Income DistributionIncome Distribution

Gene ChangGene Chang

U of ToledoU of Toledo

Income DistributionIncome Distribution

The The size distribution of incomesize distribution of income shows shows the amount of income received by rich, the amount of income received by rich, poor, and middle-class individuals or poor, and middle-class individuals or families and often is interpreted as a direct families and often is interpreted as a direct measure of welfare.measure of welfare.

Determined by…Determined by…– The number of people under the poverty lineThe number of people under the poverty line– The inequality in income distribution The inequality in income distribution

Income DistributionIncome Distribution

Popular measures:Popular measures:– Lorenz curveLorenz curve– GINI coefficientGINI coefficient– Number of people living below $1 a day (PPP)Number of people living below $1 a day (PPP)– Number of people living below $1 a day (PPP)Number of people living below $1 a day (PPP)

Lorenz Curve

To draw a Lorenz curve, income recipients are arrayed from lowest to highest income along the horizontal axis. The curve itself shows the share of total income received by an cumulative percentage of recipients. Its shape indicates the degree of inequality in the income distribution. By definition, the curve must touch the 45 degree line at both the lower-left corner (0% of recipients must receive 0% of income) and the upper-right corner (100% of recipients must receive 100% of income).

Lorenz Curve

If everyone had the same income, the Lorenz curve would lie along the 45 degree line (perfect equality). Equality means simply that everyone gets the same income (or owns the same wealth).If 1% of the population receives 100% of income and the rest of the population receives nothing, then the Lorenz curve is a right angel one.Inequality is greater the farther the Lorenz curve bends away from the 45 degree line.

Lorenz curveLorenz curve

Percentage of Income Recipients

0% 100% 0% 100%

Percentage of Income Recipients

0%

100% 100%

0%

% of income received

% of income received

Lorenz curve

When comparing two or more countries the following terminology can be used:– “Lorenz Dominates” – One country’s Lorenz

curve is above another country’s at every point.

– “Lorenz Incompatible” – Occurs when one country’s Lorenz curve intersects another country’s curve.

Example: Brazil (c. 1970)

Population Quintile Percentage of Income

Cumulative

First 20% 3.0% 3.0%

Second 20% 6.2% 9.2%

Third 20% 10.6% 19.8%

Fourth 20% 18.7% 38.5%

Fifth 20% 61.5% 100%

Lorenz curveLorenz curve

0% 20% 40% 60% 80% 100%

100%

38.5%

19.8%

9.2%

3%

GINI Coefficient

Derived from the Lorenz curve. The ratio is understood most easily as the value of area A divided by area A + B.– Gini Coefficient = A / (A + B) = A / triangular

area

A + B = . 5 so A = .5 – B Gini = (.5 – B) / .5Thus, the larger the share of the area between the 45o line and the Lorenz curve, the higher is the value of the Gini concentration ratio.

Lorenz curveLorenz curve

A

B

GINI coefficient for the Brazilian data set

A + B = (1/2) (100% ) = 50%

B = (1/2) (0 + .03) (.2) + (1/2) (.03 + .092) (.2) + (1/2) (.092 + .198) (.2) + (1/2) (.198 + .385) (.2) + (1/2) (.385 + 1) (.2)

= .1 * (.03 * 2) + (.092 * 2) + (.198 * 2) + (.385 * 2) + 1

= .1 * 2.43 = .243

GINI = (.5 – B) / .5 = (.5 - .243) / .5 = .514

Problems

Lorenz curves can intersect.

It is even possible for curves with different shapes to generate the same Gini coefficient. – This happens when one distribution is very

unequal in one part of its range, while another is unequal in a different part.

International comparison

GINI < 30 Good

GINI > 50 Bad

International comparison

International cmoparisonInternational cmoparison

International comparison

http://hdrstats.undp.org/indicators/147.html

http://en.wikipedia.org/wiki/List_of_countries_by_income_equality

Inequality and health

http://www.globalissues.org/article/4/poverty-around-the-world#InequalityandHealth

International ComparisonInternational Comparison

European welfare statesEuropean welfare states

Formal centrally planned systemFormal centrally planned system

Transitional economiesTransitional economies

East Asian countriesEast Asian countries

Fast growth economies, China and IndiaFast growth economies, China and India

Latin American countriesLatin American countries

African countriesAfrican countries

Reasons for the income Reasons for the income inequality accross countriesinequality accross countries

Resources coming more from endowment Resources coming more from endowment of land and privilegeof land and privilege

System and government policy: System and government policy: progressive tax system and transfer progressive tax system and transfer paymentpayment

Economic growthEconomic growth

Kuznets inverted U curveKuznets inverted U curve

Kuznets inverted U curveKuznets inverted U curve

Kuznets curve is the graphical representation of Simon Kuznets curve is the graphical representation of Simon Kuznets's theory that economic inequality increases Kuznets's theory that economic inequality increases before decreases during the economic growth of a before decreases during the economic growth of a countrycountry

In the primitive agrarian economy, most people living at In the primitive agrarian economy, most people living at the subsistence level, so the majority is equally poor.the subsistence level, so the majority is equally poor.

In early stages of development, when investment in In early stages of development, when investment in physical capital is the main mechanism of economic physical capital is the main mechanism of economic growth, inequality encourages growth by allocating growth, inequality encourages growth by allocating resources towards those who save and invest the most. resources towards those who save and invest the most.

Kuznets inverted U curveKuznets inverted U curve

In mature economies human capital accrual, or an In mature economies human capital accrual, or an estimate of cost that has been incurred but not yet paid, estimate of cost that has been incurred but not yet paid, takes the place of physical capital accrual as the main takes the place of physical capital accrual as the main source of growth, and inequality slows growth by source of growth, and inequality slows growth by lowering education standards because poor people lack lowering education standards because poor people lack finance for their education in imperfect credit markets. finance for their education in imperfect credit markets.

Also, in a mature economy, there are better universal Also, in a mature economy, there are better universal education and health care system, and more progressive education and health care system, and more progressive tax system, so the income distribution becomes more tax system, so the income distribution becomes more equalequal

Income distribution in CPEsIt is said that the income distribution in CPEs are very equal.

In general, the Gini coefficients in those countries are below 0.30.

The reasons are– All assets are owned by the state so individuals do

not receive income from private ownership of assets – Most people are employed by the state and difference

between salary scales are very limited among employees.

– Generous transfer payments to households

Income distribution in CPEs

But one should not overlook the inequality in CPEs:– Non-monetary income received by the

privileged class– Regional gaps and urban-rural income gap