gini co-eff,lorez curve

8/3/2019 Gini Co-eff,Lorez Curve

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GINICO-EFFICIENT

&

LORENZCURVE


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INTRODUCTION:

Measure of statistical dispersion is developed by the Italian statistician

Sir Corrado Gini .

Commonly used as a measure of inequality of income or wealth.

It has, however, also found application in the study of inequalities in

disciplines as diverse as health science, ecology, and chemistry.

The Gini coefficient can range from 0 to 1 {0-100}

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The graph shows that while the Gini is technically

equal to the area marked 'A' divided by the sum of

the areas marked 'A' and 'B' (that is, Gini =

A/(A+B)), it is also equal to 2A, since the axesscale from 0 to 1, and the total surface of the graph

therefore equals 1.

o Low Gini coefficient indicates- more equal distribution,

0 [perfect equality]

o

Higher Gini coefficients indicate more unequal distribution,with 1 corresponding to perfect inequality.

Graphical representation of the Gini coefficient.


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DIFFERENTUSES

Gini coefficient is most popular in economics.

Theory be applied in any field of science that studies a distribution.

Eg:

1.In ecology -measure of biodiversity, where the cumulative

proportion of species is plotted against cumulative proportion of

individuals.

2.In health, it has been used as a measure of the inequality of

health related quality of life in a population.

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CALCULATION:

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oThe Gini index is defined as a ratio of the areas on the Lorenz curvediagram.

oIf the area between the line of perfect equality and the Lorenz curve is

A and the area under the Lorenz curve is B, then the Gini index is

A/(A+B). Since A+B = 0.5, the Gini index, G = A/(0.5) = 2A = 1-2B. If

the Lorenz curve is represented by the function Y = L(X), the value of B

can be found with integration


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7Gini coefficient, income distribution by country.


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Gini indices, income distribution over time for selected

countries


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US INCOMEGINIINDICESOVERTIME

Gini indices for the United States at various times, according to the

US Census Bureau:

1929: 45.0 (estimated)

1947: 37.6 (estimated)

1967: 39.7 (first year reported)1968: 38.6 (lowest index reported)

1970: 39.4

1980: 40.3

1990: 42.8

2000: 46.22005: 46.9

2006: 47.0 (highest index reported)

2007: 46.3 9


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ADVANTAGES -ASAMEASUREOFINEQUALITY

Measure of inequality by means of a ratio analysis.

Compare income distributions across different population

sectors as well as countries

Demonstrates how income has changed for poor and rich.

Indicate how the distribution of income has changed within a

country over a period of time

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PRINCIPLES:

The Gini coefficient satisfies four importantprinciples:

Anonymity: It does not matter who the high and low earners are.

Scale independence: The Gini coefficient does not consider the

size of the economy, the way it is measured, or whether it is a

rich or poor country on average.

Population independence: It does not matter how large the

population of the country is.

Transfer principle: If income, is transferred from a rich person to

a poor person the resulting distribution is more equal.11


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DISADVANTAGESASAMEASUREOFINEQUALITY

Different sets of people cannot be averaged to obtain the Gini

coefficient of all the people in the sets.

The Lorenz curve may understate the actual amount of inequality if

richer households are able to use income more efficiently than lower

income households or vice versa.

Economies with similar incomes and Gini coefficients can still have

very different income distributions.

It measures current income rather than lifetime income.

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PROBLEMSINUSINGTHE GINICOEFFICIENT

Based on net income does not accurately reflect differences wealth -

a possible source of misinterpretation.

Too often only the Gini coefficient is quoted without describing the

proportions of the quantiles used for measurement.

The Gini coefficient is point-estimate of equality at a certain time,

hence it ignores life-span changes in income.

Countries can have the same Gini coefficient but have completely

different levels of wealth.

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gini co-eff,lorez curve

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