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Lecture 2: Stochastic Dominance, Inequality Decompositions and Inequality of Opportunity

Lecture 2: Stochastic Dominance, Inequality Decompositions and Inequality of Opportunity. Francisco H. G. Ferreira Poverty and Inequality Analysis Course 2011 Module 5: Inequality and Pro-Poor Growth. Outline. Stochastic Dominance and Rank Robustness

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Lecture 2: Stochastic Dominance, Inequality Decompositions and Inequality of Opportunity

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  1. Lecture 2: Stochastic Dominance, Inequality Decompositions and Inequality of Opportunity Francisco H. G. Ferreira Poverty and Inequality Analysis Course 2011 Module 5: Inequality and Pro-Poor Growth

  2. Outline • Stochastic Dominance and Rank Robustness • The Determinants of Inequality: a conceptual overview • Inequality Decompositions • By Population Subgroup • The Classic Decomposition • The ELMO modification • By Income Source • Generalizing Oaxaca-Blinder • An application: Measuring inequality of opportunity

  3. Stochastic Dominance and Rank Robustness • Welfare: First or Second Order Stochastic Dominance • Poverty: Mixed Poverty Dominance • Inequality: Lorenz Dominance

  4. 2. The Determinants of Inequality: A conceptual overview • Inequality measures dispersion in a distribution. Its determinants are thus the determinants of that distribution. In a market economy, that’s nothing short of the full general equilibrium of that economy. • One could think schematically in terms of: y = a.r • This suggests a scheme based on assets and returns: • Asset accumulation • Asset allocation / Use • Determination of returns • Demographics • Redistribution

  5. 2. The Determinants of Inequality: A conceptual overview

  6. 2. The Determinants of Inequality: A conceptual overview • Modeling these processes in an empirically testable way is quite challenging. • Though there are G.E. models of wealth and income distribution dynamics • Historically, empirical researchers have used ‘shortcuts’, such as: • decomposing inequality measures by population subgroups, and attributing “explanatory power” to those variables which had large “between” components; • Decomposing inequality by income sources, to understand which contributed most to inequality, and why; • Decomposing changes in inequality into changes in group composition, group mean and group inequality.

  7. 3. Inequality Decompositions: Population subgroups • The significance of group differences in well-being is thus often at the center of the study of inequality. • Techniques for the decomposition of inequality into a “between-group” and a “within-group” component have become a workhorse in the inequality literature. • Much of the methodological development occurred in the 1970s and early 1980s: • Bourguignon (1979), Cowell (1980), Shorrocks (1980) proposed a class of sub-group decomposable inequality measures • Pyatt (1975), Yitsaki (various) have explored the decomposability of the Gini coefficient.

  8. 3. Inequality Decompositions: Population subgroups Not all inequality measures are decomposable, in the sense that I = IW + IB. The Generalized Entropy class is. Examples include Theil – L Theil – T 0.5 CV2

  9. 3. Inequality Decompositions: Population subgroups Let Π (k) be a partition of the population into k subgroups, indexed by j. Similarly index means, n, and subgroup inequality measures. Then if we define: where Then, E = EB + EW.

  10. 3. Inequality Decompositions: Population subgroups • Given a partition and functional we can summarize between-group inequality as: • Moving from any partition to a finer sub-partition cannot decrease.

  11. An Example from Brazil Source: Ferreira, Leite and Litchfield, 2008

  12. Two concerns • Concern #1: Between-group shares in practical applications are usually quite small: • Anand (1983) decomposes Malaysian inequality and finds a between-ethnic group contribution of only about 15% • Cowell and Jenkins (1995) decompose U.S. inequality by groups defined in terms of age, sex, race and earner status of the household head, and finds that most inequality remains “unexplained” • Elbers, Lanjouw, and Lanjouw (2003) use poverty maps to show that between-community inequality (across many hundreds of communities) is still vastly outweighed by within-community inequality.

