Inequalities of Development Lorenz Curve and Gini Coefficient

Measurements

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?

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

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% 30% Percentage of Population

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

Gini Coefficient The total area under the line of equality % of National Income The total area under the line of equality The area bounded by the Lorenz Curve Percentage of Population

The Gini Coefficient Pros 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

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.

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.

Lorenz Curve for the United States, 1998

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. The Gini Coefficient

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.

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. A Limitation of the Gini Coefficient

How evenly spread is the world’s wealth? Cumulative World Pop' Cumulative Wealth (PPP)   1988 1993 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

World distribution of wealth (PPP) Lorenz Curve 100 90 80 70 60 50 40 30 20 10 Pop’ Wealth (PPP)   1988 1993 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 Line of total integration Cumulative Wealth (PPP) 10 20 30 40 50 60 70 80 90 100 Cumulative Global Population

World distribution of wealth Lorenz Curve 100 90 80 70 60 50 40 30 20 10 Pop’ Wealth (PPP)   1988 1993 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 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

World distribution of wealth Lorenz Curve 100 90 80 70 60 50 40 30 20 10 Pop’ Wealth (PPP)   1988 1993 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 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

World distribution of wealth (PPP) Lorenz Curve 100 90 80 70 60 50 40 30 20 10 Pop’ Wealth (PPP)   1988 1993 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 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

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.

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

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 Economist’s 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)   1988 1993 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

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

In 1993 the Gini of the whole world was 0.66 In 1988 it was 0.63 BACK

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

World distribution of wealth (PPP) Lorenz Curve 100 90 80 70 60 50 40 30 20 10 Pop’ Wealth (PPP)   1988 1993 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 Line of total integration Cumulative Wealth (PPP) BACK 10 20 30 40 50 60 70 80 90 100 Cumulative Global Population

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 1990’s. BACK

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 worlds’s rich and poor has never been wider. Malnutrition, AIDS, conflict and illiteracy are a daily reality for millions.” MakePovertyHistory.ORG