Poverty and Inequality

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Poverty and Inequality

• Prepared for WBI/DFID Workshop on Poverty Analysis

London, November 6-8, 2006
Jonathan Haughton Suffolk University,
Boston jonathan.haughton_at_suffolk.edu
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Basics

• Given information on
• Welfare measure
• Poverty line
• Issue is how to summarize.
• Note Measures should be based on individuals,
  but are sometimes erroneously based on
  households.
• VLSS 1998, poor
• 37 of individuals
• 32 of households
• 29 of those surveyed

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Headcount index (P0)

• The proportion of the population in poverty.
• Pro
• Simple to construct
• Easy to understand
• Con
• Ignores intensity of poverty (see table)
• Violates transfer principle
• Discontinuity unlikely (see histogram/density)

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Vietnam, 1998
Helps understand why P0 fell so fast in Vietnam.
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Poverty Gap Index (P1)

• Min cost of eliminating poverty is Gi
• Max cost of eliminating poverty is z
• P1 is the ratio of these two, so reflects
  potential efficiency of targeting.

Most would argue B has worse poverty.
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Squared Poverty Gap and FGT

• But
• Less intuitive
• What a?
• It sometimes matters (but how much?)

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Sen, and SST
Sen
Sen Shorrocks Thon
G is Gini for poverty gap ratio

• Not very intuitive. But decomposable into
  sources of change in poverty
• Note bootstrapped confidence intervals.
• Pick sample with replacement compute redo many
  times. Gives distribution of statistic.

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Watts Time to Exit
Q individuals below poverty line
Cambodia. Average exit time

• Focus axiom. No change if income of non-poor
  changes.
• Monotonicity. Any income gain to poor should
  reduce poverty.
• Transfer axiom. Inequality-reducing transfers
  among the poor should reduce poverty.

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Inequality

• Defined over entire population
• Independent of mean
• Common to find
• Quintiles
• Deciles
• Decile dispersion ratio
• Histogram/kernel density is useful too, but not a
  summary boxplots helpful

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Gini coefficient

• Lorenz curve
• Gini A/(AB)
• Min 0, max 1, bigger number is more inequality
• Typically 0.25-0.60 for income or expenditure per
  capita

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Fitting Lorenz curve

• Measuring world poverty
• Often only have quintile data. So
• Fit Lorenz curve
• Apply dollar-a-day line
• Compute headcount poverty rate.
• General quadratic works well enough.

Gaurav Datt Computational Tools for Poverty
Measurement and Analysis. IFPRI. 1998.
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Gini evaluated

• Pro
• Widely understood
• Axioms
• Mean independence
• Population size independence
• Symmetry
• Pigou-Dalton transfer sensitivity
• But
• Axioms
• Decomposability (e.g. by pop. groups) awkward
• Statistical testability. Easiest using bootstrap.

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Generalized Entropy
Theils T
Theils L Mean log deviation
Atkinson
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Measures compared

• Not much difference in ranking using these
  measures

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Decomposability
Subgroups j
Fairly typical result
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These may help steer policy