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

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viedo – Inequality & P

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Poverty Measurement

March 2007 March 2007

Inequality, Poverty and Income Distribution Inequality, Poverty and Income Distribution

University of OviedoUniversity of Oviedo

Frank CowellFrank Cowellhttp://darp.lse.ac.uk/oviedo2007http://darp.lse.ac.uk/oviedo2007

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Issues to be addressed

Builds on Lectures 3 and 4Builds on Lectures 3 and 4 ““Income Distribution and Welfare” Income Distribution and Welfare” ““Inequality measurement”Inequality measurement”

Extension of ranking criteriaExtension of ranking criteria Generalised Lorenz curve againGeneralised Lorenz curve again

Examine structure of poverty indicesExamine structure of poverty indices Link with inequality analysis Link with inequality analysis

Axiomatics of povertyAxiomatics of poverty

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Overview...Poverty concepts

Poverty measures

Empirical robustness

Poverty rankings

Conclusion

Poverty measurement

…Identification and representation

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Poverty analysis – overview Basic ideasBasic ideas

Income – similar to inequality problem?Income – similar to inequality problem? Consumption, expenditure or income?Consumption, expenditure or income? Time periodTime period RiskRisk

Income receiver – as beforeIncome receiver – as before Relation to decompositionRelation to decomposition

Development of specific measuresDevelopment of specific measures Relation to inequalityRelation to inequality What axiomatisation?What axiomatisation?

Use of ranking techniquesUse of ranking techniques Relation to welfare rankingsRelation to welfare rankings

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Poverty measurement

How to break down the basic issues.How to break down the basic issues. SenSen (1979) (1979): Two main types of issues : Two main types of issues

Identification problemIdentification problem Aggregation problemAggregation problem

Jenkins and Lambert (1997)Jenkins and Lambert (1997): “3Is”: “3Is” IncidenceIncidence IntensityIntensity InequalityInequality

Present approach:Present approach: Fundamental partitionFundamental partition Individual identificationIndividual identification Aggregation of informationAggregation of information

population

non-poor

poor

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Poverty and partition

A link between this subject and inequality A link between this subject and inequality decomposition.decomposition. Partitioning of population is crucialPartitioning of population is crucial Depends on definition of poverty lineDepends on definition of poverty line

Asymmetric treatment of informationAsymmetric treatment of information Exogeneity of partition?Exogeneity of partition?

Does it depend on the distribution of income?Does it depend on the distribution of income?

Uniqueness of partition?Uniqueness of partition? May need to deal with ambiguities in definition of May need to deal with ambiguities in definition of

poverty linepoverty line

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Counting the poor

Use the concept of individual poverty evaluationUse the concept of individual poverty evaluation Simplest version is (0,1)Simplest version is (0,1)

(non-poor, poor)(non-poor, poor) headcountheadcount

Perhaps make it depend on incomePerhaps make it depend on income poverty deficitpoverty deficit

Or on the whole distribution?Or on the whole distribution?

Convenient to work with Convenient to work with poverty gapspoverty gaps

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The poverty line and poverty gaps

xz

0

pove

rty

eval

uati

on

incomexi xj

gi

gj

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Poverty evaluation

g

0

poverty

evaluation

poverty gap

x = 0

Non-PoorNon-Poor PoorPoor

gi

A

gj

B

the “head-count”

the “poverty deficit” sensitivity to inequality amongst the poor Income equalisation amongst the poor

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Brazil 1985: How Much Poverty?

