Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Deprivation, Complaints and Inequality
June 2007 June 2007
Summer School on InequalitySummer School on InequalityUniversity of SienaUniversity of Siena
Frank CowellFrank Cowellhttp://darp.lse.ac.uk/siena2007http://darp.lse.ac.uk/siena2007
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Overview...
Introduction
Poverty and inequality
Deprivation
Complaints
Deprivation, complaints, inequality
Themes and methodology
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Purpose of lecture Look at recent theoretical developments in Look at recent theoretical developments in
distributional analysisdistributional analysis Consider some linked themes Consider some linked themes
alternative approaches to inequalityalternative approaches to inequality related welfare conceptsrelated welfare concepts
Use ideas from sociology and philosophyUse ideas from sociology and philosophy Use and reuse common concepts:Use and reuse common concepts:
Income differencesIncome differences Reference incomesReference incomes Formal methodologyFormal methodology
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Methodology Focus on the way modern methodology is appliedFocus on the way modern methodology is applied Exploit common structureExploit common structure
povertypoverty deprivationdeprivation complaints and inequalitycomplaints and inequality see see Cowell (2007)Cowell (2007)
Axiomatic methodAxiomatic method minimalist approachminimalist approach characterise structurecharacterise structure introduce ethicsintroduce ethics
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Basic components Income distribution: Income distribution: xx
an an nn-vector-vector population of size population of size nn person person ii has income has income xxii
Space of all income distributions: Space of all income distributions: DD RRnn
specification of this captures nature of income specification of this captures nature of income include zeros? negatives? include zeros? negatives?
An evaluation function An evaluation function :: D D → → RR
Axioms of two broad types of axiomAxioms of two broad types of axiom to impose standard structureto impose standard structure to give meaning to a particular economic problemto give meaning to a particular economic problem
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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“Structural” axioms Take some social evaluation function Take some social evaluation function
could be inequality, poverty, social welfarecould be inequality, poverty, social welfare apply standard axioms on structureapply standard axioms on structure
Axiom 1 (Continuity)Axiom 1 (Continuity). . is a continuous function is a continuous function DD→→RR..
Axiom 2 (Linear homogeneity).Axiom 2 (Linear homogeneity). For all For all xxDD and and > 0: > 0: ((xx) = ) = ((xx))
Axiom 3 (Translation independencAxiom 3 (Translation independence).e). For all For all xxDD and such that and such that RR such that such that xx1 1 DD ((xx11) = ) = ((xx))
Illustrate these using an exampleIllustrate these using an example the Absolute Gini coefficientthe Absolute Gini coefficient useful inequality measure: equals Gini useful inequality measure: equals Gini × mean income× mean income
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Structural axioms: illustration
x1
x3
x2
DD for for nn=3=3 An income distributionAn income distribution Perfect equalityPerfect equality Contours of “Absolute” GiniContours of “Absolute” Gini ContinuityContinuity
Continuous approach to Continuous approach to I I = 0= 0 Linear homogeneityLinear homogeneity
Proportionate increase in Proportionate increase in II Translation invarianceTranslation invariance
II constant constant
0 1•
x*
•These axioms repeatedly used in the following applications
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Overview...
