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A spatial decomposition of the Gini coefficient

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Abstract

The paper introduces a spatial decomposition of the Gini coefficient that supports the detection of spatial autocorrelation conjointly with an indicator of overall inequality. An additive pairwise decomposition based on a spatial weights matrix partitions inequality between observations that are geographically neighbors and those that are not. A framework for inference on the spatial decomposition is also suggested. The statistical properties of the decomposition measure are evaluated in a Monte Carlo simulation and an empirical illustration involving per capita income inequality in the US states is also provided.

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Notes

  1. A referee noted that the Gini Coefficient can also be consistent with multiple Lorenz curves and can thus suffer from a different form of an identification problem.

  2. Briant et al. (2010) use the term spatial Gini in reference to the application of a Gini index for a variable (income, productivity) measured on spatial units.

  3. Related work developing joint measures of inequality and concentration is reported in Arbia and Piras (2009).

  4. The original form of this statistic was first implemented in the package STARS: Space-Time Analysis of Regional Systems (Rey and Janikas 2006), but until this paper has not been formally described.

  5. The numerator of the first term for (3) is similar to the spatial autocorrelation coefficient suggested by Sokal et al. (1993).

  6. The 95 % confidence interval for the rejection frequencies under the null (\(\rho =0.05\)) is based on the distribution under the null: \(z = \frac{\hat{\alpha } - \alpha }{\sqrt{(\alpha (1-\alpha ))/(M+1)}} \). With \(\alpha =0.05\) and \(M=999\) this yields and interval of \([0.0383, 0.0617]\).

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Authors and Affiliations

  1. GeoDa Center for Geospatial Analysis and Computation, School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, USA

    Sergio J. Rey

  2. School of Social Work, Wayne State University, Detroit, USA

    Richard J. Smith

Authors
  1. Sergio J. Rey
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  2. Richard J. Smith
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Correspondence to Sergio J. Rey.

Additional information

This research was funded in part by NSF Award OCI-1047916, SI2-SSI: CyberGIS Software Integration for Sustained Geospatial Innovation.

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Rey, S.J., Smith, R.J. A spatial decomposition of the Gini coefficient. Lett Spat Resour Sci 6, 55–70 (2013). https://doi.org/10.1007/s12076-012-0086-z

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