Rural Belo Horizonte poverty lineRural Belo Horizonte poverty line

Brasilia poverty lineBrasilia poverty line

compromise poverty linecompromise 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

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The distribution of poverty gaps

$0 $20 $40 $60 gaps

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Poverty measures


Poverty rankings

Conclusion

Poverty measurement

Aggregation information about poverty

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ASP

Additively Separable Poverty measures Additively Separable Poverty measures ASP approach simplifies ASP approach simplifies poverty evaluation poverty evaluation Depends on own income and the poverty line.Depends on own income and the poverty line.

pp((xx, , zz)) Assumes decomposability amongst the poorAssumes decomposability amongst the poor Overall poverty is an additively separable functionOverall poverty is an additively separable function

P = P = pp((xx, , zz) d) dFF((xx))

Analogy with decomposable inequality measuresAnalogy with decomposable inequality measures

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A class of poverty indices ASP leads to several classes of measuresASP leads to several classes of measures Make poverty evaluation depend on poverty gapMake poverty evaluation depend on poverty gap Normalise by poverty lineNormalise by poverty line Foster-Greer-ThorbeckeFoster-Greer-Thorbecke class class

Important special case Important special case a a = 0= 0 poverty evaluation is simple: {0,1}poverty evaluation is simple: {0,1} gives poverty rate gives poverty rate = poverty count / = poverty count / nn

Important special case Important special case a a = 1= 1 poverty evaluation is simple: normalised poverty gap poverty evaluation is simple: normalised poverty gap g/zg/z gives poverty deficit gives poverty deficit measures resources needed to remove povertymeasures resources needed to remove poverty

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0

0.2

0.4

0.6

0.8

1

-0.2 0 0.2 0.4 0.6 0.8 1

a=0

a=1

a=1.5

a=2

a=2.5

Poverty evaluation functions

p(x,z)

z-x

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Other ASP measures Other ASP indices focus directly on incomes rather than gapsOther ASP indices focus directly on incomes rather than gaps Clark et al (1981)Clark et al (1981)

where where < 1 is a sensitivity parameter< 1 is a sensitivity parameter WattsWatts

Both can give rise to empirical problems Both can give rise to empirical problems Cowell. and Victoria-Cowell. and Victoria-FeserFeser, (1996), (1996)

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Quasi ASP measures

Consider also quasi-ASPConsider also quasi-ASP This allows This allows ranksranks or position in the evaluation function or position in the evaluation function

pp((xx, , zz, , FF((xx) )) )

SenSen (1976) (1976) is the primary example is the primary example Based on an axiomatic approachBased on an axiomatic approach incorporates, poverty count, poverty deficit, Gini amongst poorincorporates, poverty count, poverty deficit, Gini amongst poor

Poverty evaluation function:Poverty evaluation function:

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Poverty measures: assessment

ASP class is fruitfulASP class is fruitful neat and elegantneat and elegant interesting axiomatisation – see next lectureinteresting 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)Amiel-Cowell (1999) Many of Many of Sen (1976) axioms rejected axioms rejected In particular transfer principle rejectedIn particular transfer principle rejected which also rules out FGT measures for which also rules out FGT measures for aa > 1 > 1

Leading poverty measures are stillLeading poverty measures are still Poverty count or ratioPoverty count or ratio Poverty deficitPoverty deficit

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Poverty measures


Poverty rankings

Conclusion

Poverty measurement

Definitions and consequences

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Does it matter which poverty criterion you use?Does it matter which poverty criterion you use? Look at two key measures from the ASP classLook at two key measures from the ASP class

Head-count ratioHead-count ratio Poverty deficit (or average poverty gap)Poverty deficit (or average poverty gap)

Use two standard poverty linesUse two standard poverty lines $1.08 per day at 1993 PPP$1.08 per day at 1993 PPP $2.15 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 analysisUse World-Bank analysis

Chen-Ravallion “How have the world’s poorest fared since the early Chen-Ravallion “How have the world’s poorest fared since the early 1980s?” 1980s?” World Bank Policy Research Working Paper Series 3341World Bank Policy Research Working Paper Series 3341

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Poverty rates by region 1981

