Presentation on theme: "Income Inequality: Measures, Estimates and Policy Illustrations"— Presentation transcript:
1 Income Inequality: Measures, Estimates and Policy Illustrations
2 Focus of the Discussion: Framework: Kuznets’: explain inequality in terms of inter-sectoral disparities & intra-sectoral inequalitiesFinal outcome measures:Income generation:Sectoral perspective at the macro as well as disaggregate regional (district) levelIncome distributionProxy: consumption distribution - macro (state), regional and district levels by rural/urban sectors
3 Inequality Measures & Welfare Judgments Inequality measures have implicit normative judgments about inequality and the relative importance to be assigned to different parts of the income distribution.Some measures are clearly unattractive:Range: measures the distance between the poorest and richest; is y unaffected by changes in the distribution of income between these two extremes.
4 Simpler (statistical) measures (normalised) RangeRelative mean deviation(Shows percentage of total income that would need to be transferred to make all incomes are the same.)Coefficient of variation = standard deviation/mean75-25 gap, gap
5 Inequality measurement: Some attractive axioms Pigou-Dalton Condition (principle of transfers): a transfer from a poorer person to a richer person, ceteris paribus, must cause an increase in inequality.Range does not satisfy this property.Scale-neutrality: Inequality should remain invariant with respect to scalar transformation of incomes.Variance does not satisfy this is property.Anonymity: Inequality measure should remain invariant with respect to any permutation.
6 Gini coeficientGini coeficient: The proportion of the total area under the Lorenz curve.Discrete version:Interpretation: Gini of “X” means that the expected difference in income btw. 2 randomly selected persons is 60% of overall mean income.Restrictive:-- The welfare impact of a transfer of income only depends on “relative rankings” – e.g., a transfer from the richest to the billionth richest household counts as much as one from the billionth poorest to the poorest.
7 The Atkinson class of inequality measures Atkinson (1970) introduces the notion of ‘equally distributed equivalent’ income, YEDE.YEDE represents the level of income per head which, if equally shared, would generate the same level of social welfare as the observed distribution.A measure of inequality is given by:IA = 1- (YEDE/μ)
8 The Atkinson class of inequality measures A low value of YEDE relative to μ implies that if incomes were equally distributed the same level of social welfare could be achieved with much lower average income.; IA would be large.Everything hinges on the degree of inequality aversion in the social welfare function.With no aversion, there is no welfare gain from edistribution so YEDE is equal to μ and IA = 0.
9 The Atkinson class of inequality measures Atkinson proposes the following form for his inequality measure:
10 Atkinson’s measureThis is just an iso-elastic social welfare function defined over income (not utility) with parameter e, normalised by average income
11 The Atkinson class of inequality measures A key role here is played by the distributional parameter ε. In calculating IA you need to explicitly specify a value for ε.When ε=0 there is no social concern about inequality and so IA = 0 (even if the distribution is “objectively” unequal).When ε=∞ there is infinite weight to the poorer members of the population (“Rawls”)
12 Inequality measurement and normative judgements Coefficient of variation:Attaches equal weights to all income levelsNo less arbitrary than other judgments.Standard deviation of logarithms:Is more sensitive to transfers in the lower income brackets.Bottom line: The degree of inequality cannot in general be measured without introducing social judgments.
13 Theil’s Entropy IndexFormally, an index I(Y) is Theil decomposable if:Where Yi is a the vector of incomes of the Hi members of subgroup i, there are N subgroups, and mieHi is an Hi long vector of the average income (mi) in subgroup i. The terms wi terms are subgroup weights.Theil’s Entropy Index:
14 RecommendationsNo inequality measure is purely ‘statistical’: each embodies judgements about inequality at different points on the income scale.To explore the robustness of conclusions:Option 1: measure inequality using a variety of inequality measures (not just Gini).Option 2: employ the Atkinson measure with multiple values of ε.Option 3: look directly at Lorenz Curves, apply Stochastic Dominance results.
15 The Lorenz Curve To compare inequality in two distributions: Plot the % share of total income received by the poorest nth percentile population in the population, in turn for each n and each consumption distribution.The greater the area between the Lorenz curve and the hypotenuse the greater is inequality.Second Order Stochastic Dominance (Atkinson 1970):If Lorenz curves for two distributions do not intersect, then they can be ranked irrespective of which measure of inequality is the focus of attention.If the Lorenz curves intersect, different summary measures of inequality can be found that will rank the distributions differently.
