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# Poverty, Inequality And Vulnerability Notes

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POVERTY, INEQUALITY & VULNERABILITY 'Development Economics' Ray 1998 (Ch. 6-7)

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Economic inequality o Measurement

Four criteria of inequality measurement

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Anonymity principle - does not matter who is earning the income o Means that we can always arrange our income distribution so that:

y1 < y2 < ... < yn

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Population principle o Cloning the entire population (and their incomes) should not alter inequality

If we compare an income distribution over n people and another population of 2n people with the same income pattern repeated twice, there should be no difference in equality

Population size doesn't matter - just proportions

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Relative income principle o Only relative incomes should matter and the absolute levels of these incomes should not

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The Dalton principle o Let (y1, y2, ..., yn) be an income distribution and consider 2 incomes yi and yj with yi < yj. A transfer of income from the 'not richer' individual to the 'not poorer' individual will be called a regressive transfer.

Dalton principle states that if one income distribution can be achieved from another by constructing a sequence of regressive transfers, then the former distribution must be deemed more unequal than the latter.

The Lorenz Curve

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Figure 6.4 (pg 179)

Horizontal axis: cumulative % of the population arranged in increasing order

Vertical axis: measure the % of national income accruing to any particular fraction of the population thus arranged

With increasing inequality, the Lorenz curve falls below the diagonal line of equality

Because individuals ordered from poorest to richest, the 'marginal contribution' of an extra persons income can never fall - Lorenz curve can't get flatter as we move from left to right

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Lorenz criterion - 'says that if the Lorenz curve of a distribution lies at every point to the right of the Lorenz curve of some other

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distribution, the former should be judged to be more unequal than the latter.' o An inequality measure is consistent with the Lorenz criterion if and only if it is simultaneously consistent with the anonymity, population, relative income and Dalton principles.

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If Lorenz curves cross: o Lorenz criterion doesn't apply o There are both progressive and regressive transfers occurring

Complete measures of inequality

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m incomes, in each income class, j, the number of individuals earning that income is denoted by nj

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Mean μ

o

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Mean Absolute Deviation o o Inequality is proportional to distance from the mean income o BUT often insensitive to Dalton Principle - M only changes with income transfers from income below the mean to above the mean (not from a low income below the mean to a higher income below the mean)

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The coefficient of variation o o Lorenz consistent, satisfies Dalton principle o C increases when regressive transfer is made

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Gini coefficient o Takes difference between all pairs of incomes and totals the absolute differences o o Lorenz consistent o It is precisely the ratio of the area between the Lorenz curve and the diagonal line of perfect equality, to the area of the triangle below the diagonal line

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If Lorenz curves cross, Gini and coefficient of variation may give contradictory rankings. Inequality and development: interconnections o 'Savings rates are severely affected at low levels of income; so is the capacity to do useful work.' o 'given today's distribution of endowments and today's economic interaction in the marketplace, we generate a new distribution of endowments for tomorrow.'

'In this sense today's distribution of wealth spawns, via economic interaction, tomorrow's distribution of wealth, and the process repeats itself endlessly over time and over generations.'

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'Thus economic growth and economic inequality and evolve together.' o Inequality, income and growth

The inverted-U hypothesis

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