Frank Cowell Oviedo Inequality Poverty March 2007 Poverty

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

Frank Cowell: Oviedo – Inequality & Poverty Issues to be addressed n Builds on Lectures 3 and 4 u u n Extension of ranking criteria u n Generalised Lorenz curve again Examine structure of poverty indices u n “Income Distribution and Welfare” “Inequality measurement” Link with inequality analysis Axiomatics of poverty

Frank Cowell: Oviedo – Inequality & Poverty Overview. . . Poverty measurement Poverty concepts …Identification and representation Poverty measures Empirical robustness Poverty rankings Conclusion

Frank Cowell: Oviedo – Inequality & Poverty analysis – overview n Basic ideas u n n Income – similar to inequality problem? t Consumption, expenditure or income? t Time period t Risk u Income receiver – as before u Relation to decomposition Development of specific measures u Relation to inequality u What axiomatisation? Use of ranking techniques u Relation to welfare rankings

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

Frank Cowell: Oviedo – Inequality & Poverty and partition n A link between this subject and inequality decomposition. u u n n Asymmetric treatment of information Exogeneity of partition? u n Partitioning of population is crucial Depends on definition of poverty line Does it depend on the distribution of income? Uniqueness of partition? u May need to deal with ambiguities in definition of poverty line

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

poverty evaluation Frank Cowell: Oviedo – Inequality & Poverty The poverty line and poverty gaps gi 0 gj xi xj z x income

§ the “head-count” § the “poverty deficit” § sensitivity to inequality amongst the poor § Income equalisation amongst the poor poverty evaluation Poor Non-Poor x=0 Frank Cowell: Oviedo – Inequality & Poverty evaluation B A gj 0 gi g poverty gap

Frank Cowell: Oviedo – Inequality & Poverty 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 $0 $20 $40 $60 $80 $100 $120 $140 $160 $180 $200 $220 $240 $260 $280 $300

Frank Cowell: Oviedo – Inequality & Poverty The distribution of poverty gaps $0 $20 $40 $60 gaps

Frank Cowell: Oviedo – Inequality & Poverty Overview. . . Poverty measurement Poverty concepts Aggregation information about poverty Poverty measures Empirical robustness Poverty rankings Conclusion

Frank Cowell: Oviedo – Inequality & Poverty ASP n n n Additively Separable Poverty measures ASP approach simplifies poverty evaluation Depends on own income and the poverty line. u n n Assumes decomposability amongst the poor Overall poverty is an additively separable function u n p(x, z) P = p(x, z) d. F(x) Analogy with decomposable inequality measures

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

p(x, z) z-x Frank Cowell: Oviedo – Inequality & Poverty evaluation functions

Frank Cowell: Oviedo – Inequality & Poverty Other ASP measures n Other ASP indices focus directly on incomes rather than gaps Clark et al (1981) n where b < 1 is a sensitivity parameter Watts n u n Both can give rise to empirical problems Cowell. and Victoria-Feser, (1996)

Frank Cowell: Oviedo – Inequality & Poverty Quasi ASP measures n n Consider also quasi-ASP This allows ranks or position in the evaluation function u n Sen (1976) is the primary example u u n p(x, z, F(x) ) Based on an axiomatic approach incorporates, poverty count, poverty deficit, Gini amongst poor Poverty evaluation function:

Frank Cowell: Oviedo – Inequality & Poverty measures: assessment n ASP class is fruitful u u n n But which members of it are appropriate? Questionnaire experiments again? u u n neat and elegant interesting axiomatisation – see next lecture 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 u u Poverty count or ratio Poverty deficit

Frank Cowell: Oviedo – Inequality & Poverty Overview. . . Poverty measurement Poverty concepts Definitions and consequences Poverty measures Empirical robustness Poverty rankings Conclusion

Frank Cowell: Oviedo – Inequality & Poverty Empirical robustness n n Does it matter which poverty criterion you use? Look at two key measures from the ASP class u u n Use two standard poverty lines u u n n n Head-count ratio Poverty deficit (or average poverty gap) $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 u Chen-Ravallion “How have the world’s poorest fared since the early 1980 s? ” World Bank Policy Research Working Paper Series 3341

Frank Cowell: Oviedo – Inequality & Poverty rates by region 1981

Frank Cowell: Oviedo – Inequality & Poverty rates by region 2001

Frank Cowell: Oviedo – Inequality & Poverty: East Asia

Frank Cowell: Oviedo – Inequality & Poverty: South Asia

Frank Cowell: Oviedo – Inequality & Poverty: Latin America, Caribbean

Frank Cowell: Oviedo – Inequality & Poverty: Middle East and N. Africa

Frank Cowell: Oviedo – Inequality & Poverty: Sub-Saharan Africa

Frank Cowell: Oviedo – Inequality & Poverty: Eastern Europe and Central Asia

Frank Cowell: Oviedo – Inequality & Poverty Empirical robustness (2) n n n Does it matter which poverty criterion you use? An example from Spain u 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?

Frank Cowell: Oviedo – Inequality & Poverty in Spain 1993— 2000

Frank Cowell: Oviedo – Inequality & Poverty Overview. . . Poverty measurement Poverty concepts Another look at ranking issues Poverty measures Empirical robustness Poverty rankings Conclusion

Frank Cowell: Oviedo – Inequality & Poverty Extension of poverty analysis n n 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?

Frank Cowell: Oviedo – Inequality & Poverty rankings (1) n n n Atkinson (1987) connects poverty and welfare. Based results on the portfolio literature concerning “belowtarget returns” Theorem u u u n 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.

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

Frank Cowell: Oviedo – Inequality & Poverty concepts – more n Given poverty line z u n Poverty gap u n fundamental income difference Define the number of the poor as: u n a reference point p(x, z) : = #{i: xi ≤ z} Cumulative poverty gap

Frank Cowell: Oviedo – Inequality & Poverty 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 0 i/n p(x, z)/n

Frank Cowell: Oviedo – Inequality & Poverty Overview. . . Poverty measurement Poverty concepts Building from first principles? Poverty measures Empirical robustness Poverty rankings Conclusion

Frank Cowell: Oviedo – Inequality & Poverty Brief conclusion n Framework of distributional analysis covers a number of related problems: u u u n n Commonality of approach can yield important insights Ranking principles provide basis for broad judgments u u n Social Welfare Inequality Poverty May be indecisive specific indices could be used Poverty trends will often be robust to choice of poverty index

Frank Cowell: Oviedo – Inequality & Poverty: a way forward n Introduce a formal axiomatisation of ASP class? u u n Use standard axioms introduced earlier u u n for analysing social welfare for inequality Show this is related to u u n In particular FGT measures See Ebert and Moyes (2002) deprivation inequality See next lecture

Frank Cowell: Oviedo – Inequality & Poverty References (1) n n n n 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 Española 179 Chen, S. and Ravallion, M. (2004) “How have the world’s poorest fared since the early 1980 s? ” 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 Theory 4, 455 -473. Foster, J. E. , Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty measures, ” Econometrica, 52, 761 -776

Frank Cowell: Oviedo – Inequality & Poverty References (2) n n n n Foster , J. E. and Shorrocks, A. F. (1988 a) “Poverty orderings, ” Econometrica, 56, 173 -177 Foster , J. E. and Shorrocks, A. F. (1988 b) “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