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6. Gini coefficient

6.1. Read the text.

Gini coefficient, also known as the Gini index or Gini ratio is a measure of statistical dispersionintended to represent the income distribution of a nation's residents. It was developed by theItalianstatisticianandsociologistCorrado Giniand published in his 1912 paper "Variability and Mutability".

The Gini coefficient measures the inequality among values of a frequency distribution(for example levels ofincome). A Gini coefficient of zero expresses perfect equality, where all values are the same (for example, where everyone has the same income). A Gini coefficient of one (or 100%) expresses maximal inequality among values (for example where only one person has all the income).http://en.wikipedia.org/wiki/Gini_coefficient - cite_note-US_Census_Bureau-3 However, a value greater than one may occur if some persons represent negative contribution to the total (e.g., have negative income or wealth). For larger groups, values close to or above 1 are very unlikely in practice.

There are some issues in interpreting a Gini coefficient. The same value may result from many different distribution curves. The demographic structure should be taken into account. Countries with an aging population, or with a baby boom, experience an increasing pre-tax Gini coefficient even if real income distribution for working adults remains constant. Scholars have devised over a dozen variants of the Gini coefficient.

Graphical representation of the Gini coefficient - Lorenz curve

The Gini coefficient is usually defined mathematicallybased on theLorenz curve, which plots the proportion of the total income of the population (y axis) that is cumulatively earned by the bottom x% of the population (see diagram). The line at 45 degrees thus represents perfect equality of incomes. The Gini coefficient can then be thought of as theratioof theareathat lies between the line of equality and theLorenz curve(marked A in the diagram) over the total area under the line of equality (marked A and B in the diagram); i.e.,G = A (A + B).

If all people have non-negative income (or wealth, as the case may be), the Gini coefficient can theoretically range from 0 (complete equality) to 1 (complete inequality); it is sometimes expressed as a percentage ranging between 0 and 100. In practice, both extreme values are not quite reached. If negative values are possible (such as the negative wealth of people with debts), then the Gini coefficient could theoretically be more than 1. Normally the mean (or total) is assumed positive, which rules out a Gini coefficient less than zero.

A low Gini coefficient indicates a more equal distribution, with 0 corresponding to complete equality, while higher Gini coefficients indicate more unequal distribution, with 1 corresponding to complete inequality.

6.2. Answer the questions

1. What does Gini coefficient of zero express?

2. What does Gini coefficient of one (or 100%) express?

3. When does a value greater than one express?

4. Is a negative income or wealth common for persons or larger groups?

5. What do countries with an aging population, or with a baby boom, experience?

6. How is the Gini coefficient usually defined?

7. What does the line at 45 degrees represent?

8. How do you call the curve marked A in the diagram?

9. What is the difference between complete equality and complete inequality?