Introduction
Poverty and inequality
Deprivation
Complaints
Deprivation, complaints, inequality
An alternative approach
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Poverty concepts (1)
The poverty line The poverty line zz a reference pointa reference point exogenously givenexogenously given
Define the number of the poor:Define the number of the poor: ((xx, z, z) := #{) := #{ii:: x xii ≤≤ z z}}
Proportional headcountProportional headcount ((xx, z, z)/)/nn
Poverty gapPoverty gap fundamental income differencefundamental income difference ggii((xx, z, z) = max (0, ) = max (0, z z x xii))
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Poverty concepts (2) Foster et al (1984)Foster et al (1984) poverty index poverty index
≥≥ 0 is a sensitivity parameter0 is a sensitivity parameter Cumulative poverty gapCumulative poverty gap
Plot Plot GGii against population proportions against population proportions Get Get TIP curveTIP curve (Jenkins and Lambert 1997) (Jenkins and Lambert 1997) TIP: “TIP: “TThree ‘hree ‘I’I’s of s of PPoverty”: (Incidence, Intensity, Inequality)overty”: (Incidence, Intensity, Inequality)
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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“Three ‘I’s of Poverty”
i/n
(x,z)/n
Gi(x,z)
0
Population proportions versus Population proportions versus cumulative gapscumulative gaps
TIP curveTIP curve Proportion of poorProportion of poor Poverty deficitPoverty deficit
Incidence of poverty is the horizontal distance
•
•
G stays constant if i >
Intensity of poverty is the vertical distance
Inequality among the poor is the curvature of the TIP
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Poverty orderings TIP curves have same interpretation TIP curves have same interpretation
as Generalised Lorenz Curves as Generalised Lorenz Curves GLC-dominance implies welfare GLC-dominance implies welfare
dominancedominance for all monotonic, separable, SWFs for all monotonic, separable, SWFs
satisfying transfer principle satisfying transfer principle (Shorrocks 1983)(Shorrocks 1983)
TIP dominance implies TIP dominance implies unambiguously greater povertyunambiguously greater poverty
holds for given poverty lineholds for given poverty line ……and virtually all poverty and virtually all poverty
measures in usemeasures in use A simple link with inequality A simple link with inequality
orderings and welfareorderings and welfare For details see Zheng (2000)For details see Zheng (2000) 0 •
•
•
•
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Poverty: Axiomatic approach Characterise an ordinal poverty index Characterise an ordinal poverty index PP((xx, , zz))
See Ebert and Moyes (2002)See Ebert and Moyes (2002) Use the standard axioms we introduced earlierUse the standard axioms we introduced earlier
some of these slightly modifiedsome of these slightly modified supplement with axioms to give meaning to povertysupplement with axioms to give meaning to poverty
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.
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Poverty: The key axioms Adapt standard axioms from social welfare Adapt standard axioms from social welfare
anonymityanonymity independenceindependence monotonicitymonotonicity
Strengthen two other axiomsStrengthen two other axioms scale invariancescale invariance translation invariancetranslation invariance
Also need continuityAlso need continuity Plus a Plus a focusfocus axiom axiom
income changes only affect poverty…income changes only affect poverty… ……if they concern the incomes of those where if they concern the incomes of those where i i ≤≤
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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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 The monotonicity axiommonotonicity axiom is is
for for xx DD, , > 0 and > 0 and xxii ≤≤ zz: : PP((xx11, , xx22,…, ,…, xxii + + …… , z , z) < ) < PP((xx11, , xx22,…, ,…, xxii , , …… , z , z) )
The The focus axiomfocus axiom is is for for xx DD and and xxii > > zz, , PP is constant in is constant in xxii
Scale invariance now becomesScale invariance now becomes if if PP((xx, , zz) = ) = PP((yy, , zz) then ) then PP((xx, , zz) = ) = PP((yy, , z z ))
Independence means:Independence means: consider consider x,yx,y DD such that such that PP((xx, , zz) = ) = PP((yy, , zz) where, for some ) where, for some i i ≤≤
,, xxii = = yyii; then, for any ; then, for any xxºº such that such that xxii─1─1≤ ≤ xxºº≤≤ xxii+1+1 and and yyii─1─1≤ ≤ xxº º ≤≤ yyii+1+1 PP((xx11, , xx22, …, , …, xxii─1─1, , xxºº, , xxii+1+1,…,,…,xxnn, , zz) = ) = PP((yy11, , yy22, …, , …, yyii─1─1, , xxºº, , yyii+1+1,…,,…,yynn, , zz))
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Ebert-Moyes (2002)
Gives two types of FGT measuresGives two types of FGT measures ““relative” versionrelative” version ““absolute” versionabsolute” version
Similarity to certain families of inequality measuresSimilarity to certain families of inequality measures Additivity follows from the independence axiom Additivity follows from the independence axiom
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Poverty and inequality: lessons Poverty indexes can be constructed from scratch Poverty indexes can be constructed from scratch Exploit the poverty line as a reference pointExploit the poverty line as a reference point Use standard axiomsUse standard axioms
applied to applied to nn+1 incomes+1 incomes Impose structureImpose structure
independenceindependence scale invariancescale invariance
Axioms to give meaningAxioms to give meaning monotonicitymonotonicity focusfocus
Use the same method in other areasUse the same method in other areas deprivationdeprivation new approaches to inequalitynew approaches to inequality
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Overview...
