Inequality Empirics in Developing Countries: Measurement, Structure and Dynamics

1. Inequality Empirics in Developing Countries: Measurement, Structure and Dynamics Francisco H. G. Ferreira Development Research Group The World Bank

2. Plan of the Lecture • Motivation • The Measurement of Inequality • The indicator of individual welfare • Distribution functions (and variants) • An axiomatic approach to inequality indices • Lorenz dominance • The Structure of Inequality • Standard decomposition analyses • Inequality Dynamics • Towards an integrated approach

3. 1. Motivation (i): Why do income distributions look like this? Mexico, 2000: histogram of the household per capita income distribution, excluding the richest 1 percent Source: de Ferranti et. Al.(2003), based on the ENIGH, 2000.

4. 1. Motivation (ii): How do they change over time?

5. 1. Motivation (iii): Why do inequality levels vary so much across countries?

6. The Measurement of Inequality2.1. Inequality of What? • Different philosophical perspectives on social justice provide different foundations for welfare economics: • Utilitarianism • Jeremy Bentham (1789) • Basal Space: utilities. “Focal combination”: Sum. • Libertarianism • John Locke to Robert Nozick. • Basal Space is hierarchical and includes basic rights ahead of U(.) • Rawlsian liberalism • Basal Space: primary goods. • Liberty Principle, Opportunity Principle (incl. Difference Principle) • Sen and the capability approach • Goods Capabilities Functionings Flourishing

7. Constructing an Individual Welfare Indicator • Given the severe practical problems with: • Observing capability (i.e. choice) sets; • Identifying and collecting data on all relevant ‘functionings’, rights, and/or freedoms; • Weighting and trading off the non-market components of these vectors against one another; • Most applied welfare economists increasingly tend to adopt a three-pronged approach: • Measure expenditures (or incomes) as well as possible for those components which can be aggregated using the “exchange metric” of the price system. • Consider additional dimensions separately. • Address differences in needs “indirectly”, i.e. through equivalence scales

8. Constructing an Individual Welfare Indicator I) The Welfare Indicator: 1)Income versus Consumption Expenditure. 2) Aggregation Comprehensiveness. 3) Population Comprehensiveness. 4) Price deflation. 5) Equivalence Scales. II) The Unit of Analysis: 6) Individuals or Households.

9. 1) Income versus Consumption • There are two main reasons why consumption expenditures are generally preferred to incomes as indicators of individual welfare: • If some saving or dissaving is possible, consumption is a better proxy for permanent income. • This argument becomes stronger with the degree of completeness of capital markets. • Measurement error is greater with incomes • Particularly troublesome for mobility studies • Likely to exaggerate inequality. • See Deaton (1997) • Comes down to the quality of the questionnaire and of the survey team.

10. 2) Aggregation Comprehensiveness • For all expenditure items j, the survey should contain information on any two of (x, p, q). Information on x alone does not allow for a price check. • For expenditures: • Food and other non-durables • Durables • Production for own consumption • Housing • Publicly provided private goods and services • Public goods? • Leisure?

11. 2) Aggregation Comprehensiveness • For incomes: • Income from labor • Monetary and in-kind, from all occupations • Employment and self-employment • Income from capital • Interest; dividends; rents; capital gains. • Transfers • Public and private, net of taxes • Add: • Production for own consumption • Imputed rent for home-owners (but not rent for renters!) • Publicly provided private goods and services, if free of charge, consistently with valuation under expenditures • (public goods and leisure)

12. 3) Population comprehensiveness. • Competent Sampling Design • A sample design that is suitable for one purpose, may not be for another: RLMS in Russia. • Regional Coverage • Famous exceptions: PPV, PME • PNAD and the rural North • Urban vs. Rural Areas • Famous exception: EPH in Argentina

13. 4) Price deflation. • To control for inflation, must deflate incomes over time. (Many indices) • To control for regional price variations, must deflate over space • Prices vary. Should baskets vary?

14. 5) Equivalence Scales • Are there cost differences across individual types? (Adult equivalence) • Are there economies of scale in the consumption of some goods? • where • A “flexible” example:

15. 2.2. Distributions • Social welfare, poverty and inequality summarize different features of a distribution. • Distribution of welfare indicator per unit of analysis. • Discrete: y = {y1, y2, y3, …., yN} • Continuous: The distribution function F(y) of a variable y,defined over a population, gives the measure of that population for whom the variable has a value less than or equal to y.

16. The density function: f(x) The distribution function

17. The quantile function: y=F-1(p)

18. The Lorenz curve: or

19. The Generalized Lorenz curve:

20. 2.3. An axiomatic approach to inequality measurement. • Defined over mean-normalized complete distributions: F(y/μ); • Seeks to capture ‘dispersion’ - the second moment of the distribution; • Aggregates distances among incomes, or between them and a ‘center’ of the distribution. • Not a uniquely defined concept: different scalar indices.

21. Candidate Summary Measures • Some options from basic statistics: • Completely insensitive to changes in incomes between the extremes. • Varies with scale of measurement: dollars and cents…

22. The Axioms: Start from (five) desirable properties • Symmetry (or Anonimity) • The (Pigou-Dalton)Transfer Principle • Income Scale Independence - If x is any permutation of y, then

23. The Axioms: Start from (five) desirable properties • Population Replication Independence If y is a concatenation of k vectors x, then I(y) = I(x). (k >0, finite) • Decomposability • If {y} =

24. More Candidate Measures - Does not satisfy the Transfer Axiom… • Only satisfies the Decomposability Axiom for non- • overlapping partitions.

