Inequalities of Inequalities of DevelopmentDevelopment

Lorenz Curve and Lorenz Curve and Gini CoefficientGini Coefficient

MeasurementsMeasurements

Measurements of Income Measurements of Income DistributionDistribution

►Lorenz Curve:Lorenz Curve:►A curve showing the proportion of A curve showing the proportion of

national income earned by a given national income earned by a given percentage of the population.percentage of the population.

►e.g what proportion of national e.g what proportion of national income is earned by the top 10% income is earned by the top 10% of the population?of the population?

Lorenz CurveLorenz Curve% of National Income

Percentage of Population

This line represents the situation if income was distributed equally. The poorest 10% would earn 10% of national income, the poorest 30% would earn 30% of national income.

10%

10%

30%

30%

Lorenz Curve% of National Income

Percentage of Population

The Lorenz Curve will show the extent to which equality exists. The greater the gap between the line of equality and the curve the greater the degree of inequality.

30%

20%

In this example, the poorest 30% of the population earn 20% of the national income.

7%

In this second example, the Lorenz curve lies further below the line of equality. Now, the poorest 30% only earn 7% of the national income.

Gini CoefficientGini Coefficient

►Enables more precise comparison of Enables more precise comparison of Lorenz CurvesLorenz Curves

►The proportion of the area taken up by The proportion of the area taken up by the Lorenz Curve in relation to the the Lorenz Curve in relation to the overall area under the line of equalityoverall area under the line of equality

Gini CoefficientGini Coefficient

% of National Income

Percentage of Population

The total area under the line of equalityThe area bounded by the Lorenz Curve

The Gini CoefficientThe Gini Coefficient

ProsPros► Generally regarded Generally regarded

as gold standard in as gold standard in economic workeconomic work

► Incorporates all dataIncorporates all data► Allows direct Allows direct

comparison between comparison between units with different units with different size populationssize populations

► Attractive intuitive Attractive intuitive interpretationinterpretation

ConsCons► Requires Requires

comprehensive comprehensive individual level individual level datadata

► Requires more Requires more sophisticated sophisticated computationscomputations

Twice the area between the Lorenz curve and the equality Twice the area between the Lorenz curve and the equality diagonal.diagonal.

The Lorenz CurveThe Lorenz Curve

The Lorenz curve The Lorenz curve represents the represents the distribution of distribution of income; it expresses income; it expresses the relationship the relationship between cumulative between cumulative percentage of percentage of households and households and cumulative cumulative percentage of percentage of income.income.

A Hypothetical A Hypothetical Lorenz CurveLorenz Curve

The data in (a) were used to derive the Lorenz curve The data in (a) were used to derive the Lorenz curve in (b). The Lorenz curve shows the cumulative in (b). The Lorenz curve shows the cumulative percentage of income earned by the cumulative percentage of income earned by the cumulative percentage of households. If all households received percentage of households. If all households received the same percentage of total income, the Lorenz the same percentage of total income, the Lorenz curve would be the line of perfect income equality. curve would be the line of perfect income equality. The bowed Lorenz curve shows an unequal The bowed Lorenz curve shows an unequal distribution of income. The more bowed the Lorenz distribution of income. The more bowed the Lorenz curve is, the more unequal the distribution of income.curve is, the more unequal the distribution of income.

Lorenz Curve for the Lorenz Curve for the United States, 1998United States, 1998

The Gini The Gini CoefficientCoefficient

The Gini Coefficient is a The Gini Coefficient is a measurement of the measurement of the degree of inequality in degree of inequality in the income distribution.the income distribution.

The Gini Coefficient is The Gini Coefficient is equal to the Area equal to the Area between line of perfect between line of perfect income equality and the income equality and the actual Lorenz Curve, actual Lorenz Curve, divided by the Entire divided by the Entire Triangular are under the Triangular are under the line of perfect income line of perfect income equality.equality.

A Gini Coefficient of 0 is A Gini Coefficient of 0 is complete income equality complete income equality while a Gini Coefficient of while a Gini Coefficient of 1 means complete 1 means complete income inequality.income inequality.

A Limitation of the Gini A Limitation of the Gini CoefficientCoefficient

► The Gini Coefficient The Gini Coefficient cannot tell us what is cannot tell us what is happening in different happening in different quintiles.quintiles.

► We should not jump to We should not jump to the conclusion that the conclusion that because the Gini because the Gini coefficient is lower in coefficient is lower in country 2 than in country 2 than in country 21, the lowest country 21, the lowest fifth of households have fifth of households have a greater percentage of a greater percentage of total income, in country total income, in country 2, than in country 1.2, than in country 1.

