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Difficulty: Very hardPoverty Estimation, Inequality Metrics, and Inclusive Growth Strategies

Match the poverty and inequality metrics listed in Column I with their corresponding conceptual definitions and key mathematical characteristics listed in Column II.

  • Palma RatioCompares the gross national income share of the richest 10%10\% of the population to aggregate income share of the poorest 40%40\%.
  • Foster-Greer-Thorbecke (FGT) Squared Poverty Gap Index (α=2\alpha = 2)Calculates poverty severity by placing exponentially higher weights on individuals residing furthest below the poverty line.
  • Sen Index of PovertyCombines head-count ratio, income shortfall ratio, and the Gini coefficient among the poor into a single composite metric.
  • Atkinson Index of InequalityMeasures normative loss of social welfare due to income distribution by incorporating an explicit inequality aversion parameter.

Answer

Palma Ratio matches with the comparison of the income share of the richest 10% to the poorest 40%; FGT Index (alpha = 2) matches with calculating poverty severity by placing higher exponential weight on individuals furthest below the poverty line; Sen Index matches with combining head-count ratio, income shortfall ratio, and Gini coefficient among the poor; and Atkinson Index matches with measuring normative social welfare loss incorporating an explicit inequality aversion parameter.
The Palma Ratio specifically contrasts the income share held by the top decile (10%) against the bottom four deciles (40%). The FGT index with parameter alpha = 2 measures poverty severity by squaring individual poverty gaps, ensuring that individuals furthest below the poverty line carry greater weight. The Sen Index addresses the shortcomings of simple headcount ratios by combining incidence, average income shortfall, and inequality among the poor (Gini coefficient of the poor). The Atkinson Index is a normative social welfare measure that evaluates potential welfare gain from redistribution, defined by a parameter reflecting societal aversion to inequality.

Step-by-Step Solution

1
Analyze Palma Ratio
Identify that Gabriel Palma observed that middle-income groups (50th-90th percentiles) capture roughly half of national income, making inequality driven by the ratio of the top 10% share to the bottom 40% share.
Establishes correct matching pair for Palma Ratio.
2
Analyze FGT Index for α=2\alpha = 2
Recognize that α=0\alpha = 0 yields Head Count Ratio, α=1\alpha = 1 yields Poverty Gap Index, and α=2\alpha = 2 squares normalized gaps to capture poverty severity.
Distinguishes incidence (α=0\alpha=0), depth (α=1\alpha=1), and severity (α=2\alpha=2) in FGT metrics.
3
Analyze Sen Index of Poverty
Recall Amartya Sen's 1976 formulation PS=H[I+(1−I)Gp]P_S = H [I + (1-I)G_p], which integrates headcount HH, income gap II, and inequality among the poor GpG_p.
Connects multi-dimensional poverty gap components to Sen's composite metric.
4
Analyze Atkinson Index
Identify Anthony Atkinson's welfare-based metric A=1−yedeμA = 1 - \frac{y_{ede}}{\mu}, where yedey_{ede} is equally distributed equivalent income determined by aversion parameter ϵ\epsilon.
Matches normative welfare loss and inequality aversion coefficient to Atkinson's metric.

Key Concept

Advanced Inequality Metrics and Composite Poverty Indices
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Topics

Poverty Estimation, Inequality Metrics, and Inclusive Growth Strategies