. The Moran’s I (.590) and its corresponding p value (.001) corroborate the idea that there is a significant positive geographical pattern in the inequality of the pure neighboring counts for the Spanish provinces.

Figure 8.

Mean Spanish provincial contributions to the income inequality using the neighborhood Theil index. SP_CONT denotes the mean contribution of provinces to the income inequality index using the neighborhood Theil index.

In Figure 9, the mean Spanish provincial contributions using the specific local index are displayed for the forty-seven provinces (NUTS-3). It is shown that the pattern is very different now: the specific local (idiosyncratic) factors are not associated with a positive spatial dependence pattern. The Moran’s I (−.247; p value = .001) indicates the existence of negative spatial autocorrelation among the mean provincial contributions. This is a new result since it departs from the results in the literature (Rey 2015) where indices of inequality use to show positive spatial correlation. Our finding corroborates the idea that, isolating the neighborhood component, the local-specific components (related to idiosyncratic provincial factors) do not present similar distribution than the standard Theil index. For example, Chun-Hung, Suchandra, and Ching-Po (2015) show that, for the case of Taiwan, inequality in the neighboring provinces of a province affect positively the level of inequality in the reference province. The evidence of significant negative spatial dependence in the specific local index is a new empirical result. Nevertheless, it is important to highlight that both our results do not mean that previous authors’ findings of positive spatial autocorrelation are wrong and that our article does not contradict their works. After decontextualizing regional income inequality by trying to isolate neighborhood and specific local components, the specific local Theil index of income inequality within this Spanish regional economic system shows a spatial distribution that does not follow the positive spatial correlation usually displayed by regional income inequality. That raises the necessity to explore, within a causal model, the underlying factors that explain the regional contributions to the income inequality using the specific local index.

Figure 9.

Mean Spanish provincial contributions using the specific local Theil index. DIF_CONT denotes the mean Spanish provincial contributions to the income inequality using the specific local index.

Policy Implications

The results derived from our previous empirical application have various implications. An exclusive focus on the provincial policies could neglect the fact that the neighboring factors account for more than two-thirds of Spanish provincial inequality.⁹ At the same time, a provincial policy neglecting their underlying specific local pattern could miss the chance to focus on provincial policies. The analysis of these results suggests that economic policies to reduce inequalities should have to consider both the provincial (related to local or specific factors) and the neighborhood (related to neighborhood factors) dimensions. The challenges facing the reduction of inequalities from these two dimensions are different. From our analysis, the factors influencing provincial income inequalities are not uniform across all provinces, and they vary according to their neighborhood and their local-specific factors. In general, to reduce provincial inequalities, while provincial policies should be mainly focused on factors related to provincial active population over working-age population ratio, neighborhood policies should be focused on employment per active population factors. As conclusion, provinces could obtain benefits from policies that encourage labor force activation, while employment policies should adopt a neighborhood perspective.

Our findings can be interpreted as a call for a distinction between specific local policies and neighborhood policies. Although both types of policies are place-based-oriented policy approaches, the underlying factors are different. We advocate place-based inequalities strategies that explicitly consider the specifics of local-specific factors, but fostering interaction and collaboration to promote the important contribution of neighborhood factors to the amelioration of inequality.

Conclusions and Final Remarks

This article has provided an approach to incorporate spatial structure in a Theil index specific to take into account neighborhood features in the decomposition of cross-regional income inequality. Following the Theil index decomposition proposed by Duro and Esteban (1998) and extended by Goerlich-Gisbert (2001), this article goes further of those mentioned contributions by isolating neighborhood components of regional inequality. For this purpose, a Neighborhood Theil index is proposed that is based on the concept of “pure neighboring count.” Our inequality measure offers a qualitative view about the contribution of four different factors from a neighborhood perspective. The proposed neighborhood Theil index is subtracted from the Theil index used as reference and, as a result, within the measure of regional inequality, it is distinguished between neighborhood and local-level components. The local-level components can be added to integrate a specific local index.

In the case of Spain, it is presented as a new decomposition of the provincial economic inequality into a neighborhood and a specific local component. Our results have shown that an exclusive focus on the traditional Theil measure neglects the fact that the neighboring factors account for more than two-thirds of Spanish provincial inequality. Our approach provides both neighborhood and specific local provincial mapping to guide the appropriate setting of pro-equalities policies. While some Spanish provinces could obtain benefits from policies that encourage labor force activation, in others, employment policies should operate at neighborhood level. Moreover, the acknowledgment of the existence of a specific local component that does not show positive spatial correlation constitutes other important contribution of this article.

Hence, as a general conclusion, neighborhood features seem to influence provincial inequalities; this implies that social, economic, and physical factors in neighboring provinces play a determinant role in provincial income inequality. In addition, the considered factors do not operate in the same fashion at provincial level. Policies trying to reduce regional disparities should consider neighborhood target and/or provincial targets in order to design efficient measures. Thus, this is a call for place-based inequalities strategies that explicitly consider the specifics of local-specific factors, but fostering interaction and collaboration to promote the important contribution of neighborhood factors to provincial inequality.

