Income Inequality: Measures, Estimates and Policy Illustrations

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 inequalities • Final outcome measures: • Income generation: • Sectoral perspective at the macro as well as disaggregate regional (district) level • Income distribution • Proxy: 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) Range • Relative 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/mean • 75-25 gap, 90-10 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 coeficient • Gini 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 measure • This 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 levels • No 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 Index Formally, 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. Recommendations • No 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 Measures • Shortcomings of GDP can be addressed in part by considering inequality • Common measures of inequality • Distribution of Y by Decile or Quintile

17. Income Distribution by Decile Group: Mexico, 1992

18. Inequality Measures • Shortcomings of GDP can be addressed in part by considering inequality • Common measures of inequality • Distribution of Y by Decile or Quintile • Gini Coefficient • most commonly used summary statistic for inequality

19. Gini Coefficient 100 Lorenz Curve Cumulative Income Share 0 100 Cumulative Population Share (poorest to riches)

20. Gini Coefficient 100 Lorenz Curve 1 Lorenz Curve 2 Cumulative Income Share 0 100 Cumulative Population Share

21. Gini Coefficient 100 Lorenz Curve Cumulative Income Share Gini = A / A + B A B 0 100 Cumulative Population Share

22. Gini Coefficient • Gini varies from 0 - 1 • Higher Ginis represent higher inequality • The Gini is only a summary statistic, it doesn’t tell us what is happening over the whole distribution

23. Inequality Measures • Shortcomings of GDP can be addressed in part by considering inequality • Common measures of inequality • Distribution of Y by Decile or Quintile • Gini Coefficient • most commonly used summary statistic for inequality • Functional 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 Approach • Illustrate 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 STRATEGIES • ESIMATES OF MAGNITUDES • EVALUATION OF POLICY CONSEQUENCES • ILLUSTRATED WITH REFERENCE TO THE INDIAN EXPERIENCE ON POLICIES FOR POVERTY REDUCTION, ESTIMATES & EVALUATION

26. CHOICE OF DEVT STRATEGIES • GROWTH WITH REDISTRIBUTION • FORMULATED AND PURSUED INDEPENDENTLY • BASED ON THE PREMISES OF SEPARABILITY AND INDEPENDENCE • EXAMPLES: FIFTH & SIXTH FIVE YEAR PLANS

27. INDIAN SIXTH PLAN STRATEGY • RURAL INDIA: • BASE YEAR (BY): 1979-80 • BY POVERTY 50.70 % • TERMINAL YEAR (TY): 1984-85 • REDUE TY POVERTY TO 40.47 % BY GROTH (15.44 %) • FURTHER DOWN TO 30 % BY REDISTRIBUTION (BY REDUCING INEQUALITY FROM 0.305 TO 0.222)

28. INDIAN SIXTH PLAN STRATEGY • URBAN INDIA: • BASE YEAR (BY): 1979-80 • BY POVERTY 40.31 % • TERMINAL YEAR (TY): 1984-85 • REDUE TY POVERTY TO 33.71 % BY GROTH (11.32 %) • FURTHER DOWN TO 30 % BY REDISTRIBUTION (BY REDUCING INEQUALITY FROM 0.335 TO 0.305)

29. Growth with Redistribution

30. HOW VALID ARE THE PREMISES? • THE STRATEGIES ARE NEITHER SEPARABLE NOR INDEPENDENT • GROWTH WILL REDUCE POVERTY • AT AN INCREASING RATE IF HCR < 50% • AT A DECREASING RATE IF HCR > 50% • MAXIMUM IF HCR = 50%

31. RELATION BETWEEN GROWTH & POVERTY P* 1/2 ln x* 

32. AN INCREASE IN INEQUALITY WILL: • INCREASE POVERTY AT A DECREASING RATE IF HCR < 50% • DECREASE POVERTY AT AN INCREASING RATE IF HCR > 50% • NEUTRAL WHEN HCR = 50%

33. 1 For ln x* >  P* 1/2 For ln x* <  0 RELATION BETWEEN INEQUALITY & POVERTY

34. GROWTH vs. REDISTRIBUTION • GROWTH ALWAYS REDUCES POVERTY • PACE 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 INEQUALITY • INEQUALITY, AS MEASURED BY LORENZ RATIO, DECLINED AT THE RATE OF 0.38 % PER ANNUM IN RURAL INDIA DURING 1960-61 AND 1977-78 • INEQUALITY 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 EXPENDITURE • NSS DATA ARE AVAILABLE ONLY IN GROUP FORM, THAT IS, IN THE FORM OF SIZE DISTRIBUTION OF POPULATION ACROSS MONTHLY EXPENDITURE CLASSES • LORENZ RATIOS ARE ESTIMATED USING THE TRAPEZOIDAL RULE

39. Lorenz Ratio

40. Limitations: • UNDERESTIMATES THE CONVEXITY OF THE LORENZ CURVE; • IN OTHER WORDS, IGNORES INEQUALITY WITHIN EACH EXPENDITURE CLAS • HENCE, UNDERESTIMATES THE EXTENT OF INEQUALITY • THE EXTENT OF UNDERESTIMATION INCREASES WITH THE WIDTH OF THE CLAS INTERVAL

43. Lorenz Curve: Indian Metros 1961/62 (current unadjusted)

44. Lorenz Curve: Indian Metros 1970/71 (Current unadjusted)