Abstract
This chapter provides a discussion on the concept of spatial inequality from a multidimensional perspective. The idea put forth is to emphasize the interconnection between an unfair outcome distribution and its individual variation at the local level. The additional information on the spatial dimension allows for a different proposal in terms of both measurement and policy implications. The first step is to present a brief overview of the concept of spatial inequality. We then look at a novel aspect of the spatial pattern of inequality of opportunity. Finally, the chapter suggests several regional and national policies investigating the trade-off of equity and efficiency in the process of redistribution.
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Notes
- 1.
It implies that individuals of each type t have identical circumstances in the vector C.
- 2.
See Agovino et al. (2019) for the adoption of a Spatial Lag of X model for the determination of the spatial contiguity matrix.
- 3.
The model proposed here is a description of an ex ante approach where the within-inequality is measured for each opportunity set. The same analysis can be developed by looking at an ex post approach where the vector of circumstances enclosed individuals at the same degree of effort.
- 4.
The formal definition of the Mean Log Deviation is as follows:
$$\displaystyle \begin{aligned} MLD=\frac{1}{N}\sum_{i=1}^{N}\ln \frac{\mu }{y_{i}} \end{aligned}$$where N is the number of individuals, y i is the income of the individual i, and μ is the mean of the distribution.
- 5.
The Atkinson index for 𝜖 = 1 is:
$$\displaystyle \begin{aligned} A=\frac{\left[ \displaystyle\prod_{i=1}^{N}y_{i}\right] ^{\frac{1}{N}}}{\mu } \end{aligned} $$(5.6)while the between components is:
$$\displaystyle \begin{aligned} A_{B}=\frac{\displaystyle\prod_{j=1}^{m}\left( \mu _{j}\right) ^{p_{j}}}{\mu } \end{aligned} $$(5.7)where p j = N j∕N is the population share. Hence, we define the Atkinson’s equality index within subgroup j as follows:
$$\displaystyle \begin{aligned} A_{j}=\frac{\left[ \displaystyle\prod_{i=1}^{N_{j}}y_{ji}\right] ^{\frac{1}{N_{j}} }}{\mu _{j}}\ \ \end{aligned} $$(5.8)and the inner product is equal to
$$\displaystyle \begin{aligned} A_{W}=\frac{A}{A_{B}}=\frac{\displaystyle\prod_{j=1}^{m}\left( A_{j}\mu _{j}\right) ^{p_{j}}}{\mu }\frac{\mu }{\displaystyle\prod_{j=1}^{m}\left( \mu _{j}\right) ^{p_{j}}}=\displaystyle\prod_{j=1}^{m}A_{j}^{p_{j}} \end{aligned} $$(5.9) - 6.
- 7.
See Pignataro (2010) for a decomposition à la Shapley by population subgroups.
- 8.
Note that in this perspective even housing policies that influence the commuting of agents should be considered for the spatial effects of agents.
- 9.
The notion of the neoclassical theory of income disparities and trade suggests that a low level of productivity of a poorer region does not necessarily impede to gain from trade due to the comparative advantage. It depends naturally on the decreasing/increasing return to scale of trade integration or potential liberalization of capital movements.
- 10.
Usually, more impoverished regions with a lower level of initial resources have higher returns on capital attracting money from abroad (think about the integrated European areas). Policy interventions toward the more deprived areas are more difficult to justify in a neoclassical perspective in case the competition effect is stronger without economies of scale.
- 11.
See Pignataro (2009).
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Pignataro, G. (2021). Spatial Inequality: A Multidimensional Perspective. In: Colombo, S. (eds) Spatial Economics Volume II. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-40094-1_5
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