Foreign Direct Investment and Unequal Regional Economic Growth in China



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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