Poverty, Inequality and Development

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Poverty, Inequality and Development

• Todaro Chapter 5

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Introduction

• This section is concerned with the problems of
  poverty and highly unequal distributions of
  income
• Income and asset inequality is only one small
  part of the broader problem of inequality in the
  developing world. Inequalities exist in
• Power and status
• Gender
• Job satisfaction and working conditions
• Political participation and freedom of choice
• Education and Health
• Access to information and Technology

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Overview

• Measuring Inequality and Poverty
• Extent of Inequality in Developing Countries
• Economic Characteristics of the Poor
• Rapid Economic Growth and Equitable Distributions
  of Income
• Problems stemming from Inequality
• Policies to Reduce Absolute Poverty

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Measuring Inequality

• Size Distribution of Income
• Lorenz Curves
• Gini Coefficients and Aggregate Measures of
  Inequality
• Factor Share Distribution of Income

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Axioms of Inequality Measures

• Anonymity
• Scale Independence
• Population Independence
• Transfer

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Size Distribution of Personal Income

• The incomes of all individuals are arranged in
  ascending order, then the population is divided
  into deciles or quintiles. Then the percentage of
  national income of each group is determined.
• Kuznets ratio ratio of income received by top
  20 and income received by bottom 40 (From Table
  1 Kuznets ratio 37.16/20.10 1.848).

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Table 1 Size Distribution of Income
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Lorenz Curve

• Graphical representation of the Size Distribution
  of Personal Income.
• Shows the actual quantitative relationship
  between the percentage of income recipients and
  the percentage of total income they received
  during a given year.
• With the percentage of income on the Y-axis and
  the percentage of income recipients on the
  X-axis, the diagonal represents perfect equality.
• The further the Lorenz curve is away from the
  diagonal, the greater the degree of inequality.

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Figure 1 Using the data from Table 1
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Gini Coefficient

• The Gini coefficient is calculated by taking the
  area between the Lorenz curve and the diagonal
  and dividing it by the half-square area in which
  the curve lies.
• So, a Gini coefficient of 0 would mean perfect
  equality, and a coefficient of 1 would mean
  perfect inequality.
• Coefficients between 0.50 and 0.70 are considered
  to mean a highly unequal distribution of income.
  Coefficients between 0.20 and 0.35 are considered
  to represent relatively equitable distributions
  of income.
• Since we are dealing in percentage terms, we can
  compare Gini coefficients across countries.

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Coefficient of Variation

• Along with the Gini coefficient, the Coefficient
  of Variation satisfies all four axioms for
  inequality measures.
• The CV is simply

Standard Deviation of Income
Mean Income
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Factor Share Distribution of Income

• Rather than looking at separate individuals, this
  attempts to explain the share of national income
  received by each of the factors of production.
• It compares labours share of national income
  with that of land, financial and physical
  capital.
• With free and competitive markets for output and
  the factors of production, each factor should be
  paid according to is contribution to national
  output. However, non-market forces often
  intervene to determine the distribution of factor
  payments.

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Measuring Absolute Poverty

• Absolute Poverty the number of people living
  below the minimum level of income needed to
  satisfy basic necessities.
• International Poverty Line 1 a day or 2 a day
  in PPP dollars.

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Measures of Absolute Poverty

• Headcount Index
• Total Poverty Gap
• Human Poverty Index
• Sen-Shorrocks-Thon Index
• Foster-Greer-Thorbecke Measure (FGT)

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Axioms of Measures of Poverty

• Anonymity
• Population Independence
• Monotonicity
• Transfer/Distributional Sensitivity

The Sen index and the FGT index satisfy all four
axioms.
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Headcount Index

• N Total Population
• YP Poverty line income
• H number of people whose income falls below YP
• Headcount index is simply H/N.
• Note that in each country, a local absolute
  poverty line will need to be calculated, taking
  into account a local basket of good which would
  meet basic nutritional requirements, etc.
• The headcount index does not measure the extent
  to which the poor lie below the poverty line.
• It also fails the distributional sensitivity and
  monotonicity axioms.

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Total Poverty Gap

• Measures the total income needed to raise
  everyone who is below the poverty line to that
  line.
• Yi poor persons income
• N Population size
• H poverty headcount

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• On a per capita basis, the average poverty gap
  (APG) is simply TPG/N.
• To allow for cross-country comparisons, the
  average poverty gap can be normalized by the
  poverty line income to give the normalized
  poverty gap, which is equal to APG/YP.
• The average income shortfall (AIS) gives the
  average amount by which the income of a poor
  person falls below the poverty line. AIS TPG/H.
  Fails the transfer and monotonicity axioms.
• normalized income shortfall is simply AIS/YP

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Human Poverty Index

• Analogous to the Human Development Index, it goes
  beyond income measures and looks at human poverty
  in three areas of deprivation
• Life Expectancy
• Education
• Economic Provisioning
• A low HPI is good (smaller percentage of the
  population is deprived), and a high HPI is bad.

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Sen-Shorrocks-Thon Index

• The index is a weighted sum of the poverty gap
  ratios of the poor. The decrease with rank order
  in the income distribution so that more weight is
  given to the poverty gap of the poorer
  individuals.

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Foster-Greer-Thorbecke Measure

• A poverty measure is said to be decomposable if
  the poverty measure of a group is a weighted
  average of the poverty measures of the
  individuals in the group. An important property
  of decomposable poverty measures is that, ceteris
  paribus, a reduction in the poverty measure of a
  subgroup always decreases poverty of the
  population as a whole. The Headcount Index and
  AIS are both decomposable but fail the transfer
  and monotinicity axioms.
• The FGT indicator is decomposable and satisfies
  all four axioms

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where CVP is the coefficient of variation of
income among the poor.
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The FGT index can be decomposed additively.
Suppose that the population of size N is divided
into M subgroups that we index by g, g 1, ,M.
Let Ng denote the size of group g.
where FGTg is the FGT index for the group g.
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Generalized FGT
where represents the degree of aversion
to inequality.