frank cowell: oviedo – inequality & poverty poverty measurement march 2007 inequality, poverty...
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Frank C
owell:
Frank C
owell: O
viedo – Inequality & P
overty O
viedo – Inequality & P
overty
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
Frank C
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viedo – Inequality & P
overty O
viedo – Inequality & P
overty
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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owell:
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viedo – Inequality & P
overty O
viedo – Inequality & P
overty
Overview...Poverty concepts
Poverty measures
Empirical robustness
Poverty rankings
Conclusion
Poverty measurement
…Identification and representation
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viedo – Inequality & P
overty O
viedo – Inequality & P
overty
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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viedo – Inequality & P
overty O
viedo – Inequality & P
overty
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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viedo – Inequality & P
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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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viedo – Inequality & P
overty O
viedo – Inequality & P
overty
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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overty O
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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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viedo – Inequality & P
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overty
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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viedo – Inequality & P
overty O
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The distribution of poverty gaps
$0 $20 $40 $60 gaps
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viedo – Inequality & P
overty O
viedo – Inequality & P
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Overview...Poverty concepts
Poverty measures
Empirical robustness
Poverty rankings
Conclusion
Poverty measurement
Aggregation information about poverty
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viedo – Inequality & P
overty O
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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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overty O
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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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viedo – Inequality & P
overty O
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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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viedo – Inequality & P
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overty
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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owell:
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viedo – Inequality & P
overty O
viedo – Inequality & P
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Overview...Poverty concepts
Poverty measures
Empirical robustness
Poverty rankings
Conclusion
Poverty measurement
Definitions and consequences
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overty O
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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 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
Headcount at $2.15 per day
Poverty gap at $1.08 per day
Poverty gap at $2.15 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
19
91
19
93
19
95
19
97
19
99
20
01
Headcount at $1.08 per day
Headcount at $2.15 per day
Poverty gap at $1.08 per day
Poverty gap at $2.15 per day
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Poverty: Latin America, Caribbean
0
5
10
15
20
25
30
35
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
Headcount at $1.08 per day
Headcount at $2.15 per day
Poverty gap at $1.08 per day
Poverty gap at $2.15 per day
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viedo – Inequality & P
overty O
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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
89
19
91
19
93
19
95
19
97
19
99
20
01
Headcount at $1.08 per day
Headcount at $2.15 per day
Poverty gap at $1.08 per day
Poverty gap at $2.15 per day
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viedo – Inequality & P
overty O
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Poverty: Sub-Saharan Africa
0
10
20
30
40
50
60
70
80
90
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
Headcount at $1.08 per day
Headcount at $2.15 per day
Poverty gap at $1.08 per day
Poverty gap at $2.15 per day
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viedo – Inequality & P
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Poverty: Eastern Europe and Central Asia
0
5
10
15
20
25
19
81
19
83
19
85
19
87
19
89
19
91
19
93
19
95
19
97
19
99
20
01
Headcount at $1.08 per day
Headcount at $2.15 per day
Poverty gap at $1.08 per day
Poverty gap at $2.15 per day
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owell:
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viedo – Inequality & P
overty O
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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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viedo – Inequality & P
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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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Overview...Poverty concepts
Poverty measures
Empirical robustness
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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viedo – Inequality & P
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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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viedo – Inequality & P
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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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overty O
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Overview...Poverty concepts
Poverty measures
Empirical robustness
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