China 63.80 1 88.10 3 23.41 1 50.82 1

East Asia 57.70 2 84.80 4 20.58 2 47.20 3

India 54.40 3 89.60 1 17.27 3 47.22 2

South Asia 51.50 4 89.10 2 16.06 5 45.78 4

Sub-Saharan Africa 41.60 5 73.30 5 17.03 4 38.54 5

All regions 40.40 6 66.70 6 13.92 6 35.02 6

Latin America and Caribbean 9.70 7 26.90 8 2.75 7 10.66 7

Middle East and North Africa 5.10 8 28.90 7 1.00 8 8.81 8

Eastern Europe and Central Asia 0.70 9 4.70 9 0.17 9 1.39 9

Headcount Poverty gap$1.08 $2.15 $1.08 $2.15

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Poverty rates by region 2001

Sub-Saharan Africa 46.90 1 76.60 3 20.29 1 41.42 1India 34.70 2 79.90 1 7.08 2 34.43 2South Asia 31.30 3 77.20 2 6.37 3 32.35 3All regions 21.10 4 52.90 4 5.96 4 21.21 4

China 16.60 5 46.70 6 3.94 5 18.44 5East Asia 14.90 6 47.40 5 3.35 7 17.78 6Latin America and Caribbean 9.50 7 24.50 7 3.36 6 10.20 7Eastern Europe and Central Asia 3.70 8 19.70 9 0.79 8 5.94 9Middle East and North Africa 2.40 9 23.20 8 0.45 9 6.14 8

Headcount Poverty gap$1.08 $2.15 $1.08 $2.15

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Poverty: East Asia

0

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90

Headcount at $1.08 per day


Poverty gap at $1.08 per day


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Poverty: South Asia

0

10

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30

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50

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80

90

100

19

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Poverty: Latin America, Caribbean

0

5

10

15

20

25

30

35

19

81

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Poverty: Middle East and N.Africa

0

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19

81

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Poverty: Sub-Saharan Africa

0

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90

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Poverty: Eastern Europe and Central Asia

0

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Empirical robustness (2) Does it matter which poverty criterion you use?Does it matter which poverty criterion you use? An example from SpainAn example from Spain

BárcenaBárcena and Cowell (2006) and Cowell (2006) Data are from ECHPData are from ECHP OECD equivalence scale OECD equivalence scale Poverty line is 60% of 1993 median incomePoverty line is 60% of 1993 median income Does it matter which FGT index you use?Does it matter which FGT index you use?

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Poverty in Spain 1993—2000

40

50

60

70

80

90

100

110

120

1993 1994 1995 1996 1997 1998 1999 2000

FGT(1) FGT(2) FGT(3) FGT(4) FGT(5)

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Poverty measures


Poverty rankings

Conclusion

Poverty measurement

Another look at ranking issues

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Extension of poverty analysis

Now consider some further generalisationsNow 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 Can we find a counterpart to second order dominance in

welfare analysis?welfare analysis? What if we try to construct poverty indices from first What if we try to construct poverty indices from first

principles?principles?

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Poverty rankings (1)

Atkinson (1987)Atkinson (1987) connects poverty and welfare. connects poverty and welfare. Based results on the portfolio literature concerning Based results on the portfolio literature concerning

“below-target returns” “below-target returns” Theorem Theorem

Given a bounded range of poverty lines (Given a bounded range of poverty lines (zzminmin, z, zmaxmax)) and poverty measures of the ASP form and poverty measures of the ASP form a necessary and sufficient condition for poverty to be lower in a necessary and sufficient condition for poverty to be lower in

distribution distribution FF than in distribution than in distribution GG is that the poverty deficit is that the poverty deficit be no greater in be no greater in FF than in than in GG for all for all zz ≤ ≤ zzmaxmax..

Equivalent to requiring that the second-order dominance Equivalent to requiring that the second-order dominance condition hold for all condition hold for all zz. .

