APPENDIX 2: REGIONAL INCOME INEQUALITY INDEXES
The measures of income inequality follow the commonly used methods: (1) A simple
dispersion indices, based on standard deviation; (2) Gini coefficients and the
dissimilarity index; (3) the Shannon entropy measure; (4) the rank-size function.
The dissimilarity is measured by the following index:
1 „ y. POP
D ` ɪ ∑n.1∣ ½ & -----i- *
(1)
2 i Y POP
where yi = per capita income in region i;
Y = per capita income in the country;
POPi = population in region i;
POP = total population in the country;
The dissimilarity index evaluates the maximum vertical deviation between the
Lorenz Curve and the diagonal. When measuring in a time period, a descending trend
shows that the dissimilarity in income among the regions is reduced.
The modified Shannon entropy measure is also called the total inequality measured
by:
I ' 3in'1zilognzi (2)
where zi = yi / ∑ yi , in which the value zi shows the fraction of region i’s per capita
income, while n is the total number of regions.
From this formula complete inequality exists when the per capita income of one
region is equal to the sum, i.e. zi = 1, in which case I would be as its maximum, log n.
Conversely, complete equality is achieved when all regions have the same per capita
income, so that z1 = z2 = .... = zn, and I is at 0, which is also its minimum. When I
tends to decrease, it means income inequality is reduced, when I tends to increase,
the income gap is enlarged.
The rank-size function describes the relations between the size and rank of
observations when they are arranged in the descending order according to size. The
logarithmic form is applied:
ln y = a + b ln r (3)
where y is size, expressed by the size of per capita income, r is rank arranged from
the largest per capita income of the region to the smallest one.
19
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