poverty measurement

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Poverty Measurement

July 2006 July 2006

Inequality and Poverty Measurement Inequality and Poverty Measurement

Technical University of LisbonTechnical University of Lisbon

Frank CowellFrank Cowellhttp://darp.lse.ac.uk/lisbon2006http://darp.lse.ac.uk/lisbon2006

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Issues to be addressed

Builds on @@Builds on @@ ““Distributional Equity, Social Welfare” Distributional Equity, Social Welfare”

Extension of ranking criteriaExtension of ranking criteria Parade diagramsParade diagrams Generalised Lorenz curveGeneralised Lorenz curve

Extend SWF analysis to inequalityExtend SWF analysis to inequality Examine structure of inequalityExamine structure of inequality Link with the analysis of povertyLink with the analysis of poverty

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Overview...Poverty concepts

Poverty measures

Empirical robustness

Poverty rankings

Axiomatisation

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. Sen (1979): Two main types of issues Sen (1979): Two main types of issues

Identification problemIdentification problem Aggregation problemAggregation problem

Jenkins and Lambert (1997)Jenkins and Lambert (1997): “3Is”: “3Is” IdentificationIdentification 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

Depends on definition of poverty lineDepends on definition of poverty line Exogeneity of partition?Exogeneity of partition? Asymmetric treatment of informationAsymmetric treatment of information

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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

xx*

0

pove

rty

eval

uati

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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” 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

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The distribution of poverty gaps

$0 $20 $40 $60 gaps

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Poverty measures


Poverty rankings

Axiomatisation

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, , x*x*)) 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, , x*x*) 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 depends on poverty gap.Make poverty evaluation depends on poverty gap. Normalise by poverty lineNormalise by poverty line Foster-Greer-ThorbeckeFoster-Greer-Thorbecke class class

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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,x*)

x*-x

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Poverty measures


Poverty rankings

Axiomatisation

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

10

20

30

40

50

60

70

80

90

Headcount at $1.08 per day


Poverty gap at $1.08 per day


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Poverty: South Asia

0

10

20

30

40

50

60

70

80

90

100

19

81

19

83

19

85

19

87

19

89

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91

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93

19

95

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Poverty: Latin America, Caribbean

0

5

10

15

20

25

30

35

19

81

19

83

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85

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Poverty: Middle East and N.Africa

0

5

10

15

20

25

30

35

19

81

19

83

19

85

19

87

19

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Poverty: Sub-Saharan Africa

0

10

20

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60

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80

90

19

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83

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85

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87

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Poverty: Eastern Europe and Central Asia

0

5

10

15

20

25

19

81

19

83

19

85

19

87

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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

Bárcena and Cowell (2005)Bárcena and Cowell (2005) 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

Axiomatisation

Poverty measurement

Another look at ranking issues

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Extension of poverty analysis (1)

Finally consider some generalisationsFinally 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 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 (xx**minmin, x, x**

maxmax)) 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 xx** ≤ ≤ xx**

maxmax..

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

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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 Given poverty line Given poverty line zz

a reference pointa reference point

Poverty gapPoverty gap fundamental income differencefundamental income difference

Foster et al (1984) poverty index againFoster et al (1984) poverty index again

Cumulative poverty gapCumulative poverty gap

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TIP / Poverty profile

i/n

p(x,z)/n

G(x,z)

0

Cumulative gaps versus Cumulative gaps versus population proportionspopulation proportions

Proportion of poorProportion of poor TIP curveTIP curve

Cumulative gaps versus Cumulative gaps versus population proportionspopulation proportions

Proportion of poorProportion of poor TIP curveTIP curve

TIP curves have same interpretation as GLC

TIP dominance implies unambiguously greater poverty

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Poverty measures


Poverty rankings

Axiomatisation

Poverty measurement

Building from first principles?

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Poverty: Axiomatic approach

Characterise an ordinal poverty index Characterise an ordinal poverty index PP((xx , ,zz)) See Ebert and See Ebert and MoyesMoyes (JPET 2002) (JPET 2002)

Use some of the standard axioms we introduced for Use some of the standard axioms we introduced for analysing social welfareanalysing social welfare

Apply them to Apply them to nn+1 incomes – those of the +1 incomes – those of the nn individuals individuals and the poverty lineand the poverty line

Show that Show that given just these axioms…given just these axioms… ……you are bound to get a certain type of poverty measure.you are bound to get a certain type of poverty measure.