25. The Generalized Entropy Classwhich satisfies all five axioms.

27. The Structure of Inequalitya. Inequality Decomposition by Population Subgroup 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.

28. An Example from Brazil The Rise and Fall of Brazilian Inequality: 1981-2004

29. A cross-country example: Race and ethnicity decompositions. Source: WDR 2006

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

32. 4. Inequality Dynamics Towards an integrated approach: Growth (in the mean), poverty dynamics and inequality dynamics are simply different aspect of the same process. Growth in Thailand, 1975-1992, seen as rightward shifts in the Cumulative Distribution Function. Source: Ahuja et al. 1997

33. Growth in mean incomes • Growth in mean incomes is simply a weighted average of income growth along the distribution, with weights given by relative incomes. • This can be written in terms of the growth incidence curve (GIC): • So growth (in the mean) is simply a particular aggregation of the percentile-specific growth rates in the GIC. The Growth Incidence Curve was first formally described by Ravallion and Chen, 2003.

34. Changes in PovertyDrawing on Kraay (2003) Write a general poverty measure formulation as: where gives you the FGT class, for instance, and gives you the Watts index. Differentiating with respect to time yields with and So poverty changes are also simply a particular aggregation of the information in the GIC.

35. Changes in inequality • Like poverty measures, most inequality indices can be written as functions of a sum of “individual distance indicators”: • So, gives you the Generalized Entropy Class. • And gives you the Atkinson Class, etc.. Differentiating with respect to time yields with and

36. So economic growth, changes in poverty and changes in inequality are effectively different ways of weighing the income changes along the distribution which are presented in a growth incidence curve. ∆P0 = +2pp ∆P0 = -9pp

37. 4.2. Understanding changes in distributions: statistical counterfactual decompositions. • To seek an understanding of changes in the distribution of incomes is to seek an understanding of why the GIC looks the way it does. • To understand the nature and determinants of the incidence or distribution of economic growth. • The first step is statistical: Counterfactual income distribution Residual Counterfactual GIC

38. Statistical counterfactual decompositions(continued) • Of course, this is just another way of describing generalized Oaxaca-Blinder decompositions such as • Where the counterfactual distribution is constructed from: • By simulating a change in in either the conditional distribution of y on X, or on the joint distribution of X. • For example:

39. Statistical counterfactual decompositions(continued) • There are a number of ways to implement such simulations in practice. • They may be based simply on reweighing the sample, so as to reproduce the changes in the distribution of some exogenous characteristic, such as the age composition of the labor force, or the number of people receiving the minimum wage. • DiNardo, Fortin and Lemieux (1996) • Hyslop and Maré (2005) • They may be based in importing parameters from models estimated in one year to the other. • Bourguignon, Ferreira and Lustig (2004) • They may be based on aggregating counterfactual transfers (with or without simulated household response • Bourguignon, Ferreira and Leite (2003)

40. An Example from Brazil, 1976-1996.(Ferreira and Paes de Barros, 1999) Level 1: g (y | X) Aggregation rule: Earnings: Level 2: (X) Occupational Choice: Education: MLE (EA, R, r, g, nah; ) Fertility: MLC ( nch E, A, R, r, g, nah; ) Other Incomes: T ( y0h E, A, R, r, g, nah; )

41. Comparing g(p) and gs(p) (i): The price effect.

42. Comparing g(p) and gs(p) (ii): The price effect and the occupational structure effect combined.

43. Comparing g(p) and gs(p) (i): Price, Occupation, Education and Fertility effects.

44. 4.3. Understanding changes in distributions: towards economic decompositions? • Generalized Oaxaca-Blinder decompositions such as those discussed above, whether parametric or semi-parametric, suffer from two shortcomings: • Path-dependence • The counterfactuals do not correspond to an economic equilibrium. There is no guarantee that those counterfactual incomes would be sustained after agents were allowed to respond and the economy reached a new equilibrium.

45. (a) Partial Equilibrium Approaches • The first step towards economic decompositions, in which the counterfactual distributions may be interpreted as corresponding to a counterfactual economic equilibrium, are partial in nature. • One example comes from attempts to simulate distributions after some transfer, in which household responses to the transfer (in terms of child schooling and labor supply) are incorporated. • Bourguignon, Ferreira and Leite (2003) • Todd and Wolpin (2005) • (These two papers differ considerably in how they model behavior. Todd and Wolpin are much more structural.)

46. (b) General Equilibrium Approaches • However, a number of changes which are isolated in statistical counterfactuals – such as changes in returns to education, or in the distribution of years of schooling – are likely to have general equilibrium effects. • Similarly, certain policies one might like to simulate may require a general equilibrium setting. • There are two basic approaches to generate GE-compatible counterfactual income distributions (and thus counterfactual GICs): • Fully disaggregated CGE models, where each household is individually linked to the production and consumption modules. E.g. Chen and Ravallion, 2003, for China. • “Leaner” macroeconomic models linked to microsimulation modules on a household survey dataset. E.g. Bourguignon, Robilliard and Robinson, 2005, for Indonesia.

47. Conclusions • Growth, changes in poverty and changes in inequality are all summary measures of changes in the disaggregated distribution of incomes. • Understanding these changes requires understanding the determinants of the growth incidence curve. • Counterfactual simulations that isolate the individual impacts of changes in prices, in occupational structure, in the distribution of household endowments, or in transfers, are a useful first step. • Counterfactual GICs that are consistent with (partial or general) economic equilibria are more difficult to estimate, as they involve modeling behavior. But starts have been made. • Beware of Lucas critique and the ‘black-box’ critique. • When thinking about policies, do not think of “growth versus distribution”. Think ‘policy incidence’.