Introduction
Poverty and inequality
Deprivation
Complaints
Deprivation, complaints, inequality
An economic interpretation of a sociological concept
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Relative deprivation Individual Individual deprivationdeprivation
concern with position relative to others in society (Runciman, 1966) negative welfare effects when friends and neighbours become better-off?
Related to income satisfaction? D’Ambrosio and Frick (2007) D’Ambrosio and Frick (2007) focus on E. and W. Germany, 1990-2004 show happiness/satisfaction is a relative notion derive perceived well-being from being richer not simply from being rich
Do all people care about it?Do all people care about it? Ravallion and Lokshin 2005) Ravallion and Lokshin 2005) test for perceived welfare effects of relative test for perceived welfare effects of relative
deprivation in Malawideprivation in Malawi Relative deprivation is not a concern for most people, although it is for the Relative deprivation is not a concern for most people, although it is for the
comparatively well off.comparatively well off. AggregateAggregate deprivation deprivation
a social concepta social concept related to individual deprivationrelated to individual deprivation relationship to inequality and poverty?relationship to inequality and poverty?
Runciman Runciman, 1966 :“If people have no reason to expect or hope for more than they can achieve, they will be less discontent with what they have, or even grateful simply to be able to hold on to it. But if, on the other hand, they have been led to see as a possible goal the relative prosperity of some more fortunate community with which they can directly compare themselves, then they will remain discontent with their lot until they have succeeded in catching up” .
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Individual deprivation: model YitzhakiYitzhaki (1979) (1979) definition of individual deprivatoin: definition of individual deprivatoin:
Can write this in equivalent formCan write this in equivalent form
In discrete notationIn discrete notation
Use the conditional mean Use the conditional mean
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Deprivation: Axiomatic approach 1 The Better-than set for The Better-than set for ii
Focus Focus works like the poverty conceptworks like the poverty concept
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Deprivation: Axiomatic approach 2 NormalisationNormalisation
Additivity Additivity works like the independence axiomworks like the independence axiom
Frank Cow
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owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Bossert-D’Ambrosio (2006)
This is just the Yitzhaki individual deprivation This is just the Yitzhaki individual deprivation index index
There is an alternative axiomatisation There is an alternative axiomatisation Ebert and Moyes (2000)Ebert and Moyes (2000) Different structure of reference groupDifferent structure of reference group
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Aggregate deprivation Simple approach: just sum individual deprivationSimple approach: just sum individual deprivation
Could consider an ethically transformed variantCould consider an ethically transformed variant
As with poverty consider relative as well as absolute indicesAs with poverty consider relative as well as absolute indices
ChakravartyChakravarty and and ChakrabortyChakraborty (1984) (1984) Chakravarty and Mukherjee Chakravarty and Mukherjee (1999a)(1999a) (1999b)(1999b)
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Aggregate deprivation (2) Alternative approachAlternative approach Based aggregate deprivation on the generalised-GiniBased aggregate deprivation on the generalised-Gini
where where wwii are positional weightsare positional weights
Duclos and Duclos and GrégoireGrégoire (2002) (2002)
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
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Overview...
Introduction
Poverty and inequality
Deprivation
Complaints
Deprivation, complaints, inequality
Reference groups and distributional judgments
•Model•Inequality results•Rankings and welfare
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
The Temkin approach Larry Temkin (Larry Temkin (1986 1986 , 1993) approach to inequality, 1993) approach to inequality
UnconventionalUnconventional Not based on utilitarian welfare economicsNot based on utilitarian welfare economics But not a complete “outlier” But not a complete “outlier”
Common ground with other distributional analysisCommon ground with other distributional analysis PovertyPoverty deprivationdeprivation
Contains the following elements:Contains the following elements: Concept of a complaintConcept of a complaint The idea of a reference groupThe idea of a reference group A method of aggregationA method of aggregation
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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A “complaint?”