  13. Two Concerns • Such findings have left some observers worried: • Kanbur (2000) states that the use of such decompositions “…assists the easy slide into a neglect of inter-group inequality in the current literature” • He argues that social stability and racial harmony can (and does) break down once the average differences between groups go beyond a certain threshold. • Concern #2: It is difficult to compare decompositions across settings • Over time • Across settings

  14. Concern 2, cont. An example from three countries • The shares of income inequality attributable to differences between racial groups in Brazil, and South Africa are 16%, and 38%, respectively. In the U.S. the between-race inequality share is only 8% • In each country, the mean income of the non-white groups is much below that of the white group, but the non-white groups form the majority in South Africa (80%), half of the population in Brazil (50%), and a minority in the U.S. (28%). • The standard decomposition, is sensitive to differences in relative mean incomes across groups, but also to the numbers of groups, their population shares, and their “internal” inequality. Does it capture the “salience” of horizontal inequality as we might wish?

  15. 3. Inequality Decompositions:The ELMO Modification • Elbers, Lanjouw, Mistiaen, and Ozler (2007) propose comparing IB against a benchmark of maximum between-group inequality holding the number and relative sizes of groups constant: J groups in partition of size j(n).

  16. Properties • cannot be smaller than • However, may not rise with finer sub-partitioning. • for both the numerator and denominator change as a result of finer partitioning. • For any finer partitioning of an original partition, the rate of change of is lower than or equal to that of .

  17. Calculating • We calculate in the usual way. • Maximum between-group inequality: • For a maximum, groups must occupy non-overlapping intervals (Shorrocks and Wan, 2004). • In the case of n sub-groups in the partition we take a particular permutation of sub-groups {g(1),….g(n)} allocate lowest incomes to g(1), then to g(2), etc. • Calculate the corresponding between group inequality. • Repeat this for all n! permutations of sub-groups. • Select the highest resulting between-group inequality. • Calculate the ratio of the two

  18. An example (ELMO, 2007)

  19. 3. Inequality Decompositions:By income sources • Shorrocks A.F. (1982): “Inequality Decomposition by Factor Components, Econometrica, 50, pp.193-211. • Noted that could be written as: Correlation of income source with total income Share of income source Internal inequality of the source

  20. 3. Inequality Decompositions:By income sources Source: Ferreira, Leite and Litchfield, 2008.

  21. 3. Inequality Decompositions:Dynamics for scalar measures Mookherjee, D. and A. Shorrocks (1982): "A Decomposition Analysis of the Trend in UK Income Inequality", Economic Journal, 92, pp.886-902. Pure inequality Group Size Relative means

  22. The (obligatory) example from Brazil… Source: Ferreira, Leite and Litchfield, 2008.

  23. 3. Inequality Decompositions: Dynamics for the whole distribution • In practice, decompositions of changes in scalar measures suffer from serious shortcomings: • Informationally inefficient, as information on entire distribution is “collapsed” into single number. • Decompositions do not ‘control’ for one another. • Can not separate asset redistribution from changes in returns. • With increasing data availability and computational power, studies that decompose entire distributions have become more common. • Juhn, Murphy and Pierce, JPE 1993 • DiNardo, Fortin and Lemieux, Econometrica, 1996

  24. 3. Inequality Decompositions: The Oaxaca-Blinder Decomposition • These approaches draw on the standard Oaxaca-Blinder Decompositions (Oaxaca, 1973; Blinder, 1973) • Let there be two groups denoted by r = w, b. • Then and • So that • Or: • Caveats: (i) means only; (ii) path-dependence; (iii) statistical decomposition; not suitable for GE interpretation. “returns component” “characteristics component”

  25. 3. Inequality Decompositions: Juhn, Murphy and Pierce (1993) where Define: Then: Returns component Unobserved charac. component Observed charac. Component.

  26. 3. Inequality Decompositions: Bourguignon, Ferreira and Lustig (2005)

  27. 3. Inequality Decompositions: Bourguignon, Ferreira and Lustig (2005)

  28. 3. Inequality Decompositions: Bourguignon, Ferreira and Lustig (2005)

  29. 4. Measuring Inequality of opportunity motivation • Amartya Sen’s Tanner Lectures (1980) question: “Equality of what?” • Modern theories of social justice want to move beyond the distribution-neutral, sum-based approach of utilitarianism. • Desire to place some value on “equality”. • But are outcomes, such as incomes, the appropriate space? • What role for individual effort and responsibility? • Are all inequalities unjust? “We know that equality of individual ability has never existed and never will, but we do insist that equality of opportunity still must be sought” (Franklin D. Roosevelt, second inaugural address.)

