I will review techniques and results examining regional wealth inequalities based on research recently worked out with Roy Cerqueti (Univ. Macerata). In brief, correlations between macro-economy and micro-economy features are searched for. See the following papers:
R. Cerqueti and MA, Statistical Assessment of Regional Wealth Inequalities: the Italian Case, Quality and Quantity, in press (2014) doi: 10.1007/s11135-014-0111-y
R. Cerqueti and MA, Evidence of economic regularities and disparities of Italian regions from aggregated tax income size data, Physica A 421 (2015) 187-207 doi:10.1016/j.physa.2014.11.027
R. Cerqueti and MA, Cross Ranking of Cities and Regions: Population vs. Income, J. Stat. Mech. 7(2015) P07002 doi:10.1088/1742-5468/2015/07/P07002
R. Cerqueti and MA, Socio-economical Analysis of Italy: the case of hagiotoponym cities, The Social Science Journal, in press (2015) doi:10.1016/j.soscij.2015.03.004
MA and R. Cerqueti, Religion-based Urbanization Process in Italy: Statistical Evidence from Demographic and Economic Data, Quality and Quantity in press (2015). doi: 10.1007/s11135-015-0220-2
The data pertains to Italy (IT), over the period 2007-2011: the number of cities in regions, the number of inhabitants in cities and in regions, as well as the aggregated tax income of the cities and of regions, - but the ideas can be carried forward to other countries or systems. Frequency-size plots and cumulative distribution function plots, scatter plots and rank-size plots are displayed. The rank-size rule (for IT) is found not to be a standard power law, as in many other studies, but a doubly decreasing power law; the Kendall $\tau$ and the Spearman $\rho$ rank correlation coefficients are calculated. Yearly data of the aggregated tax income is transformed into a few indicators: the Gini, Theil, and Herfindahl-Hirschman indices. Numerical results confirm that IT is divided into very different regional realities. Communities can be, very clearly, distinguished, when specific criteria are numerically sound. Attention is given to cultural aspects through linguistic and religiosity criteria and the historical evolution of IT urbanization process. A specific urban distribution modeling is presented for the doubly decreasing power law, emphasizing the "phase system", based on urn filling statistics theory.