Decomposition of Inequality with Special Reference to Spatial Inequality

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Decomposition of Inequality with Special
Reference to Spatial Inequality Anthony
Shorrocks, UNU-WIDER Italy, July 2007
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• Inequality, poverty, living standard comparisons
  involve
• conceptual issues meaning of inequality,
  poverty etc
• ? comparability issues how to compare
  households with different
• resources (eg income)
• household characteristics (eg family size)
• environment (eg climate, prices)
• ? aggregation issues
• construction of measures of inequality, poverty
  etc,
• use in analysing distributional questions

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Exercise Provide an inequality ranking of the
following income distributions A (1, 5, 6) B
(5, 6, 1) C (2, 4, 6) D (4, 8, 12) E (2,
3, 7) F (0, 0, 12) G (0, 0, 0, 0, 12, 12)
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Inequality Indices
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Inequality Indices

• All these indices satisfy
• ? symmetry
• ? replication invariance
• ? scale invariance
• Pigou-Dalton principle of transfers
• normalisation (zero if complete equality)
• hence members of set of Lorenz consistent indices

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• What to do with multiplicity of indices?
• rely on unanimity orderings (eg Lorenz
  Dominance)
• narrow down choice of indices using additional
  criteria
• simple interpretation (Gini, Atkinson)
• strengthened Pigou-Dalton condition transfer
  sensitivity
• (Entropy, Atkinson)
• explicit link with social welfare functions
  (Atkinson)
• decomposability/subgroup consistency (Entropy)

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Inequality Decomposition by Population Subgroups I
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Inequality Decomposition by Population
Subgroups IIIGeneral Formulation
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Inequality Decomposition by Population Subgroups
IV
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Inequality Decomposition by Population Subgroups V
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Inequality Decomposition by Income Components
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Kanbur-Zhang China 1983-95
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Kanbur-Zhang China 1983-95
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Kanbur-Zhang China 1983-95
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Kanbur-Zhang China 1983-95
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Kanbur-Zhang China 1983-95
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Shorrocks-Wan
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Shorrocks-Wan
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Shorrocks-Wan
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Shorrocks-Wan
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Shorrocks-Wan
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Extensions to Inequality Decompositions

• dynamic decompositions
• (subgroup) decomposable poverty indices
• growth-redistribution decomposition of poverty
  change
• price-quantity decompositions of value change
• simulation approaches
• But problems
• some decompositions restrict choice of inequality
  index
• multivariate decompositions?
• cannot mix subgroup and source decompositions
• contributions may not sum to unity (eg
  price-quantity)

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General Structure

• Formal similarities with
• (1) Cooperative Game theory
• how to share surplus or cost amongst
  agents
• (2) Econometrics
• how to assess importance of contributory
  variables

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Shapley value

• Properties
• (1) symmetric (anonymous)
• (2) exact decomposition
• (3) marginalist
• (4) not aggregation consistent when factors are
  grouped

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Regional Poverty Rates in Russia
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Growth and Redistribution Effects on Poverty
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Growth and Redistribution Effects on Poverty
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Growth and Redistribution Effects on Poverty
(cont)
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Shapley Decomposition
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Kolenikov-Shorrocks II
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Kolenikov-Shorrocks III
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Kolenikov-Shorrocks IV
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Kolenikov-Shorrocks V
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Inequality Decomposition by Subgroups
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Inequality Decomposition by Subgroups (cont)