MEASURING POVERTY AND INEQUALITY

Chapter- 6&8- Debraj Ray

What Is Inequality?

Economic inequality is the fundamental disparity that permits an individual certain material choices, while denying another individuals those very same choices.

Criterion for Measuring Inequality

There are 4 criterions for inequality measurement:1. Anonymity Principle2. Population Principle3. Relative Income Principle4. The Dalton Principle

Anonymity Principle states that it does not matter whoearns the income.

Population Principle states that the absolute population size does not matter; Proportions of the population that earns different levels of income matters.

Relative Income Principle states that relative incomes should matter, not the absolute levels of these incomes.

The Dalton Principle states that in an income distribution, a regressive transfer will lead to increased inequality.

The Lorenz Curve

-Diagrammatic way to depict the distribution of income in any society

-Horizontal axis depicts cumulative percentages of population arranged in increasing order of income; Vertical axis depicts percentage of nationalincome accruing to any fraction of population

-Slope at any point gives the contribution of the person at that point to the cumulative share of national income

The Lorenz Curve

Line

of E

qual

ity

Lorenz Curve is always bowed to the right of the line of equality.

The difference between the 45 degree line and the Lorenz curves depicts the level of inequality. More skewed the curve, greater the Inequality.

Measures of Inequality

There are 5 measures of inequality taken in consideration-

1. The Range

2. The Kuznets Ratio

3. The Mean Absolute Deviation

4. The Coefficient of Variation

5. The Gini Coefficient

The Range

* Given by the difference in the incomes of the richest and the poorest individuals, divided by the mean.

R= (Ym-Y1)/u, Where Ym gives the distinct incomes and u is the mean income.

*Crude measure, used when detailed info is missing

*Pays no attention to the incomes falling in b/w the richest or the poorest on the income scale

* Does not satisfy the Dalton’s Principle.

The Kuznets Ratio

Refers to the share of income owned by the poorest 20/40% of the population, or the richest 10%, or more commonly to the ratio of the shares of income of the richest X% to the poorest y%

As illustrated in the diagram, Kuznets Hypothesis says that income inequality should follow an inverse U-shaped curve along the development process

The Mean Absolute Deviation

* Considers the entire income distribution

* Inequality is proportional to the distance from the mean income.

Where u stands for mean income and n is the total population

* Insensitive to the Dalton Principle.

The Coefficient of Variation

Nothing but the standard deviation divided by the mean, so that only the relative incomes matter.

•Satisfies all the four principles, including the Dalton Principle

• Lorenz-consistent

The Gini Coefficient

* Takes the difference b/w all pairs of incomes & totals the absolute differences, normalized by dividing by population squared as well as the mean income.

* Inequality thus is the sum of all pair-wise comparisons of “two-person inequalities” .

* Satisfies all principles.

* Lorenz consistent

What Is Poverty Line?

A critical threshold of income, consumption, or more generally, access to goods and services below which individuals are declared to be poor.

It represents a minimum level of “acceptable” economicparticipation in a given society at a given point of time.

POVERTY MEASURES-

(i) HEAD COUNT/HEAD COUNT RATIO(ii) POVERTY GAP RATIO(iii) INCOME GAP RATIO(iv) FOSTER-GREER THORBECKE CLASS

Head Count RatioRepresents the number of people below poverty line as a ratio of the total population. HCR= HC/nDRAWBACK: Fails to capture the extent to which individual income falls below poverty line.

Poverty Gap RatioDefined as the ratio of the average of income needed to getall poor people to the poverty line, divided by the mean income of the society.

* Not really a measure of poverty itself, but a measure of resources required to eradicate it.

Income Gap Ratio

Depicts the total shortfall of the poor from the poverty line, divided by the total income required to bring allthe poor people to the poverty line.

•Captures directly the acuteness of poverty, as it measures it relative to the total income needed to eradicate poverty

DRAWBACK: Both PGR & IGR only capture the “per-capita intensity "of poverty. HCR does not suffer from this problem.

Foster-Greer Thorbecke Class

Distributional sensitivity is achieved by raising the poverty gaps (p-yi) to a power, a.

For a=0, the measure Po is just the head-count ratio.

For a=1, the measure P1 is the Poverty Gap Ratio. As a increases, larger poverty gaps begin to acquire greaterweight& the measure becomes increasingly sensitive.

For a=2, tells that when there’s no inequality, poverty can be captured by HCR & IGR but inequality, given by Cp, raises poverty.

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