Different Concepts of Welfare Indices and complete orderings

Different Concepts of Welfare: Indices and complete orderings Inequality, Poverty, Polarization measurement

Inequality • At the heart of the Pigou-Dalton Principle, its very essence is interpersonal comparison, if you’ve got more than me we’re unequal. • How to measure it? • Relative or absolute? • What particular features (groups).

Measures of Inequality: Relative Range, Relative Mean Deviation and Variance.

Coef of Var C, Log St. Dev. L, Gini G, Theil’s Entropy T, Shutz Coef S

Poverty Measurement: The Axioms

Further Poverty Measure Axioms

Absolute Poverty Measures

More Absolute Poverty Measures

Relative Poverty Measures • Rather than think about an absolute poverty cutoff “z” we may substitute some other measure which is “relative” to the population of interest (e. g. some function of median income in the population). • Can insert this formulation of the cut-off in all of the preceding formulae. • Presents difficulties with inter-temporal comparisons. • Presents difficulties with inferences.

A Digression: The LICO and other sample dependent measures • Canadian Council on Social Development (1992) claimed that 1. 1 million children were living below the poverty line. • LICO “Low Income Cut Off” = income level below which a household unit will spend on average at least 56. 2% on food, shelter and clothing. • Cut off changes over time with tastes, prices etc. • Problem if the income elasticity around the poverty cut off is greater than one.

Overall Income Elasticities

Income Elasticities by Income Quantile

Polarization

Polarization Measurement: The Axioms

Polarization: The Measures

Other Polarization and Alienation Measures. • Focusing on just two groups or clubs Alienation measures such as the Gini based pooled mean normalized difference in subgroup means, and the distributional overlap measure are candidates for distributional overlap (Anderson (2006)). • Recently a new measure, the Bipolar Trapezoid, particularly useful in multi-dimensional environments has been developed (Anderson (2008).

AGINI

An Overlap Measure.

The Trapezoidal Measure

The Trapezoid measure (details)