Poverty Measurement

1. Poverty Measurement Inequality and Poverty Measurement Technical University of Lisbon Frank Cowell http://darp.lse.ac.uk/lisbon2006 July 2006

2. Issues to be addressed • Builds on @@ • “Distributional Equity, Social Welfare” • Extension of ranking criteria • Parade diagrams • Generalised Lorenz curve • Extend SWF analysis to inequality • Examine structure of inequality • Link with the analysis of poverty

3. Poverty measurement Overview... Poverty concepts Poverty measures …Identification and representation Empirical robustness Poverty rankings Axiomatisation

4. Poverty analysis – overview • Basic ideas • Income – similar to inequality problem? • Consumption, expenditure or income? • Time period • Risk • Income receiver – as before • Relation to decomposition • Development of specific measures • Relation to inequality • What axiomatisation? • Use of ranking techniques • Relation to welfare rankings

5. population non-poor poor Poverty measurement • How to break down the basic issues. • Sen (1979): Two main types of issues • Identification problem • Aggregation problem • Jenkins and Lambert (1997): “3Is” • Identification • Intensity • Inequality • Present approach: • Fundamental partition • Individual identification • Aggregation of information

6. Poverty and partition • Depends on definition of poverty line • Exogeneity of partition? • Asymmetric treatment of information

7. Counting the poor • Use the concept of individual poverty evaluation • Simplest version is (0,1) • (non-poor, poor) • headcount • Perhaps make it depend on income • poverty deficit • Or on the whole distribution? • Convenient to work with poverty gaps

8. The poverty line and poverty gaps poverty evaluation gi gj x* 0 x xi xj income

9. Poverty evaluation • the “head-count” • the “poverty deficit” • sensitivity to inequality amongst the poor • Income equalisation amongst the poor poverty evaluation Poor Non-Poor x = 0 B A g gj gi poverty gap 0

10. $0 $20 $40 $60 $80 $100 $120 $140 $160 $180 $200 $220 $240 $260 $280 $300 Brazil 1985: How Much Poverty? • A highly skewed distribution • A “conservative” x* • A “generous” x* • An “intermediate” x* • The censored income distribution Rural Belo Horizonte poverty line compromise poverty line Brasilia poverty line

11. gaps $0 $20 $40 $60 The distribution of poverty gaps

12. Poverty measurement Overview... Poverty concepts Poverty measures Aggregation information about poverty Empirical robustness Poverty rankings Axiomatisation

13. ASP • Additively Separable Poverty measures • ASP approach simplifies poverty evaluation • Depends on own income and the poverty line. • p(x, x*) • Assumes decomposability amongst the poor • Overall poverty is an additively separable function • P = p(x, x*) dF(x) • Analogy with decomposable inequality measures

14. A class of poverty indices • ASP leads to several classes of measures • Make poverty evaluation depends on poverty gap. • Normalise by poverty line • Foster-Greer-Thorbecke class

15. Poverty evaluation functions p(x,x*) x*-x

16. Poverty measurement Overview... Poverty concepts Poverty measures Definitions and consequences Empirical robustness Poverty rankings Axiomatisation

17. Empirical robustness • Does it matter which poverty criterion you use? • Look at two key measures from the ASP class • Head-count ratio • Poverty deficit (or average poverty gap) • Use two standard poverty lines • $1.08 per day at 1993 PPP • $2.15 per day at 1993 PPP • How do different regions of the world compare? • What’s been happening over time? • Use World-Bank analysis • Chen-Ravallion “How have the world’s poorest fared since the early 1980s?” World Bank Policy Research Working Paper Series 3341

18. Poverty rates by region 1981

19. Poverty rates by region 2001

20. Poverty: East Asia

21. Poverty: South Asia

22. Poverty: Latin America, Caribbean

23. Poverty: Middle East and N.Africa

24. Poverty: Sub-Saharan Africa

25. Poverty: Eastern Europe and Central Asia

26. Empirical robustness (2) • Does it matter which poverty criterion you use? • An example from Spain • Bárcena and Cowell (2005) • Data are from ECHP • OECD equivalence scale • Poverty line is 60% of 1993 median income • Does it matter which FGT index you use?

