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- *

2 i Y POP

where      y_i = per capita income in region i;

Y = per capita income in the country;

POP_i = 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 ' 3_iⁿ_'1z_ilognz_i                            (2)

where z_i = y_i / ∑ y_{i ,} in which the value z_i 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. z_i = 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 = .... = z_n, 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.

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