Poverty Measurement

1. Poverty Measurement Inequality, Poverty and Income Distribution University of Oviedo Frank Cowell http://darp.lse.ac.uk/oviedo2007 March 2007

2. Issues to be addressed • Builds on Lectures 3 and 4 • “Income Distribution and Welfare” • “Inequality measurement” • Extension of ranking criteria • Generalised Lorenz curve again • Examine structure of poverty indices • Link with inequality analysis • Axiomatics of poverty

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

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” • Incidence • Intensity • Inequality • Present approach: • Fundamental partition • Individual identification • Aggregation of information

6. Poverty and partition • A link between this subject and inequality decomposition. • Partitioning of population is crucial • Depends on definition of poverty line • Asymmetric treatment of information • Exogeneity of partition? • Does it depend on the distribution of income? • Uniqueness of partition? • May need to deal with ambiguities in definition of poverty line

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 z 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” z • A “generous” z • An “intermediate” z • 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 Conclusion

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

14. A class of poverty indices • ASP leads to several classes of measures • Make poverty evaluation depend on poverty gap • Normalise by poverty line • Foster-Greer-Thorbecke class • Important special case a = 0 • poverty evaluation is simple: {0,1} • gives poverty rate • = poverty count / n • Important special case a = 1 • poverty evaluation is simple: normalised poverty gap g/z • gives poverty deficit • measures resources needed to remove poverty

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

16. Other ASP measures • Other ASP indices focus directly on incomes rather than gaps • Clark et al (1981) • where b < 1 is a sensitivity parameter • Watts • Both can give rise to empirical problems Cowell. and Victoria-Feser, (1996)

17. Quasi ASP measures • Consider also quasi-ASP • This allows ranks or position in the evaluation function • p(x, z, F(x) ) • Sen (1976) is the primary example • Based on an axiomatic approach • incorporates, poverty count, poverty deficit, Gini amongst poor • Poverty evaluation function:

18. Poverty measures: assessment • ASP class is fruitful • neat and elegant • interesting axiomatisation – see next lecture • But which members of it are appropriate? • Questionnaire experiments again? • Amiel-Cowell (1999) • Many of Sen (1976) axioms rejected • In particular transfer principle rejected • which also rules out FGT measures for a > 1 • Leading poverty measures are still • Poverty count or ratio • Poverty deficit

19. Poverty measurement Overview... Poverty concepts Poverty measures Definitions and consequences Empirical robustness Poverty rankings Conclusion

20. 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

21. Poverty rates by region 1981

22. Poverty rates by region 2001

23. Poverty: East Asia

24. Poverty: South Asia

25. Poverty: Latin America, Caribbean

26. Poverty: Middle East and N.Africa

27. Poverty: Sub-Saharan Africa

28. Poverty: Eastern Europe and Central Asia

29. Empirical robustness (2) • Does it matter which poverty criterion you use? • An example from Spain • Bárcena and Cowell (2006) • Data are from ECHP • OECD equivalence scale • Poverty line is 60% of 1993 median income • Does it matter which FGT index you use?

30. Poverty in Spain 1993—2000

31. Poverty measurement Overview... Poverty concepts Poverty measures Another look at ranking issues Empirical robustness Poverty rankings Conclusion

32. Extension of poverty analysis • Now consider some further 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?

33. 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 (zmin, zmax) • 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 z ≤ zmax. • Equivalent to requiring that the second-order dominance condition hold for all z.

34. 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.)

35. Poverty concepts – more • Given poverty line z • a reference point • Poverty gap • fundamental income difference • Define the number of the poor as: • p(x, z) := #{i: xi≤ z} • Cumulative poverty gap

36. 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

37. Poverty measurement Overview... Poverty concepts Poverty measures Building from first principles? Empirical robustness Poverty rankings Conclusion

38. 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

39. Poverty: a way forward • Introduce a formal axiomatisation of ASP class? • In particular FGT measures • See Ebert and Moyes (2002) • Use standard axioms introduced earlier • for analysing social welfare • for inequality • Show how this is related to • deprivation • inequality • See next lecture

40. References (1) • Amiel, Y. and Cowell, F.A. (1999) Thinking about Inequality, Cambridge University Press • Atkinson, A. B. (1987) “On the measurement of poverty,” Econometrica, 55, 749-764 • Bárcena, E. and Cowell, F.A. (2006) “Static and Dynamic Poverty in Spain, 1993-2000,” Hacienda Pública Española179 • 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 • Clark, S.,Hemming, R. and Ulph, D. (1981) “On indices for the measurement of poverty, The Economic Journal, 91, 515-526 • Cowell, F. A. and Victoria-Feser, M.-P. (1996) “Poverty Measurement with Contaminated Data: A Robust Approach,” European Economic Review, 40, 1761-1771 • 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

41. References (2) • 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 • Watts, H. W. (1968) “An economic definition of poverty,” in Moynihan, D. P. (ed) Understanding Poverty, Basic Books, New York, Chapter, 11, 316-329 • Zheng, B. (1993) “An axiomatic characterization of the Watts index,” Economics Letters, 42, 81-86 • Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings,” Journal of Economic Theory, 95, 116-137