27. Poverty in Spain 1993—2000

28. Poverty measurement Overview... Poverty concepts Poverty measures Another look at ranking issues Empirical robustness Poverty rankings Axiomatisation

29. Extension of poverty analysis (1) • Finally consider some generalisations • @@What if we do not know the poverty line? • Can we find a counterpart to second order dominance in welfare analysis? • What if we try to construct poverty indices from first principles?

30. Poverty rankings (1) • Atkinson (1987) connects poverty and welfare. • Based results on the portfolio literature concerning “below-target returns” • Theorem • Given a bounded range of poverty lines (x*min, x*max) • and poverty measures of the ASP form • a necessary and sufficient condition for poverty to be lower in distribution F than in distribution G is that the poverty deficit be no greater in F than in G for all x* ≤ x*max. • Equivalent to requiring that the second-order dominance condition hold for all x*.

31. Poverty rankings (2) • Foster and Shorrocks (1988a, 1988b) have a similar approach to orderings by P, • But concentrate on the FGT index’s particular functional form: • Theorem: Poverty rankings are equivalent to • first-order welfare dominance for a = 0 • second-degree welfare dominance for a = 1 • (third-order welfare dominance for a = 2.)

32. Poverty concepts • Given poverty line z • a reference point • Poverty gap • fundamental income difference • Foster et al (1984) poverty index again • Cumulative poverty gap

33. TIP / Poverty profile • Cumulative gaps versus population proportions • Proportion of poor • TIP curve G(x,z) • TIP curves have same interpretation as GLC • TIP dominance implies unambiguously greater poverty i/n 0 p(x,z)/n

34. Poverty measurement Overview... Poverty concepts Poverty measures Building from first principles? Empirical robustness Poverty rankings Axiomatisation

35. Poverty: Axiomatic approach • Characterise an ordinal poverty index P(x ,z) • See Ebert and Moyes (JPET 2002) • Use some of the standard axioms we introduced for analysing social welfare • Apply them to n+1 incomes – those of the n individuals and the poverty line • Show that • given just these axioms… • …you are bound to get a certain type of poverty measure.

36. Poverty: The key axioms • Standard ones from lecture 2 • anonymity • independence • monotonicity • income increments reduce poverty • Strengthen two other axioms • scale invariance • translation invariance • Also need continuity • Plus a focus axiom

37. A closer look at the axioms • Let D denote the set of ordered income vectors • The focus axiom is • Scale invariance now becomes • Define the number of the poor as • Independence means:

38. Ebert-Moyes (2002) • Gives two types of FGT measures • “relative” version • “absolute” version • Additivity follows from the independence axiom

39. Brief conclusion • Framework of distributional analysis covers a number of related problems: • Social Welfare • Inequality • Poverty • Commonality of approach can yield important insights • Ranking principles provide basis for broad judgments • May be indecisive • specific indices could be used • Poverty trends will often be robust to choice of poverty index • Poverty indexes can be constructed from scratch using standard axioms

40. References • Atkinson, A. B. (1987) “On the measurement of poverty,” Econometrica, 55, 749-764 • Bárcena, E. and Cowell, F.A. (2005) “Static and Dynamic Poverty in Spain, 1993-2000,” Distributional Analysis research Programme Discussion Paper 77, STICERD, LSE. • Chen, S. and Ravallion, M. (2004) “How have the world’s poorest fared since the early 1980s?” World Bank Policy Research Working Paper Series, 3341 • Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer-Thorbecke poverty orderings,” Journal of Public Economic Theory4, 455-473. • Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty measures,” Econometrica, 52, 761-776 • Foster , J. E. and Shorrocks, A. F. (1988a) “Poverty orderings,” Econometrica, 56, 173-177 • Foster , J. E. and Shorrocks, A. F. (1988b) “Poverty orderings and welfare dominance,” Social Choice and Welfare, 5,179-198 • Jenkins, S. P. and Lambert, P. J. (1997) “Three ‘I’s of poverty curves, with an analysis of UK poverty trends,” Oxford Economic Papers, 49, 317-327. • Sen, A. K. (1976) “Poverty: An ordinal approach to measurement,” Econometrica, 44, 219-231 • Sen, A. K. (1979) “Issues in the measurement of poverty,” Scandinavian Journal of Economics, 91, 285-307 • Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings,” Journal of Economic Theory, 95, 116-137