Question

Explain the following measures of income inequality. [8 marks]

(i) Range

(ii) Coefficient of variation

(iii) Gini coefficient

(iv) Theil index

Answer 1

1). Range is an important and easily understood measure of inequality. It is the difference between the higest item and the lowest item. Given a vector representation of an income distribution in a population with n individuals, the range is obtained by the ratio of the difference between the maximum and the minimum income and the mean income. Range has zero as minimum value and one as maximum value.

Range = Higest value- Lowest value.

2). Coffuicient of variation (cov) is another important measure of inequality. Income Distributions with a coefficient of variation to be less than 1 are considered to be low-variance, whereas those with a CV higher than 1 are considered to be high variance. This measure of income inequality is calculated by the dividing the standard deviation of the income distribution by its mean. More equal income distributions will have smaller standard deviations; as such, the CV will be smaller in more equal societies.

3). Gini-Cofficient is another important measure of inequality in an economy. We know that Gini index or Gini coefficient is a statistical measure of distribution.itis developed by the Italian statistician Corrado Gini in 1912. It is often used as a gauge of economic inequality, measuring income distribution or, less commonly, wealth distribution among a population. We know that Gini-Cofficient ranges from 0 to 1. Zero represt the perfect equality and the 1 represent the perfect inequality of income. A higher Gini index indicates greater inequality, with high income individuals receiving much larger percentages of the total income of the population.

4). Theil index is an important method to measure the economic inequality in an economy. Altough  it has also been used to measure racial segregation. The Theil index T_T is the same as redundancy in information theory which is the maximum possible entropy of the data minus the observed entropy. The Theil index measures an entropic "distance" the population is away from the "ideal" egalitarian state of everyone having the same income. The numerical result is in terms of negative entropy so that a higher number indicates more order that is further away from the "ideal" of maximum disorder.

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