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Poverty: The key axioms

Standard ones from lecture 2Standard ones from lecture 2 anonymityanonymity independenceindependence monotonicitymonotonicity

income increments reduce povertyincome increments reduce poverty Strengthen two other axiomsStrengthen two other axioms

scale invariancescale invariance translation invariancetranslation invariance

Also need continuityAlso need continuity Plus a focus axiomPlus a focus axiom

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A closer look at the axioms

Let Let DD denote the set of ordered income vectors denote the set of ordered income vectors The focus axiom is The focus axiom is

Scale invariance now becomesScale invariance now becomes

Independence means:Independence means:

Define the number of the poor asDefine the number of the poor as

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Ebert-Moyes (2002)

Gives two types of FGT measuresGives two types of FGT measures ““relative” versionrelative” version ““absolute” versionabsolute” version

Additivity follows from the independence axiom Additivity follows from the independence axiom

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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

Poverty indexes can be constructed from scratch using Poverty indexes can be constructed from scratch using standard axiomsstandard axioms

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References Atkinson, A. B. (1987)Atkinson, A. B. (1987) “On the measurement of poverty,” “On the measurement of poverty,” EconometricaEconometrica, , 5555, 749-764, 749-764 Bárcena, E. and Cowell, F.A. (2005) “Bárcena, E. and Cowell, F.A. (2005) “Static and Dynamic Poverty in Spain, 1993-2000Static and Dynamic Poverty in Spain, 1993-2000,” ,”

Distributional Analysis research Programme Discussion Paper 77, STICERD, LSE. Distributional Analysis research Programme Discussion Paper 77, STICERD, LSE. Chen, S. and Chen, S. and RavallionRavallion, M. (2004), M. (2004) “How have the world’s poorest fared since the early “How have the world’s poorest fared since the early

1980s?” World Bank Policy Research Working Paper Series, 33411980s?” World Bank Policy Research Working Paper Series, 3341 Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer-Thorbecke Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer-Thorbecke

poverty orderings,” poverty orderings,” Journal of Public Economic TheoryJournal of Public Economic Theory 44, 455-473., 455-473. Foster, J. E., Greer, J. and Thorbecke, E. (1984)Foster, J. E., Greer, J. and Thorbecke, E. (1984) “A class of decomposable poverty “A class of decomposable poverty

measures,” measures,” EconometricaEconometrica, , 5252, 761-776, 761-776 Foster , J. E. and Foster , J. E. and ShorrocksShorrocks, A. F. (1988a), A. F. (1988a) “Poverty orderings,” “Poverty orderings,” EconometricaEconometrica, , 5656, 173-, 173-

177177 Foster , J. E. and Shorrocks, A. F. (1988b) “Poverty orderings and welfare dominance,” Foster , J. E. and Shorrocks, A. F. (1988b) “Poverty orderings and welfare dominance,”

Social Choice and WelfareSocial Choice and Welfare, , 55,179-198,179-198 Jenkins, S. P. and Lambert, P. J. (1997) “Three ‘I’s of poverty curves, with an analysis Jenkins, S. P. and Lambert, P. J. (1997) “Three ‘I’s of poverty curves, with an analysis

of UK poverty trends,” of UK poverty trends,” Oxford Economic PapersOxford Economic Papers, , 4949, 317-327., 317-327. Sen, A. K. (1976) “Poverty: An ordinal approach to measurement,” Sen, A. K. (1976) “Poverty: An ordinal approach to measurement,” EconometricaEconometrica, , 4444, ,

219-231219-231 Sen, A. K. (1979) “Issues in the measurement of poverty,” Sen, A. K. (1979) “Issues in the measurement of poverty,” Scandinavian Journal of Scandinavian Journal of

EconomicsEconomics, , 9191, 285-307, 285-307 Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Zheng, B. (2000) “Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty

Orderings,” Orderings,” Journal of Economic TheoryJournal of Economic Theory, , 9595, 116-137, 116-137

poverty measurement

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