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Economic Inequality

Chapter 6. Economic Inequality. Preview. What is Economic Inequality? Measurement of Inequality Anonymity, Population, Relative Income, and Dalton Principles The Lorenz Curve Complete Measures: Coefficient of Variation and the Gini Coefficient. What is Economic Inequality?.

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Economic Inequality

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  1. Chapter 6 Economic Inequality

  2. Preview • What is Economic Inequality? • Measurement of Inequality • Anonymity, Population, Relative Income, and Dalton Principles • The Lorenz Curve • Complete Measures: Coefficient of Variation and the Gini Coefficient

  3. What is Economic Inequality? • Economic inequality refers to the distribution of an economic attribute, such as income or wealth, across citizens within a country or across countries themselves. • For example, how is the total income in a country distributed across its citizens? What proportion of total wealth is held by the richest? the poorest? • Economists study inequality for • intrinsic reasons (reducing inequality can be seen as an objective in itself) • functional reasons (inequality may affect other indicators of economic performance, such as growth). • The first step in understanding economic inequality is to know how to measure it.

  4. Measurement of Inequality • Suppose there are n individuals in a society, indexed by i = 1,2,3,…,n • An income distribution describes how much income is received by each individual i: • We are interested in comparing “relative inequality” between two such distributions (over time, or between regions/countries, etc.)

  5. Four Criteria for Measuring Inequality • The Anonymity Principle • Names do not matter, incomes can always be ranked without reference to who is earning it • The Population Principle • As long as the composition of income classes remain unchanged, changing the size of the population does not matter for inequality • What matters are the proportions of the population that earn different levels of income

  6. The Anonymity and Population Principles: An Illustration

  7. Four Principles (Continued) • The Relative Income Principle • Only relative income matters, and not levels of absolute income • Scaling everyone’s income by the same percentage should not affect inequality

  8. The Relative Income Principle: An Illustration

  9. Four Measures (Continued) • The Dalton Principle • If a transfer is made from a relatively poor to a relatively rich individual, inequality must increase • “Regressive” transfers (taking from poor and giving to the rich) must worsen inequality

  10. Measurement of Inequality: A Formal Summary • An inequality index is a function of the form • A higher value of this measure I(.) indicates greater inequality • The Anonymity Principle: the function I(.) is insensitive to all permutations of the income distribution among the individuals

  11. Measurement of Inequality: A Formal Summary • The Population Principle: For every distribution , • “cloning” has no effect on inequality • The Relative Income Principle: For every positive number ,

  12. Measurement of Inequality: A Formal Summary • The Dalton Principle: The function I(.) satisfies the Dalton Principle, if, for every distribution and every transfer

  13. The Lorenz Curve • The Lorenz curve illustrates how cumulative shares of income are earned by cumulatively increasing fractions of the population, arranged from the poorest to the richest. • A graphical method for measuring inequality

  14. The Lorenz Curve

  15. The Lorenz Curve: Properties • If everyone has the same income, then the Lorenz curve is the 450 line • The slope of the Lorenz curve is the contribution of the person at that point to the cumulative share of national income • The “distance” between the 450 line and the Lorenz curve indicates the amount of inequality in the society • The greater is inequality, the further will the Lorenz curve be from the 450 line

  16. Measuring Inequality using the Lorenz Curve

  17. The Lorenz Criterion • The previous graph gives us a measure of inequality called the Lorenz Criterion • An inequality measure Iis Lorenz-consistent if, for every pair of income distributions , whenever the Lorenz curve of lies to the right of

  18. Lorenz Curves for Different Countries

  19. Lorenz Curves for Different Countries

  20. Complete Measures of Inequality • Can we summarize inequality by a number? • Attractive for policymakers and researchers • When Lorenz curves cross, we cannot rank inequality across two distributions • A numerical measure of inequality helps rank distributions unambiguously

  21. Measuring Inequality • Let there be m distinct incomes, divided into j classes • In each income class j, the number of individuals earning that income is • The total population is then given by • The mean or average of the distribution is given by

  22. Measures of Inequality • Range • Kuznets Ratio • Mean Absolute Deviation • Coefficient of Variation • Gini Coefficient

  23. The Range • Difference in the incomes of the richest and the poorest individuals, divided by the mean • Very crude measure of inequality • Does not consider people between the richest and poorest on the income scale • Fails to satisfy the Dalton Principle (why?)

  24. The Kuznets Ratio • The ratio of the share of income of the richest x % to the poorest y % where x and y represent population shares • Example: share of income of the richest 10% relative to the poorest 60% • These ratios are basically “snapshots” of the Lorenz curve • Useful when detailed inequality data in not available

  25. The Mean Absolute Deviation • The sum of all income distances from average income, expressed as a fraction of total income • The idea: inequality is proportional to distance from mean income • May not satisfy the Dalton Principle, if regressive transfers are made between income classes that are all above or below the mean

  26. The Coefficient of Variation • Essentially the standard deviation(sum of squared deviations from the mean), divided by the mean • Gives greater weight to larger deviations from the mean • Lorenz-consistent (satisfies the four principles)

  27. The Gini Coefficient • Sum of the absolute differences between all pairs of incomes, normalized by (squared) population and mean income • Takes the difference between all pairs of income and sums the absolute differences • Inequality is the sum of all pair-wise comparisons of two-person inequalities • Double summation: first sum over all k’s, holding each j constant. Then, sum over all the j’s. • Most commonly used measure of inequality

  28. The Gini Coefficient (continued) • Satisfies all four principles: Lorenz-consistent

  29. Which Measure is More Appropriate?

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