From our proposal, although the statistical information required is elementary and the neighborhood effects obtained are conditional upon the chosen neighborhood structure, the analytical possibilities that it offers are quite large. Besides, in our opinion, the present article opens a future research agenda in the inequality decomposition literature.

Finally, four additional comments are remarked here. First, even the application is done with NUTS-3 data, it is likely that using microeconomic survey data, in which we can identify the enumeration district of the observation (if sample design were available), will offer a wide range of more interesting applications. This could be explained by the fact that neighborhood effects are likely to be stronger; so, the applications of the proposed decomposition are potentially more useful using survey data than regional data. Second, and following the example on the neighborhood decomposition of the Theil index into the contribution to total inequality of variation in mean incomes presented in this article, the extension to the “between–within” decomposition of the Theil index into the neighborhood domain would be immediate. Third, the approach proposed in this article can be also extended in a natural way to other concentration statistics usually used in regional analysis. Fourth, a topic for future empirical research is to attempt to distinguish between different explanations for both provincial and neighborhood inequalities. Our results attempt to add a new dimension to the empirical literature on regional inequality proposing the use of the new components of inequality as dependent variables. For example, in order to explain the determinants of regional inequality, rather than explain regional inequality, the neighborhood Theil index or the specific local index could be used as dependent variables in the context of a causal model. On the other hand, when examining the effects of inequality on regional growth, the usage of these new indices could incorporate significant information into the model.

Footnotes

Appendix

Table A2.

Neighboring Decomposition of Theil Index.

Year	THEIL	NTHEIL	Share NTHEIL on THEIL (%)	LPROD	LEMP	LACT	LPOP
1981	0.01202	0.00788	65.52	0.00443	−0.00035	0.00082	−0.00075
1982	0.01176	0.00770	65.45	0.00450	−0.00056	0.00092	−0.00080
1983	0.01177	0.00792	67.25	0.00502	−0.00089	0.00057	−0.00085
1984	0.01072	0.00769	71.73	0.00373	−0.00067	0.00077	−0.00080
1985	0.00995	0.00721	72.50	0.00359	−0.00062	0.00062	−0.00085
1986	0.01180	0.00831	70.41	0.00408	−0.00056	0.00093	−0.00096
1987	0.01105	0.00790	71.46	0.00335	−0.00020	0.00105	−0.00104
1988	0.01055	0.00779	73.78	0.00327	−0.00018	0.00072	−0.00104
1989	0.01107	0.00833	75.21	0.00303	0.00008	0.00072	−0.00108
1990	0.01080	0.00814	75.37	0.00267	0.00008	0.00096	−0.00104
1991	0.01093	0.00829	75.82	0.00255	0.00022	0.00085	−0.00098
1992	0.01065	0.00815	76.48	0.00214	0.00047	0.00086	−0.00096
1993	0.01071	0.00838	78.17	0.00213	0.00042	0.00070	−0.00092
1994	0.01081	0.00849	78.50	0.00187	0.00028	0.00085	−0.00067
1995	0.01120	0.00886	79.11	0.00169	0.00007	0.00089	−0.00031
1996	0.01157	0.00920	79.51	0.00155	0.00011	0.00086	−0.00015
1997	0.01164	0.00918	78.94	0.00138	0.00021	0.00094	−0.00007
1998	0.01237	0.00957	77.34	0.00167	0.00008	0.00111	−0.00006
1999	0.01298	0.00999	76.96	0.00152	0.00019	0.00135	−0.00007
2000	0.01264	0.00967	76.49	0.00148	0.00017	0.00139	−0.00006
2001	0.01226	0.00938	76.50	0.00121	0.00007	0.00167	−0.00007
2002	0.01129	0.00869	76.96	0.00095	0.00025	0.00146	−0.00006
2003	0.01039	0.00809	77.91	0.00086	0.00031	0.00123	−0.00010
2004	0.00997	0.00778	78.06	0.00093	0.00026	0.00112	−0.00012
2005	0.00986	0.00758	76.82	0.00096	0.00017	0.00131	−0.00015
2006	0.00958	0.00732	76.44	0.00098	0.00015	0.00129	−0.00017
2007	0.00930	0.00712	76.61	0.00100	0.00015	0.00120	−0.00018
2008	0.00918	0.00705	76.78	0.00095	0.00023	0.00114	−0.00018
2009	0.00957	0.00728	76.08	0.00105	0.00036	0.00105	−0.00017
2010	0.01003	0.00784	78.10	0.00090	0.00046	0.00106	−0.00022
2011	0.01051	0.00811	77.14	0.00100	0.00057	0.00104	−0.00020

Note: From expression (4), THEIL denotes Theil index; NTHEIL denotes Neighborhood Theil index, Share NTHEIL on THEIL shows the share (percentage) that the Neighborhood Theil index represents on the Theil index; LPROD denotes the specific local index related to provincial productivity per employed worker; LEMP denotes the specific local index related to provincial employment rate; LACT denotes the specific local index related to provincial active population over working-age population rate; LPOP denotes the specific local index related to provincial working-age population over total population rate.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

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