Involves the individual’s relationship Involves the individual’s relationship with the income distributionwith the income distribution
The complaint exists independentlyThe complaint exists independently does not depend on how people feeldoes not depend on how people feel does not invoke “utility” or (dis)satisfaction does not invoke “utility” or (dis)satisfaction
Complaint depends on position in Complaint depends on position in distributiondistribution
Requires a reference groupRequires a reference group effectively a reference incomeeffectively a reference income a variety of specifications a variety of specifications see also see also DevooghtDevooght (2003) (2003)
Temkin(Temkin 1986, p. 102):“To say that the best-off have nothing to complain about is in no way to impugn their moral sensibilities. They may be just as concerned about the inequality in their world as anyone else. Nor is it to deny that, insofar as one is concerned about inequality, one might have a complaint about them being as well o. as they are. It is only to recognize that, since they are at least as well o. as every other member of their world, they have nothing to complain about. Similarly, to say that the worst-off have a complaint is not to claim that they will in fact complain (they may not). It is only to recognize that it is a bad thing (unjust or unfair) for them to be worse o. than the other members of their world through no fault of their own”
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Types of reference point BOPBOP
The Best-Off PersonThe Best-Off Person Possible ambiguity if there is more than onePossible ambiguity if there is more than one By extension could consider the best-off groupBy extension could consider the best-off group
AVEAVE The AVErage incomeThe AVErage income Obvious tie-in with conventional inequality measuresObvious tie-in with conventional inequality measures A conceptual difficulty for those above the mean?A conceptual difficulty for those above the mean?
ATBOATBO All Those Better OffAll Those Better Off A “conditional” reference pointA “conditional” reference point
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Aggregation The complaint is an individual phenomenon.The complaint is an individual phenomenon. How to make the transition from this to society as How to make the transition from this to society as
a whole?a whole? Temkin makes two suggestions:Temkin makes two suggestions: Simple sumSimple sum
Just add up the complaintsJust add up the complaints Weighted sumWeighted sum
Introduce distributional weights Introduce distributional weights Then sum the weighted complaintsThen sum the weighted complaints
Frank Cow
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owell: Siena – Inequality Sum
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Siena – Inequality Summ
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The BOP Complaint
Let Let rr((xx) be the first richest person you find in ) be the first richest person you find in NN.. Person Person rr (and higher) has income (and higher) has income xxnn.. For “lower” persons, there is a natural definition of For “lower” persons, there is a natural definition of
complaint:complaint: kkii((xx) := ) := xxnn x xii
Similar to fundamental difference for poverty:Similar to fundamental difference for poverty: ggii((xx, z, z) = max (0, ) = max (0, z z x xii))
Other similarities:Other similarities: replace “replace “” with “” with “rr” ” instead of the last poor person we now have the first rich personinstead of the last poor person we now have the first rich person
Frank Cow
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owell: Siena – Inequality Sum
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Siena – Inequality Summ
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BOP-Complaint: Axiomatisation Use same structural axioms as before. Plus…Use same structural axioms as before. Plus… Monotonicity: income increments reduce complaintMonotonicity: income increments reduce complaint
IndependenceIndependence
NormalisationNormalisation
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Overview...
Introduction
Poverty and inequality
Deprivation
Complaints
Deprivation, complaints, inequality
A new approach to inequality
•Model•Inequality results•Rankings and welfare
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Implications for inequality Broadly two types of axioms with different roles.Broadly two types of axioms with different roles. Axioms on structure: Axioms on structure:
use these to determine the “shape” of the measures. use these to determine the “shape” of the measures. Transfer principles and properties of measures: Transfer principles and properties of measures:
use these to characterise ethical nature of measures use these to characterise ethical nature of measures
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owell: Siena – Inequality Sum
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A BOP-complaint class The The Cowell and Ebert (2004)Cowell and Ebert (2004) result result
Similarity of form to FGTSimilarity of form to FGT Characterises a family of distributions …Characterises a family of distributions …
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The transfer principle Do BOP-complaint measures satisfy transfer principle?Do BOP-complaint measures satisfy transfer principle?