  30. 4. Measuring Inequality of opportunity motivation • Equality of opportunity is a normatively appealing concept. Many philosophers (and politicians) increasingly see it as the appropriate “currency of egalitarian justice”. • Dworkin (1981): What is Equality? Part 1: Equality of Welfare; Part 2: Equality of Resources”, Philos. Public Affairs, 10, pp.185-246; 283-345. • Arneson (1989): “Equality of Opportunity for Welfare”, Philosophical Studies, 56, pp.77-93. • Cohen (1989): “On the Currency of Egalitarian Justice”, Ethics, 99, pp.906-944. • Roemer (1998): Equality of Opportunity, (Cambridge, MA: Harvard University Press) • Sen (1985): Commodities and Capabilities, (Amsterdam: North Holland)

  31. 4. Measuring Inequality of opportunity motivation • Economists have also become interested. Van de Gaer (1993) and John Roemer (1993, 1998) suggested an influential definition, based on the distinction between “circumstances” and“efforts” among the determinants of individual advantage. • Circumstances are morally-irrelevant, pre-determined factors over which individuals have no control. • Equality of opportunity is attained when advantage is distributed independently of circumstances. “According to the opportunity egalitarian ethics, economic inequalities due to factors beyond the individual responsibility are inequitable and [should] be compensated by society, whereas inequalities due to personal responsibility are equitable, and not to be compensated” (Peragine, 2004, p.11)

  32. 4. Measuring Inequality of opportunity Dominance Approach • Roemer’s definition of equality of opportunity: “Leveling the playing field means guaranteeing that those who apply equal degrees of effort end up with equal achievement, regardless of their circumstances. The centile of the effort distribution of one’s type provides a meaningful intertype comparison of the degree of effort expended in the sense that the level of effort does not” (Roemer, 1998, p.12) • Inverting the quantile function yields: • Test for equality of conditional distributions across types: Lefranc, Pistolesi and Trannoy (2008).

  33. 4. Measuring Inequality of opportunity Dominance Approach • An example of : Distribution of p.c.h. consumption conditional on mother’s education

  34. 4. Measuring Inequality of opportunityCardinal Indices: the Ex-Post Approach • Partition population into circumstance-homogeneous groups: types. • Consider inequality in the value of opportunity sets faced by people with different exogenous circumstances. • Compute between-type inequality: • IOL: • IOR: • Standard inequality decomposition, interpreted as a lower-bound on inequality of opportunity. • Can be computed non-parametrically or parametrically • Bourguignon, Ferreira and Menendez (2007) • Checchi and Peragine (2010) • Ferreira and Gignoux (2011)

  35. 4. Measuring Inequality of opportunityCardinal Indices: the Ex-Ante Approach • Partition population into effort-homogeneous groups: tranches • Consider inequality among those people who exert same degree of effort • Compute within-tranche inequality. • Checchi and Peragine (2010) • The two approaches do not yield identical solutions. • Related to the debate between • Roemer’s “Mean of mins” • Van de Gaer’s “Min of Means”

  36. 4. Measuring Inequality of opportunityIllustration for Latin America • In Latin America, (lower-bound ex-post) inequality of economic opportunity: • ranges from 23% to 35% for income per capita. • ranges from 24% to 50% for consumption per capita.

  37. 4. Measuring Inequality of opportunityOpportunity-Deprivation Profiles “The rate of economic development should be taken to be the rate at which the mean advantage level of the worst-off types grows over time. […] I look forward to a future number of the WDR that carries out the computation, across countries, of this new definition of economic development” (p.243). Roemer, John E. (2006): “Review Essay, ‘The 2006 world development report: Equity and development”, Journal of Economic Inequality (4): 233-244 • Define an opportunity profile: • And an opportunity-deprivation profile:

  38. 4. Measuring Inequality of opportunityOpportunity-Deprivation Profiles The Brazilian profile, by income per capita Brazil’s “opportunity-deprivation profile” in 1996: six poorest “social types” (adding up to 10% of the population), defined by pre-determined background characteristics.

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