The Role of Neighborhood in the Analysis of Spatial Economic Inequality

For example, for countries with no survey information, Bourguignon and Morrison (2002) use the concept of “regional proximity” to forecast the within country distributions of income, assigning the within country distributions of neighboring countries.

Neighborhood policies are proposed from the European Union to help poor regions.

Following Partridge et al. (2015), place-based policies have two basic characteristics: local policies are always "place-based" and place-based policies result in mobile local investment such that the local population will benefit from the policy only while in the region.

The NUTS classification (Nomenclature of territorial units for statistics) is a hierarchical system for dividing up the economic territory of the European Union; in the case of the NUTS3, the purpose is the socio-economic analyses of small regions for specific diagnoses.

Although there have been a number of studies that measure regional income inequalities using the coefficient of variation (as the weighted coefficient of variation, Williamson 1965), the Gini index and the generalized entropy inequality measures, the Theil index is most often undertaken to decompose economic inequality according to a partition of the aggregate population into a set of geographical regions (Shorrocks and Wan 2005). The Theil index belongs to the family of generalized entropy inequality measures. The generalized entropy inequality measures satisfy the criteria that should be required to a good measure of economic inequality (see, for example, Haughton and Khandker 2009): mean independence, population size independence, symmetry, Pigou–Dalton transfer sensitivity, statistical testability and decomposability. The coefficient of variation does not satisfy the property of mean independence, since this inequality index changes if all regional values vary in the same proportion. In the context of additive decomposability, the generalized entropy class of inequality indexes is a good alternative since total inequality can be written as the sum of between-group and within-group inequalities and their economic interpretation is therefore straightforward. In this sense, it is well known that in general the Gini index for a regional economic system is not equal to the sum of the Gini coefficients of its regional subgroups (Deutsch and Silber 1999). On the other hand, among the generalized entropy inequality measures, some of them are more sensitive to changes in the lower tail of the distribution, while others are more sensitive to changes that affect the upper tail (Cowell 2011). When analyzing the differences in GVA per capita among regions, the units of observations are regions; i.e., each region is considered an individual. This would imply to give the same weight to all the regions, being the Theil index the special case of the generalized entropy inequality measures that assigns a same weight to all the regions. In summary, the Theil index was chosen by the aforementioned advantages (decomposability by regional subgroups and assignation of the same weight to all the regions).

Equation (1) follows the Akita’s first stage formulation (Akita 2003) that it is also similar to the Theil equation proposed by Anand (1983, p. 328). In our case the subscripts “r” (countries) is equivalent to Akita’s “i” (regions), and our subscript “p” (NUTS3) is similar to Akita’s “j” (provinces).

We used the Theil index to measure regional inequality. The Theil index has been applied in the analysis of regional economic inequality (e.g. Chen and Wang 2015; Paredes et al. 2016). Higher values reflect greater regional inequality (Shorrocks and Wan 2005).

The Goerlich-Gisbert index decomposes inequality into the unweighted sum of the inequality indices due to four factors; specifically, productivity per employed worker, employment rate, active population over working-age population rate, and working-age population over total population rate.

As indicated by a referee, the specific Theil is conditioned by the conceptualization and quantification of neighborhood that is used in Eq. (2). So, if the neighborhood Theil is defined in other way, a new specific Theil will be derived. This would require defining the appropriate concept of regional neighborhood (identifying the right neighborhood of analysis) by theorizing about the configuration of neighborhood that realistically shapes regional economic inequality.

Following the equivalences shown in footnote 6, Eqs. (4) and (5) are similar to Akita’s Eqs. (2) and (3) (Akita 2003, p. 58).

Following the arguments provided by Blank (2011), and adapting these arguments to the regional field, there are different effects that should stimulate the analysis of regional economic inequality. First, increases in regional economic inequality may indicate declines in regional economic income, and so, decreasing regional well-being in lagged regions. Second, regional economic inequality may intensify socio-economic regional differences, reducing regional economic mobility. Third, regional economic inequality could have negative effects on aggregate economic growth over time. Finally, regional economic inequality may have adverse consequences on non-economic outcomes, like political processes, social welfare or public policy concerns.

As the European Union reached its current size of 28 member countries with the accession of Croatia on 1 July 2013, our analysis does not consider Croatia. Thus, the country sample is composed of 27 countries that are members of the EU from 2007. Additionally, Noruega was considered in the analysis because this country is member of the Schengen border-free area.

With respect to the spatial weights matrix, in our application, we experiment with a binary first-order geographical contiguity matrix, being the results similar to the results obtained with the 5-nearest neighbors matrix. Nevertheless, due to the presence of some regions that do not present geographical connection with other regions, the 5-nearest neighbors matrix was used in order to capture the contextual process that could account for how regional neighborhoods affect regional inequality.

Similar results were presented by Doran and Jordan (2016) for the case of the composition of income inequality among United States counties from 1969 to 2009; these authors find that income inequality has increased, with Between-State inequality decreasing and within-State inequality increasing.

Additionally, as it was indicated by a referee, inferential exercises could be performed in line with both Rey and Smith (2013) and Novotny and Nosek (2012). Another future development would be to individuate some comparisons between the behavior of Moran's I and our spatial Theil index.