If transfer is from richest, yesIf transfer is from richest, yes But if transfers are amongst hoi polloi, maybe not But if transfers are amongst hoi polloi, maybe not
From From Cowell and Ebert (2004) Cowell and Ebert (2004) ::
Look at some examples that do/do not satisfy this:Look at some examples that do/do not satisfy this: take the case take the case nn = 3 = 3 draw contours of draw contours of TT––inequality inequality both the sensitivity parameter both the sensitivity parameter and the weights and the weights ww are of interest… are of interest…
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Siena – Inequality Summ
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Inequality contours (=2)
w1=0.5 w2=0.5
•Now change the weights…
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Inequality contours (=2)
w1=0.75 w2=0.25
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owell: Siena – Inequality Sum
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Inequality contours (= 1)
w1=0.75 w2=0.25
Frank Cow
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owell: Siena – Inequality Sum
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By contrast: Gini contours
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Inequality contours (= 0)
w1=0.5 w2=0.5
Again change the weights…Again change the weights…
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owell: Siena – Inequality Sum
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Inequality contours (= –1)
w1=0.75 w2=0.25
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Inequality contours (= –1)
w1=0.5 w2=0.5
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Special cases If If then inequality just becomes the range, then inequality just becomes the range, xxnn––xx11
contour map becomes a set of trianglescontour map becomes a set of triangles If If –– then inequality just becomes the “upper- then inequality just becomes the “upper-
middle class” complaint: middle class” complaint: xxnn––xxn-n-1 1 . . contour map becomes a set of “Y-shapes”contour map becomes a set of “Y-shapes”
If If = 1 then inequality is a generalised absolute Gini = 1 then inequality is a generalised absolute Gini contour map is a set of hexagonscontour map is a set of hexagons
Different values of Different values of may give very different rankings may give very different rankings not all concur with orthodox view…not all concur with orthodox view… ……. corresponding to Dalton transfer principle. corresponding to Dalton transfer principle
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owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Which is more unequal?
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
A
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
B
Two points of view...
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Focus on one type of BOP complaint
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
A
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
B
B is more unequal?
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owell: Siena – Inequality Sum
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Orthodox approach
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
A
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
B
A is more unequal?
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T – inequality
16
17
18
19
20
21
22
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
in
equa
lity
A: (2,5,9,20,30)B: (2,6,9,19,30)
A is more unequal for high values of
Frank Cow
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The “sequence” Temkin also offers an intuitive approach to considering Temkin also offers an intuitive approach to considering
changes in inequalitychanges in inequality Take a simple model of a ladder with just two rungs Take a simple model of a ladder with just two rungs
The rungs are fixed, but the numbers on them are notThe rungs are fixed, but the numbers on them are not Initially everyone is on the upper rungInitially everyone is on the upper rung
One by one, people are transferred to the lower rungOne by one, people are transferred to the lower rung Start with Start with mm = 0 on lower rung = 0 on lower rung Carry on until Carry on until mm = = nn on lower rung on lower rung
What happens to inequality? What happens to inequality? Obviously zero at the two endpoints of the sequenceObviously zero at the two endpoints of the sequence But in between?But in between?
Frank Cow
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Siena – Inequality Summ
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The “sequence” (2) For the case of For the case of TT––inequality we haveinequality we have
This is increasing in This is increasing in mm if if > 0 > 0 For other cases there is a degenerate sequence in the For other cases there is a degenerate sequence in the
same directionsame direction
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
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Siena – Inequality Summ
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Overview...
Introduction
Poverty and inequality
Deprivation
Complaints
Deprivation, complaints, inequality
A replacement for the Lorenz order?
