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

2. Frank Cowell: TU Lisbon – Inequality & Poverty Issues to be addressed Builds on @@ Builds on @@  “Distributional Equity, Social Welfare” Extension of ranking criteria Extension of ranking criteria  Parade diagrams  Generalised Lorenz curve Extend SWF analysis to inequality Extend SWF analysis to inequality Examine structure of inequality Examine structure of inequality Link with the analysis of poverty Link with the analysis of poverty

3. Frank Cowell: TU Lisbon – Inequality & Poverty Overview... Poverty concepts Poverty measures Empirical robustness Poverty rankings Axiomatisation Poverty measurement …Identification and representation

4. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty analysis – overview Basic ideas 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 Development of specific measures  Relation to inequality  What axiomatisation? Use of ranking techniques Use of ranking techniques  Relation to welfare rankings

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

6. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty and partition Depends on definition of poverty line Depends on definition of poverty line Exogeneity of partition? Exogeneity of partition? Asymmetric treatment of information Asymmetric treatment of information

7. Frank Cowell: TU Lisbon – Inequality & Poverty Counting the poor Use the concept of individual poverty evaluation Use the concept of individual poverty evaluation Simplest version is (0,1) Simplest version is (0,1)  (non-poor, poor)  headcount Perhaps make it depend on income Perhaps make it depend on income  poverty deficit Or on the whole distribution? Or on the whole distribution? Convenient to work with poverty gaps Convenient to work with poverty gaps

8. Frank Cowell: TU Lisbon – Inequality & Poverty The poverty line and poverty gaps x x* 0 poverty evaluation income xixi xjxj gigi gjgj

9. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty evaluation g 0 poverty evaluation poverty gap x = 0 Non-Poor Poor gigi A gjgj B   the “head-count”   the “poverty deficit”   sensitivity to inequality amongst the poor   Income equalisation amongst the poor

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

11. Frank Cowell: TU Lisbon – Inequality & Poverty The distribution of poverty gaps $0$20$40$60 gaps

12. Frank Cowell: TU Lisbon – Inequality & Poverty Overview... Poverty concepts Poverty measures Empirical robustness Poverty rankings Axiomatisation Poverty measurement Aggregation information about poverty

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

14. Frank Cowell: TU Lisbon – Inequality & Poverty A class of poverty indices ASP leads to several classes of measures ASP leads to several classes of measures Make poverty evaluation depends on poverty gap. Make poverty evaluation depends on poverty gap. Normalise by poverty line Normalise by poverty line Foster-Greer-Thorbecke class Foster-Greer-Thorbecke class Foster-Greer-Thorbecke

15. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty evaluation functions p(x,x*) x*-x

16. Frank Cowell: TU Lisbon – Inequality & Poverty Overview... Poverty concepts Poverty measures Empirical robustness Poverty rankings Axiomatisation Poverty measurement Definitions and consequences

17. Frank Cowell: TU Lisbon – Inequality & Poverty Empirical robustness Does it matter which poverty criterion you use? Does it matter which poverty criterion you use? Look at two key measures from the ASP class Look at two key measures from the ASP class  Head-count ratio  Poverty deficit (or average poverty gap) Use two standard poverty lines 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? How do different regions of the world compare? What’s been happening over time? What’s been happening over time? Use World-Bank analysis 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 World Bank Policy Research Working Paper Series 3341World Bank Policy Research Working Paper Series 3341

18. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty rates by region 1981

19. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty rates by region 2001

20. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: East Asia

21. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: South Asia

22. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: Latin America, Caribbean

23. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: Middle East and N.Africa

24. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: Sub-Saharan Africa

25. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: Eastern Europe and Central Asia

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

27. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty in Spain 1993—2000

28. Frank Cowell: TU Lisbon – Inequality & Poverty Overview... Poverty concepts Poverty measures Empirical robustness Poverty rankings Axiomatisation Poverty measurement Another look at ranking issues

29. Frank Cowell: TU Lisbon – Inequality & Poverty Extension of poverty analysis (1) Finally consider some generalisations Finally consider some generalisations @@What if we do not know the poverty line? @@What if we do not know the poverty line? Can we find a counterpart to second order dominance in welfare analysis? Can we find a counterpart to second order dominance in welfare analysis? What if we try to construct poverty indices from first principles? What if we try to construct poverty indices from first principles?

30. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty rankings (1) Atkinson (1987) connects poverty and welfare. Atkinson (1987) connects poverty and welfare. Atkinson (1987) Atkinson (1987) Based results on the portfolio literature concerning “below- target returns” Based results on the portfolio literature concerning “below- target returns” Theorem 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 *. Equivalent to requiring that the second-order dominance condition hold for all x *.

31. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty rankings (2) Foster and Shorrocks (1988a, 1988b) have a similar approach to orderings by P, Foster and Shorrocks (1988a, 1988b) have a similar approach to orderings by P,1988a But concentrate on the FGT index’s particular functional form: But concentrate on the FGT index’s particular functional form: Theorem: Poverty rankings are equivalent to 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. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty concepts Given poverty line z Given poverty line z  a reference point Poverty gap Poverty gap  fundamental income difference Foster et al (1984) poverty index again Foster et al (1984) poverty index again Cumulative poverty gap Cumulative poverty gap

33. Frank Cowell: TU Lisbon – Inequality & Poverty TIP / Poverty profile i/n p(x,z)/n G(x,z) 0 Cumulative gaps versus population proportions Cumulative gaps versus population proportions Proportion of poor Proportion of poor TIP curve TIP curve Cumulative gaps versus population proportions Cumulative gaps versus population proportions Proportion of poor Proportion of poor TIP curve TIP curve   TIP curves have same interpretation as GLC   TIP dominance implies unambiguously greater poverty

34. Frank Cowell: TU Lisbon – Inequality & Poverty Overview... Poverty concepts Poverty measures Empirical robustness Poverty rankings Axiomatisation Poverty measurement Building from first principles?

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

36. Frank Cowell: TU Lisbon – Inequality & Poverty Poverty: The key axioms Standard ones from lecture 2 Standard ones from lecture 2  anonymity  independence  monotonicity  income increments reduce poverty Strengthen two other axioms Strengthen two other axioms  scale invariance  translation invariance Also need continuity Also need continuity Plus a focus axiom Plus a focus axiom

37. Frank Cowell: TU Lisbon – Inequality & Poverty A closer look at the axioms Let D denote the set of ordered income vectors Let D denote the set of ordered income vectors The focus axiom is The focus axiom is Scale invariance now becomes Scale invariance now becomes Independence means: Independence means: Define the number of the poor as Define the number of the poor as

38. Frank Cowell: TU Lisbon – Inequality & Poverty Ebert-Moyes (2002) Gives two types of FGT measures Gives two types of FGT measures  “relative” version  “absolute” version Additivity follows from the independence axiom Additivity follows from the independence axiom

39. Frank Cowell: TU Lisbon – Inequality & Poverty Brief conclusion Framework of distributional analysis covers a number of related problems: Framework of distributional analysis covers a number of related problems:  Social Welfare  Inequality  Poverty Commonality of approach can yield important insights Commonality of approach can yield important insights Ranking principles provide basis for broad judgments 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 trends will often be robust to choice of poverty index Poverty indexes can be constructed from scratch using standard axioms Poverty indexes can be constructed from scratch using standard axioms

40. Frank Cowell: TU Lisbon – Inequality & Poverty References Atkinson, A. B. (1987) “On the measurement of poverty,” Econometrica, 55, 749-764 Atkinson, A. B. (1987) “On the measurement of poverty,” Econometrica, 55, 749-764 Atkinson, A. B. (1987) Atkinson, A. B. (1987) Bárcena, E. and Cowell, F.A. (2005) “Static and Dynamic Poverty in Spain, 1993- 2000,” Distributional Analysis research Programme Discussion Paper 77, STICERD, LSE. Bárcena, E. and Cowell, F.A. (2005) “Static and Dynamic Poverty in Spain, 1993- 2000,” Distributional Analysis research Programme Discussion Paper 77, STICERD, LSE. Bárcena, E. and Cowell, F.A. (2005) Bárcena, E. and Cowell, F.A. (2005) 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 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 Chen, S. and Ravallion, M. (2004) Chen, S. and Ravallion, M. (2004) Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer-Thorbecke poverty orderings,” Journal of Public Economic Theory 4, 455-473. Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer-Thorbecke poverty orderings,” Journal of Public Economic Theory 4, 455-473. Ebert, U. and P. Moyes (2002) Ebert, U. and P. Moyes (2002) Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty measures,” Econometrica, 52, 761-776 Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty measures,” Econometrica, 52, 761-776 Foster, J. E., Greer, J. and Thorbecke, E. (1984) Foster, J. E., Greer, J. and Thorbecke, E. (1984) Foster, J. E. and Shorrocks, A. F. (1988a) “Poverty orderings,” Econometrica, 56, 173- 177 Foster, J. E. and Shorrocks, A. F. (1988a) “Poverty orderings,” Econometrica, 56, 173- 177 Foster, J. E. and Shorrocks, A. F. (1988a) Foster, J. E. and Shorrocks, A. F. (1988a) Foster, J. E. and Shorrocks, A. F. (1988b) “Poverty orderings and welfare dominance,” Social Choice and Welfare, 5,179-198 Foster, J. E. and Shorrocks, A. F. (1988b) “Poverty orderings and welfare dominance,” Social Choice and Welfare, 5,179-198 Foster, J. E. and Shorrocks, A. F. (1988b) Foster, J. E. and Shorrocks, A. F. (1988b) 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. 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. Jenkins, S. P. and Lambert, P. J. (1997) Jenkins, S. P. and Lambert, P. J. (1997) Sen, A. K. (1976) “Poverty: An ordinal approach to measurement,” Econometrica, 44, 219-231 Sen, A. K. (1976) “Poverty: An ordinal approach to measurement,” Econometrica, 44, 219-231 Sen, A. K. (1976) Sen, A. K. (1976) Sen, A. K. (1979) “Issues in the measurement of poverty,” Scandinavian Journal of Economics, 91, 285-307 Sen, A. K. (1979) “Issues in the measurement of poverty,” Scandinavian Journal of Economics, 91, 285-307 Sen, A. K. (1979) Sen, A. K. (1979) Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings,” Journal of Economic Theory, 95, 116-137 Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings,” Journal of Economic Theory, 95, 116-137 Zheng, B. (2000) Zheng, B. (2000)