16 Inequality MeasuresShortcomings of GDP can be addressed in part by considering inequalityCommon measures of inequalityDistribution of Y by Decile or Quintile
17 Income Distribution by Decile Group: Mexico, 1992
18 Inequality MeasuresShortcomings of GDP can be addressed in part by considering inequalityCommon measures of inequalityDistribution of Y by Decile or QuintileGini Coefficientmost commonly used summary statistic for inequality
19 Gini Coefficient 100 Lorenz Curve 100 Cumulative Income Share 100Cumulative Population Share (poorest to riches)
20 Gini Coefficient 100 Lorenz Curve 1 Lorenz Curve 2 100 Cumulative Income Share100Cumulative Population Share
21 Gini Coefficient Gini = A / A + B A B 100 Lorenz Curve 100 Cumulative Income ShareGini = A / A + BAB100Cumulative Population Share
22 Gini Coefficient Gini varies from 0 - 1 Higher Ginis represent higher inequalityThe Gini is only a summary statistic, it doesn’t tell us what is happening over the whole distribution
23 Inequality MeasuresShortcomings of GDP can be addressed in part by considering inequalityCommon measures of inequalityDistribution of Y by Decile or QuintileGini Coefficientmost commonly used summary statistic for inequalityFunctional distribution of income
24 Inequality: Policy Instrument Illustrate How Policy Strategies are made Little Realizing that the Very Framework used does not permit such an ApproachIllustrate How Wrong Inferences are drawn on Empirical Estimates of Inequality, which finally form the basis for theoretically implausible Strategies for Poverty Reduction
25 DOES SPECIFICATION MATTER? CHOICE OF STRATEGIESESIMATES OF MAGNITUDESEVALUATION OF POLICY CONSEQUENCESILLUSTRATED WITH REFERENCE TO THE INDIAN EXPERIENCE ON POLICIES FOR POVERTY REDUCTION, ESTIMATES & EVALUATION
26 CHOICE OF DEVT STRATEGIES GROWTH WITH REDISTRIBUTIONFORMULATED AND PURSUED INDEPENDENTLYBASED ON THE PREMISES OF SEPARABILITY AND INDEPENDENCEEXAMPLES: FIFTH & SIXTH FIVE YEAR PLANS
27 INDIAN SIXTH PLAN STRATEGY RURAL INDIA:BASE YEAR (BY):BY POVERTY %TERMINAL YEAR (TY):REDUE TY POVERTY TO % BY GROTH (15.44 %)FURTHER DOWN TO 30 % BY REDISTRIBUTION (BY REDUCING INEQUALITY FROM TO 0.222)
28 INDIAN SIXTH PLAN STRATEGY URBAN INDIA:BASE YEAR (BY):BY POVERTY %TERMINAL YEAR (TY):REDUE TY POVERTY TO % BY GROTH (11.32 %)FURTHER DOWN TO 30 % BY REDISTRIBUTION (BY REDUCING INEQUALITY FROM TO 0.305)
29 Growth with Redistribution Base YearTerminal Year:HCR (%)Growth (%)Inequality change (%)Rural India50.715.440.5-27.430Urban India40.311.333.7-8.8
30 HOW VALID ARE THE PREMISES? THE STRATEGIES ARE NEITHER SEPARABLE NOR INDEPENDENTGROWTH WILL REDUCE POVERTYAT AN INCREASING RATE IF HCR < 50%AT A DECREASING RATE IF HCR > 50%MAXIMUM IF HCR = 50%
34 GROWTH vs. REDISTRIBUTION GROWTH ALWAYS REDUCES POVERTYPACE OF REDUCION VARIES BETWEEN LEVELS OF DEVT.REDISTRIBUTION REDUCES POVERTY ONLY WHEN THE SIZE OF THE CAKE ITSELF IS LARGE ENOUGH & POVERTY < 50%
35 What are the Bases for Indian Devt. Strategy? GROWTH & REDUCTION IN INEQUALITYINEQUALITY, AS MEASURED BY LORENZ RATIO, DECLINED AT THE RATE OF 0.38 % PER ANNUM IN RURAL INDIA DURING ANDINEQUALITY DECLINED AT THE RATE OF 0.59% PER ANNUM IN URBAN INDIA DURING THE SAME PERIOD
38 How Valid are the Estimates? ESTIMATES ARE BASED ON THE NATIONAL SAMPLE SURVEY (NSS) DATA ON CONSUMER EXPENDITURENSS DATA ARE AVAILABLE ONLY IN GROUP FORM, THAT IS, IN THE FORM OF SIZE DISTRIBUTION OF POPULATION ACROSS MONTHLY EXPENDITURE CLASSESLORENZ RATIOS ARE ESTIMATED USING THE TRAPEZOIDAL RULE
40 Limitations: UNDERESTIMATES THE CONVEXITY OF THE LORENZ CURVE; IN OTHER WORDS, IGNORES INEQUALITY WITHIN EACH EXPENDITURE CLASHENCE, UNDERESTIMATES THE EXTENT OF INEQUALITYTHE EXTENT OF UNDERESTIMATION INCREASES WITH THE WIDTH OF THE CLAS INTERVAL