•Model•Inequality results•Rankings and welfare
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Rankings Move beyond simple inequality measuresMove beyond simple inequality measures The notion of complaint can also be used to generate a The notion of complaint can also be used to generate a
ranking principle that can be applied quite generallyranking principle that can be applied quite generally This is rather like the use of Lorenz curves to specify a This is rather like the use of Lorenz curves to specify a
Lorenz ordering that characterises inequality comparisonsLorenz ordering that characterises inequality comparisons Also similar to poverty rankings with given poverty linesAlso similar to poverty rankings with given poverty lines
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owell: Siena – Inequality Sum
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Cumulative complaints Define cumulative complaintsDefine cumulative complaints
Gives the CCC Gives the CCC cumulative-complaint contourcumulative-complaint contour Just like TIPJust like TIP
Use this to get a ranking Use this to get a ranking principleprinciple
i/n
r(x) / n
K(x)
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Complaint-ranking The class of BOP-complaint indicesThe class of BOP-complaint indices
Define complaint rankingDefine complaint ranking
Like the generalised-Lorenz resultLike the generalised-Lorenz result
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Social welfare Temkin’s complaints approach to income distribution was to Temkin’s complaints approach to income distribution was to
be viewed in terms of “better” or “worse”be viewed in terms of “better” or “worse” Not just “less” or “more” inequality. Not just “less” or “more” inequality. Can incorporate the complaint-inequality index in a welfare-Can incorporate the complaint-inequality index in a welfare-
economic framework: economic framework: WW((xx) = ) = ((XX, , TT)) XX: total income: total income TT: Temkin inequality: Temkin inequality
Linear approximation:Linear approximation: WW((xx) = ) = XX φφTT φφ is the weight attached to inequality in welfare is the weight attached to inequality in welfare gives three types of distinct pattern:gives three types of distinct pattern:
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owell: Siena – Inequality Sum
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Siena – Inequality Summ
er School
Welfare contours (φ = 1)Ja
net’
s inc
ome
Irene’s income0
ray o
f equali
ty
Two person caseTwo person case Diagram is symmetricDiagram is symmetric xx-values giving constant -values giving constant WW
Similar to “max-min” welfare function
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Welfare contours (φ < 1)Ja
net’
s inc
ome
0 Irene’s income
Two person caseTwo person case Diagram is symmetricDiagram is symmetric xx-values giving constant -values giving constant WW
Similar to Gini case
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Welfare contours (φ > 1)Ja
net’
s inc
ome
0 Irene’s income
Two person caseTwo person case Diagram is symmetricDiagram is symmetric xx-values giving constant -values giving constant WW
Captures “superegalitarianism” (Meade 1976)
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
The ATBO Complaint Again, a natural definition of complaint:Again, a natural definition of complaint:
Similar to fundamental difference for deprivation:Similar to fundamental difference for deprivation:
Use this complaint in the Temkin classUse this complaint in the Temkin class Get a form similar to Chakravarty deprivationGet a form similar to Chakravarty deprivation
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
Summary: complaints ““Complaints” provide a useful basis for inequality Complaints” provide a useful basis for inequality
analysis.analysis. Intuitive links with poverty and deprivation as Intuitive links with poverty and deprivation as
well as conventional inequality. well as conventional inequality. BOP extension provides an implementable BOP extension provides an implementable
inequality measure.inequality measure. CCCs provide an implementable ranking principleCCCs provide an implementable ranking principle
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
References (1) BossertBossert, W. and C. , W. and C. D’AmbrosioD’Ambrosio (2006) (2006) “Reference groups and individual deprivation,” “Reference groups and individual deprivation,”
Economics LettersEconomics Letters, , 9090, 421-426, 421-426 ChakravartyChakravarty, S. R. and A. B. , S. R. and A. B. ChakrabortyChakraborty (1984) (1984) “On indices of relative deprivation,” “On indices of relative deprivation,”
Economics Letters,Economics Letters, 1414, 283-287, 283-287 ChakravartyChakravarty, S. R. and D. , S. R. and D. MukherjeeMukherjee (1999a) (1999a) “Measures of deprivation and their “Measures of deprivation and their
meaning in terms of social satisfaction.” meaning in terms of social satisfaction.” Theory and DecisionTheory and Decision 47, 89-100 47, 89-100 ChakravartyChakravarty, S. R. and D. , S. R. and D. MukherjeeMukherjee (1999b) (1999b) “Ranking income distributions by “Ranking income distributions by
deprivation orderings,” deprivation orderings,” Social Indicators ResearchSocial Indicators Research 4646, 125-135.., 125-135.. Cowell, F. A. (2007)Cowell, F. A. (2007) “Gini, Deprivation and Complaints.” “Gini, Deprivation and Complaints.” inin Betti, G. and Lemmi, A. Betti, G. and Lemmi, A.