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Poverty rankings (2)

Foster and Shorrocks (Foster and Shorrocks (1988a1988a, 1988b) have a similar , 1988b) have a similar approach to orderings by approach to orderings by PP, ,

But concentrate on the FGT index’s particular functional But concentrate on the FGT index’s particular functional form:form:

Theorem: Poverty rankings are equivalent to Theorem: Poverty rankings are equivalent to first-order welfare dominance for first-order welfare dominance for aa = 0 = 0 second-degree welfare dominance for second-degree welfare dominance for aa = 1 = 1 (third-order welfare dominance for (third-order welfare dominance for aa = 2.) = 2.)

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Poverty concepts – more Given poverty line Given poverty line zz

a reference pointa reference point

Poverty gapPoverty gap fundamental income differencefundamental income difference

Define the number of the poor asDefine the number of the poor as:: ((xx, z, z) := #{) := #{ii:: x xii ≤≤ z z}}

Cumulative poverty gapCumulative poverty gap

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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

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Poverty measures


Poverty rankings

Conclusion

Poverty measurement

Building from first principles?

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Brief conclusion

Framework of distributional analysis covers a number of Framework of distributional analysis covers a number of related problems:related problems: Social WelfareSocial Welfare InequalityInequality PovertyPoverty

Commonality of approach can yield important insightsCommonality of approach can yield important insights Ranking principles provide basis for broad judgments Ranking principles provide basis for broad judgments

May be indecisiveMay be indecisive specific indices could be usedspecific indices could be used

Poverty trends will often be robust to choice of poverty Poverty trends will often be robust to choice of poverty indexindex

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Poverty: a way forward

Introduce a formal axiomatisation of ASP class?Introduce a formal axiomatisation of ASP class? In particular FGT measuresIn particular FGT measures See See Ebert and Moyes (2002)Ebert and Moyes (2002)

Use standard axioms introduced earlierUse standard axioms introduced earlier for analysing social welfarefor analysing social welfare for inequalityfor inequality

Show how this is related toShow how this is related to deprivationdeprivation inequalityinequality

See next lecture See next lecture

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References (1) Amiel, Y. and Cowell, F.A. (1999) Thinking about Inequality,

Cambridge University Press Atkinson, A. B. (1987)Atkinson, A. B. (1987) “On the measurement of poverty,” “On the measurement of poverty,”

EconometricaEconometrica, , 5555, 749-764, 749-764 BárcenaBárcena,, E. and Cowell, F.A. (2006) E. and Cowell, F.A. (2006) “ “Static and Dynamic Poverty in Static and Dynamic Poverty in

Spain, 1993-2000Spain, 1993-2000,” ,” Hacienda PHacienda Púública Espablica Españolañola 179179 Chen, S. and Ravallion, M. (2004)Chen, S. and Ravallion, M. (2004) “How have the world’s poorest “How have the world’s poorest

fared since the early 1980s?” World Bank Policy Research Working fared since the early 1980s?” World Bank Policy Research Working Paper Series, 3341Paper Series, 3341

Clark, S.,Hemming, R. and Ulph, D. (1981) “On indices for the Clark, S.,Hemming, R. and Ulph, D. (1981) “On indices for the measurement of poverty, measurement of poverty, The Economic JournalThe Economic Journal, , 9191, 515-526, 515-526

Cowell, F. A. and Victoria-Feser, M.-P. (1996) “Poverty Measurement Cowell, F. A. and Victoria-Feser, M.-P. (1996) “Poverty Measurement with Contaminated Data: A Robust Approach,” with Contaminated Data: A Robust Approach,” European Economic European Economic ReviewReview, , 4040, 1761-1771, 1761-1771

Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer-Thorbecke poverty orderings,” Foster-Greer-Thorbecke poverty orderings,” Journal of Public Journal of Public Economic TheoryEconomic Theory 44, 455-473., 455-473.

Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty measures,” decomposable poverty measures,” EconometricaEconometrica, , 5252, 761-776, 761-776

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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

Documents

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