- 1 - 9/18/08 PP253/ARE253 Alain de Janvry & Elisabeth Sadoulet Fall 2008 Handout #3 - Inequality Positive analysis: Indicators and determinants By contrast to measurement of poverty, an inequality measure does not require specification of a poverty line. On the other hand, it requires information on all incomes, not just income of the poor. 1. Describing and measuring inequality 1.1. Describing inequality: Graphic representation of inequality with the Lorenz curve (Figure 1) Objective: Represent inequality in income, consumption, wealth, and/or landholdings. Figure 1. Lorenz curves If two Lorenz curves cross, inequality comparisons require additional criteria. 1.2. Measuring inequality: alternative indicators Desirable properties of inequality indicators (Dalton): - Anonymity principle: Permutations of people should not affect the inequality measure. - Dalton transfer principle: A transfer from a richer to a poorer person should reduce inequality. - Population principle: The inequality index should be unaffected by population size. - Relative income principle: Index should be unaffected by changes in absolute income levels, only by relative incomes. An inequality index is said to be Lorenz-consistent if it satisfies these four properties. Define: n = number of persons in the population ri = income rank of household i, 1 ! ri! n yi = income of household i µ = average income. σ = standard deviation of income. Y = total income of the population. For group data: k = 1, ..., m groups nk = number of households in group k. µk = average income in group k. • Coefficient of variation: C V =!µ. CV index is Lorenz-consistent. • Gini coefficient: G =AA + B=2nµcov(y , r ). Gini index is Lorenz-consistent. • Theil entropy index: T =yiYi =1n!lnyi/ Y1 / n" # $ % & ' Limits: equality = 0 ! T ! ln n = maximum inequality. Does not satisfy the population principle. • Income shares and Kuznets ratios Income shares: Share of income of the poorest 20% (say) in total income. Kuznets ratios: Ratio of income of richest 20% (say) to poorest 40% (say) Does not satisfy the transfer principle. Two useful properties of indicators are: - Decomposable in between and within sub-populations inequality (regions, socio-economic groups). Gini is not decomposable, Theil and CV are decomposable - Possibility to compute the index, even with some negative income yi. Possible with Gini, and CV, not with Theil. 2. Decomposition of the Gini coefficient by sources of income G =2nµcov y,r( )=µiµi!2nµicov yi, ri( )" # $ % & ' cov yi, r( )cov yi,ri( )= wiGiRi wii!GiGRi= wii!gi= 1 wi = share of source i in average income, Gi = Gini coefficient of income source i, Ri = correlation of income source to overall inequality relative to correlation of income source to within source inequality, gi = relative concentration coefficient If gi > 1, i-th source increases inequality; If gi < 1, i-th source decreases inequality. wigi = share of total inequality contributed by income source i. Comments on decomposition of GINI for Egypt by sources of income (Table 1): - Role of wi: Agricultural is the most important source of income. - Role of gi: Remittances (gi > 1) contribute to increase total inequality; non-agriculture (gi < 1) contributes to reduce total inequality; agriculture is about neutral (gi near 1). - Role of Gi: Remittances have the highest source Gini (as few households get them, and they are very large). - Role of Ri: Remittance income is highly correlated to total inequality, increasing inequality. Conclusion: - Agriculture makes the highest contribution to inequality (60.9%, measured by wi gi) due to its high income share (wi). Remittances contributes 27.3% of total inequality in spite of its low income share because it has a large Gini (Gi) and a high correlation with overall income inequality (Ri).- 2 - 9/18/08 Example: Decomposition of inequality measures, Egypt, 1986-87Sources of incomeAgricultureNon AgricultureRemittancesTotalWeight of income sourcewi = µi/µ0.578 0.326 0.096 1.000Decomposition of coefficient of variationOverall CV CV 0.392Corr(yi, y) * CV of income source!i CVi0.267 0.335 1.340Relative concentration coefficients CVci = !i CVi/CV0.681 0.855 3.418Decomposition of CV wi ci0.393 0.279 0.328 1.000Decomposition of Gini coefficientGini of income source Gi0.509 0.675 0.932Ratio of correlationsRi0.626 0.161 0.924Overall Gini G 0.302Relative concentration coefficients Gini gi = Ri Gi/G 1.054 0.359 2.848Decomposition of Gini wi gi0.609 0.117 0.273 1.000Source: R. Adams, IFPRI Research Report No. 86, 1991. 3. Relationship between level of income (GNPpc) and inequality: Empirical evidence on the Kuznets curve (inverted-U). Kuznets hypothesis: Inverted U curve between Gini and GDPpc. If true, inevitable rise in inequality at low levels of income. Need reach critical level of GDPpc for inequality to fall with income. Policy implication: growth will take care of inequality Gini LA SE Asia China Africa OECD South Asia $4,000 GDPpc Does it hold? Cross section data: In general yes due to Latin America effect at middle income level. But does not imply causality: Africa will not become Latin America; LA will not become SE Asia! Time series data by country: In general rejected. hence, cannot simply wait for income growth to reduce inequality. Need special policy interventions if want to reduce inequality. Policy implication If holds: Growth takes care of inequality If does not hold: Need special policy interventions to reduce inequality. 4. Role of GDPpc growth on inequality - Growth is neutral on inequality: Dollar and Kraay (2000); Deininger and Squire. Elasticity of income of poor with respect to aggregate income = 1. Is this pro-poor growth? - de Janvry and Sadoulet (1999) for Latin America: growth does not reduce inequality, but recession increases inequality creating a ratchet effect. Hence, importance of “socially responsible macroeconomics” to avoid the social costs of instability (Lustig and Kanbur). Gini Growth 1990s (open economy) Recession 1980s Growth 60s, 70s (ISI) GDPpc 5. Role of inequality on growth: six causal channels i) Good for growth if inequality increases the aggregate rate of
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