A Limitation of A Limitation of the Gini the Gini

CoefficientCoefficient

By itself the Gini coefficient By itself the Gini coefficient cannot tell us anything cannot tell us anything about the income share of about the income share of a particular quintile. a particular quintile. Although there is a Although there is a tendency to believe that tendency to believe that the larger percentage of the larger percentage of total income the lower the total income the lower the Gini coefficient, this need Gini coefficient, this need not be the case. In the not be the case. In the diagram, the Gini diagram, the Gini coefficient for Lorenz curve coefficient for Lorenz curve 2 is lower than the Gini 2 is lower than the Gini coefficient for Lorenz curve coefficient for Lorenz curve 1. But the bottom 20 % of 1. But the bottom 20 % of households obtains a households obtains a smaller percentage of total smaller percentage of total income in the lower Gini income in the lower Gini Coefficient case.Coefficient case.

How evenly spread is the How evenly spread is the world’s wealth?world’s wealth?

Cumulative World Pop'Cumulative World Pop' Cumulative Wealth (PPPCumulative Wealth (PPP))

   19881988 19931993

00 00 00

1010 0.90.9 0.80.8

2020 2.32.3 22

5050 9.69.6 8.58.5

7575 25.925.9 22.322.3

8585 4141 37.137.1

9090 53.153.1 49.249.2

9595 69.869.8 66.366.3

9999 91.791.7 91.591.5

100100 100100 100100

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

100100

9090

8080

7070

6060

5050

4040

3030

2020

1010

Cumulative Global Population

Cum

ulat

ive

Wea

lth (

PP

P)

World distribution of wealth (PPP) Lorenz Curve

Pop’Pop’WealthWealth(PPP)(PPP)

   19881988199199

33

00 00 00

1010 0.90.9 0.80.8

2020 2.32.3 22

5050 9.69.6 8.58.5

7575 25.925.922.22.

33

8585 414137.37.

11

9090 53.153.149.49.

22

9595 69.869.866.66.

33

9999 91.791.791.91.

55

100100 100100 100100

Line

of to

tal i

nteg

ratio

n

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

100100

9090

8080

7070

6060

5050

4040

3030

2020

1010

Cumulative Global Population

Cum

ulat

ive

Wea

lth (

PP

P)

World distribution of wealth Lorenz Curve

Pop’Pop’WealthWealth(PPP)(PPP)

   19881988199199

33

00 00 00

1010 0.90.9 0.80.8

2020 2.32.3 22

5050 9.69.6 8.58.5

7575 25.925.922.22.

33

8585 414137.37.

11

9090 53.153.149.49.

22

9595 69.869.866.66.

33

9999 91.791.791.91.

55

100100 100100 100100

Line

of to

tal i

nteg

ratio

n

The richest 10% possessed

46.9% of the world wealth in

1988.

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

100100

9090

8080

7070

6060

5050

4040

3030

2020

1010

Cumulative Global Population

Cum

ulat

ive

Wea

lth (

PP

P)

World distribution of wealth Lorenz Curve

Pop’Pop’WealthWealth(PPP)(PPP)

   19881988199199

33

00 00 00

1010 0.90.9 0.80.8

2020 2.32.3 22

5050 9.69.6 8.58.5

7575 25.925.922.22.

33

8585 414137.37.

11

9090 53.153.149.49.

22

9595 69.869.866.66.

33

9999 91.791.791.91.

55

100100 100100 100100

Line

of to

tal i

nteg

ratio

n

The richest 10% possessed

50.8% of the world wealth in

1993.

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

100100

9090

8080

7070

6060

5050

4040

3030

2020

1010

Cumulative Global Population

Cum

ulat

ive

Wea

lth (

PP

P)

World distribution of wealth (PPP) Lorenz Curve

Pop’Pop’WealthWealth(PPP)(PPP)

   19881988199199

33

00 00 00

1010 0.90.9 0.80.8

2020 2.32.3 22

5050 9.69.6 8.58.5

7575 25.925.922.22.

33

8585 414137.37.

11

9090 53.153.149.49.

22

9595 69.869.866.66.

33

9999 91.791.791.91.

55

100100 100100 100100

Line

of to

tal i

nteg

ratio

n

The greater this area the more unequal the distribution

What is a Gini Coefficient?What is a Gini Coefficient?

