Frank Cowell: Oviedo – Inequality & Poverty Poverty Measurement March 2007 Inequality, Poverty and Income Distribution University of Oviedo Frank Cowell

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

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

Frank Cowell: Oviedo – 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

Frank Cowell: Oviedo – 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 Sen (1979) Sen (1979)  Identification problem  Aggregation problem Jenkins and Lambert (1997): “3Is” Jenkins and Lambert (1997): “3Is” Jenkins and Lambert (1997) Jenkins and Lambert (1997)  Incidence  Intensity  Inequality Present approach: Present approach:  Fundamental partition  Individual identification  Aggregation of information population non-poor poor

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

Frank Cowell: Oviedo – 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

Frank Cowell: Oviedo – Inequality & Poverty The poverty line and poverty gaps x z 0 poverty evaluation income xixi xjxj gigi gjgj

Frank Cowell: Oviedo – 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

Frank Cowell: Oviedo – 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” z   A “generous” z   An “intermediate” z   The censored income distribution $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 concepts Poverty measures Empirical robustness Poverty rankings Conclusion Poverty measurement Aggregation information about poverty

Frank Cowell: Oviedo – 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, z) 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, z) dF(x) Analogy with decomposable inequality measures Analogy with decomposable inequality measures

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

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

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

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

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

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

Frank Cowell: Oviedo – 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

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

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

Frank Cowell: Oviedo – Inequality & Poverty Poverty: East Asia

Frank Cowell: Oviedo – Inequality & Poverty Poverty: South Asia

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

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

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

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

Frank Cowell: Oviedo – 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 (2006) Bárcena and Cowell (2006) Bárcena and Cowell (2006) 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?

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

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

Frank Cowell: Oviedo – Inequality & Poverty Extension of poverty analysis Now consider some further generalisations Now consider some further 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?

Frank Cowell: Oviedo – 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 (z min, z 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 z ≤ z max. Equivalent to requiring that the second-order dominance condition hold for all z. Equivalent to requiring that the second-order dominance condition hold for all z.

Frank Cowell: Oviedo – 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.)

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

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

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

Frank Cowell: Oviedo – 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

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

Frank Cowell: Oviedo – Inequality & Poverty 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, Atkinson, A. B. (1987) “On the measurement of poverty,” Econometrica, 55, Atkinson, A. B. (1987) Atkinson, A. B. (1987) Bárcena, E. and Cowell, F.A. (2006) “Static and Dynamic Poverty in Spain, ,” Hacienda Pública Española 179 Bárcena, E. and Cowell, F.A. (2006) “Static and Dynamic Poverty in Spain, ,” Hacienda Pública Española 179 Bárcena, E. and Cowell, F.A. (2006) Bárcena, E. and Cowell, F.A. (2006) 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) Clark, S.,Hemming, R. and Ulph, D. (1981) “On indices for the measurement of poverty, The Economic Journal, 91, Clark, S.,Hemming, R. and Ulph, D. (1981) “On indices for the measurement of poverty, The Economic Journal, 91, Clark, S.,Hemming, R. and Ulph, D. (1981) Clark, S.,Hemming, R. and Ulph, D. (1981) Cowell, F. A. and Victoria-Feser, M.-P. (1996) “Poverty Measurement with Contaminated Data: A Robust Approach,” European Economic Review, 40, Cowell, F. A. and Victoria-Feser, M.-P. (1996) “Poverty Measurement with Contaminated Data: A Robust Approach,” European Economic Review, 40, Cowell, F. A. and Victoria-Feser, M.-P. (1996) Cowell, F. A. and Victoria-Feser, M.-P. (1996) Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster- Greer-Thorbecke poverty orderings,” Journal of Public Economic Theory 4, Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster- Greer-Thorbecke poverty orderings,” Journal of Public Economic Theory 4, 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, Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty measures,” Econometrica, 52, Foster, J. E., Greer, J. and Thorbecke, E. (1984) Foster, J. E., Greer, J. and Thorbecke, E. (1984)

Frank Cowell: Oviedo – Inequality & Poverty References (2) Foster, J. E. and Shorrocks, A. F. (1988a) “Poverty orderings,” Econometrica, 56, 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, 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, Jenkins, S. P. and Lambert, P. J. (1997) Sen, A. K. (1976) “Poverty: An ordinal approach to measurement,” Econometrica, 44, Sen, A. K. (1976) Sen, A. K. (1979) “Issues in the measurement of poverty,” Scandinavian Journal of Economics, 91, Sen, A. K. (1979) Watts, H. W. (1968) “An economic definition of poverty,” in Moynihan, D. P. (ed) Understanding Poverty, Basic Books, New York, Chapter, 11, Zheng, B. (1993) “An axiomatic characterization of the Watts index,” Economics Letters, 42, Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings,” Journal of Economic Theory, 95, Zheng, B. (2000)