Inequalities of Development Lorenz Curve and Gini Coefficient

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Inequalities of DevelopmentLorenz Curve and
Gini Coefficient
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Measurements
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Measurements of Income Distribution

• Lorenz Curve
• A curve showing the proportion of national income
  earned by a given percentage of the population.
• e.g what proportion of national income is earned
  by the top 10 of the population?

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Lorenz Curve
of National Income
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.
30
10
10
30
Percentage of Population
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Lorenz Curve
of National Income
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.
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.
In this example, the poorest 30 of the
population earn 20 of the national income.
20
7
Percentage of Population
30
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Gini Coefficient

• Enables more precise comparison of Lorenz Curves
• The proportion of the area taken up by the Lorenz
  Curve in relation to the overall area under the
  line of equality

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Gini Coefficient
of National Income
The area bounded by the Lorenz Curve
Percentage of Population
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The Gini Coefficient
Twice the area between the Lorenz curve and the
equality diagonal.

• Pros
• Generally regarded as gold standard in economic
  work
• Incorporates all data
• Allows direct comparison between units with
  different size populations
• Attractive intuitive interpretation

• Cons
• Requires comprehensive individual level data
• Requires more sophisticated computations

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The Lorenz Curve

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

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A Hypothetical Lorenz Curve

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

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Lorenz Curve for the United States, 1998
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The Gini Coefficient

• The Gini Coefficient is a measurement of the
  degree of inequality in the income distribution.
• The Gini Coefficient is equal to the Area between
  line of perfect income equality and the actual
  Lorenz Curve, divided by the Entire Triangular
  are under the line of perfect income equality.
• A Gini Coefficient of 0 is complete income
  equality while a Gini Coefficient of 1 means
  complete income inequality.

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A Limitation of the Gini Coefficient

• The Gini Coefficient cannot tell us what is
  happening in different quintiles.
• We should not jump to the conclusion that because
  the Gini coefficient is lower in country 2 than
  in country 21, the lowest fifth of households
  have a greater percentage of total income, in
  country 2, than in country 1.

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A Limitation of the Gini Coefficient

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

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How evenly spread is the worlds wealth?
Cumulative World Pop' Cumulative Wealth (PPP) Cumulative Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
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World distribution of wealth (PPP) Lorenz Curve
100
90
80
70
60
50
40
30
20
10










Pop Wealth (PPP) Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
Line of total integration
Cumulative Wealth (PPP)
10 20 30 40 50 60 70 80 90 100
Cumulative Global Population
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World distribution of wealth Lorenz Curve
100
90
80
70
60
50
40
30
20
10










Pop Wealth (PPP) Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
The richest 10 possessed 46.9 of the world
wealth in 1988.
Line of total integration
Cumulative Wealth (PPP)
10 20 30 40 50 60 70 80 90 100
Cumulative Global Population
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World distribution of wealth Lorenz Curve
100
90
80
70
60
50
40
30
20
10










Pop Wealth (PPP) Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
The richest 10 possessed 50.8 of the world
wealth in 1993.
Line of total integration
Cumulative Wealth (PPP)
10 20 30 40 50 60 70 80 90 100
Cumulative Global Population
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World distribution of wealth (PPP) Lorenz Curve
100
90
80
70
60
50
40
30
20
10










Pop Wealth (PPP) Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
Line of total integration
Cumulative Wealth (PPP)
The greater this area the more unequal the
distribution
10 20 30 40 50 60 70 80 90 100
Cumulative Global Population
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What is a Gini Coefficient?

• The Gini coefficient, invented by the Italian
  statistitian Corado Gini, is a number between
  zero and one that measures the degree of
  inequality in the distribution of something.
• The coefficient would register zero (0.0
  minimum inequality) for a society in which each
  member received exactly the same amount.
• A coefficient of one (1.0 maximum inequality)
  would mean one member got everything and the rest
  got nothing.

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Calculating the Gini Coefficient
100
90
80
70
60
50
40
30
20
10










Although the Lorenz Curve is good visual
indicator of distribution equality, the Gini
Coefficient provides a clearer quantatitive
value. A / B Gini Values should lie between 0
(total integration) to 1 (total segregation).
B
Line of total integration
Cumulative Wealth (PPP)
A
10 20 30 40 50 60 70 80 90
Cumulative Global Population
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Tasks

• Plot Lorenz Curves for 1988 and 1993 data on
  graph paper. Answer
• Calculate the Gini Coefficient for both. What do
  these tell you about trends in world distribution
  of wealth between 1988 and 1993? Answer
• Economists estimate that the world's Gini
  coefficient fell to 0.63 in 1998 from 0.66 in
  1970. Plot a graph to show fluctuations over
  time. Answer

Pop Wealth (PPP) Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
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What are typical Gini Coefficients for countries
around the world?

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

Sourcehttp//berclo.net/inden.html
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• In 1993 the Gini of the whole world was 0.66
• In 1988 it was 0.63

BACK
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• In 1993 the Gini of the whole world was 0.66
• In 1988 it was 0.63. The early 1990s saw a
  worrying increase in Global inequalities of
  wealth. However, some experts say that things are
  improving.

BACK
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World distribution of wealth (PPP) Lorenz Curve
100
90
80
70
60
50
40
30
20
10










Pop Wealth (PPP) Wealth (PPP)
  1988 1993
0 0 0
10 0.9 0.8
20 2.3 2
50 9.6 8.5
75 25.9 22.3
85 41 37.1
90 53.1 49.2
95 69.8 66.3
99 91.7 91.5
100 100 100
Line of total integration
Cumulative Wealth (PPP)
BACK
10 20 30 40 50 60 70 80 90 100
Cumulative Global Population
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• The fraction of the world's population below the
  poverty line (defined as an income of 2 a day)
  fell to 19 in 1998 from 41 in 1970 (chart).
• Overall inequality has decreased as well. the
  world's Gini coefficient fell to 0.63 in 1998
  from 0.66 in 1970.
• However, there have been fluctuations such as
  that seen in the early 1990s.

BACK
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A Fairer Future for the World?

• Global trends for the Gini coefficient of wealth
  can be rather confusing and distorted by the
  rapid growth of large Tiger Economies like China.
• The gap between the worldss rich and poor has
  never been wider. Malnutrition, AIDS, conflict
  and illiteracy are a daily reality for millions.
  MakePovertyHistory.ORG