► The Gini coefficient, invented by the Italian The Gini coefficient, invented by the Italian statistitian Corado Gini, is a number between statistitian Corado Gini, is a number between zero and one that measures the degree of zero and one that measures the degree of inequality in the distribution of something. inequality in the distribution of something.

► The coefficient would register zero (0.0 = The coefficient would register zero (0.0 = minimum inequality) for a society in which minimum inequality) for a society in which each member received exactly the same each member received exactly the same amount.amount.

► A coefficient of one (1.0 = maximum A coefficient of one (1.0 = maximum inequality) would mean one member got inequality) would mean one member got everything and the rest got nothing. everything and the rest got nothing.

1010 2020 3030 4040 5050 6060 7070 8080 9090

100100

9090

8080

7070

6060

5050

4040

3030

2020

1010

Cumulative Global Population

Cum

ulat

ive

Wea

lth (

PP

P)

Calculating the Gini Coefficient

A

B

Although the Lorenz Curve is good visual indicator of distribution equality, the Gini Coefficient provides a clearer quantatitive value.

A / B = GiniValues should lie between 0 (total integration) to 1 (total segregation).Lin

e of

tota

l int

egra

tion

TasksTasks

► Plot Lorenz Curves for 1988 and Plot Lorenz Curves for 1988 and 1993 data on graph paper. 1993 data on graph paper. AnswerAnswer

► Calculate the Gini Coefficient for Calculate the Gini Coefficient for both. What do these tell you about both. What do these tell you about trends in world distribution of trends in world distribution of wealth between 1988 and 1993? wealth between 1988 and 1993? AnswerAnswer

► Economist’s estimate that the Economist’s estimate that the world's Gini coefficient fell to 0.63 world's Gini coefficient fell to 0.63 in 1998 from 0.66 in 1970. Plot a in 1998 from 0.66 in 1970. Plot a graph to show fluctuations over graph to show fluctuations over time. time. AnswerAnswer

Pop’Pop’WealthWealth(PPP)(PPP)

   19881988 19931993

00 00 00

1010 0.90.9 0.80.8

2020 2.32.3 22

5050 9.69.6 8.58.5

7575 25.925.9 22.322.3

8585 4141 37.137.1

9090 53.153.1 49.249.2

9595 69.869.8 66.366.3

9999 91.791.7 91.591.5

100100 100100 100100

What are typical Gini What are typical Gini Coefficients for countries around Coefficients for countries around

the world?the world?In practice, coefficient values range from around 0.2 for In practice, coefficient values range from around 0.2 for historically equalitarian countries like Bulgaria, historically equalitarian countries like Bulgaria, Hungary, the Slovak and Czech republics and Poland to Hungary, the Slovak and Czech republics and Poland to over 0.6 for Central and South American countries over 0.6 for Central and South American countries (such as Brazil) where powerful elites dominate the (such as Brazil) where powerful elites dominate the economy. economy. The evolution of the Gini coefficient is particularly The evolution of the Gini coefficient is particularly useful as it reveals trends. It shows the evolution useful as it reveals trends. It shows the evolution towards greater equality in Cuba from 1953 to 1986 towards greater equality in Cuba from 1953 to 1986 (0.55 to 0.22) and the growth of inequality in the USA (0.55 to 0.22) and the growth of inequality in the USA in the last three decades during which the Gini went in the last three decades during which the Gini went from 0.35 in the '70's to 0.40 now (and it is still rising!). from 0.35 in the '70's to 0.40 now (and it is still rising!). Most European countries and Canada rate around 0.30, Most European countries and Canada rate around 0.30, Japan and some Asian countries get around 0.35, some Japan and some Asian countries get around 0.35, some reach 0.40 while most African countries exceed 0.45. reach 0.40 while most African countries exceed 0.45.

Source:Source:http://berclo.net/http://berclo.net/inden.htmlinden.html

A Fairer Future for the World?A Fairer Future for the World?

►Global trends for the Gini coefficient of Global trends for the Gini coefficient of wealth can be rather confusing and wealth can be rather confusing and distorted by the rapid growth of large distorted by the rapid growth of large Tiger Economies like China.Tiger Economies like China.

►““The gap between the worlds’s rich The gap between the worlds’s rich and poor has never been wider. and poor has never been wider. Malnutrition, AIDS, conflict and Malnutrition, AIDS, conflict and illiteracy are a daily reality for illiteracy are a daily reality for millions.” MakePovertyHistory.ORGmillions.” MakePovertyHistory.ORG