(ed.) (ed.) Advances in income inequality and concentration measuresAdvances in income inequality and concentration measures , Routledge, London. , Routledge, London. Chapter 3. Chapter 3.
Cowell, F. A. and U. Ebert (2004)Cowell, F. A. and U. Ebert (2004) “Complaints and inequality,” “Complaints and inequality,” Social Choice and Social Choice and WelfareWelfare 2323, 71-89. , 71-89.
D’Ambrosio, C. and J. R. Frick (2007) “Income satisfaction and relative deprivation: an D’Ambrosio, C. and J. R. Frick (2007) “Income satisfaction and relative deprivation: an empirical link,” empirical link,” Social Indicators Research Social Indicators Research 8181, 497–519, 497–519
DevooghtDevooght, K. (2003), K. (2003) “Measuring inequality by counting ‘complaints:’ theory and “Measuring inequality by counting ‘complaints:’ theory and empirics,” empirics,” Economics and PhilosophyEconomics and Philosophy 1919, 241 - 263,, 241 - 263,
Duclos, J.-Y. and P. Duclos, J.-Y. and P. GrégoireGrégoire (2002) (2002) “Absolute and relative deprivation and the “Absolute and relative deprivation and the measurement of poverty,” measurement of poverty,” Review of Income and WealthReview of Income and Wealth 4848, 471-492., 471-492.
Ebert, U. and P. Moyes (2000). An axiomatic characterization of Yitzhaki’s index of Ebert, U. and P. Moyes (2000). An axiomatic characterization of Yitzhaki’s index of individual deprivation. individual deprivation. Economics LettersEconomics Letters 6868, 263-270. , 263-270.
Frank Cow
ell: Frank C
owell: Siena – Inequality Sum
mer School
Siena – Inequality Summ
er School
References (2) Ebert, U. and P. Moyes (2002)Ebert, U. and P. Moyes (2002) “A simple axiomatization of the Foster-Greer- “A simple axiomatization of the Foster-Greer-
Thorbecke poverty orderings,” Thorbecke 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 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. Meade, J.E. (1976) Meade, J.E. (1976) The Just EconomyThe Just Economy, Allen and Unwin, London, Allen and Unwin, London Ravallion, M. and M. Lokshin (2005) “Who Cares About Relative Deprivation?” Ravallion, M. and M. Lokshin (2005) “Who Cares About Relative Deprivation?”
World Bank Policy Research,Working Paper, 3782World Bank Policy Research,Working Paper, 3782 Runciman, W.G. (1966) Runciman, W.G. (1966) Relative Deprivation and Social JusticeRelative Deprivation and Social Justice , Routledge, London., Routledge, London. ShorrocksShorrocks, A. F. (1983), A. F. (1983) “Ranking Income Distributions,” “Ranking Income Distributions,” EconomicaEconomica, , 5050, 3-17, 3-17 TemkinTemkin, L. S. (1986), L. S. (1986) “Inequality.” “Inequality.” Philosophy and Public AffairsPhilosophy and Public Affairs 15, 99-121. 15, 99-121. Temkin, L. S. (1993) Temkin, L. S. (1993) Inequality, Inequality, Oxford University Press, Oxford.Oxford University Press, Oxford. YitzhakiYitzhaki, S. (1979), S. (1979) “Relative deprivation and the Gini coefficient,” “Relative deprivation and the Gini coefficient,” Quarterly Journal Quarterly Journal
of Economicsof Economics 9393, 321-324. , 321-324. Zheng, B. (2000) “Poverty orderings,” Zheng, B. (2000) “Poverty orderings,” Journal of Economic SurveysJournal of Economic Surveys, , 1414, 427-466, 427-466