Frank Cowell: Frank Cowell: UB Public Economics UB Public Economics Deprivation, Complaints and Inequality June June 2005 2005 Public Economics: University of Barcelona Public Economics: University of Barcelona Frank Cowell Frank Cowell http://darp.lse.ac.uk/ub http://darp.lse.ac.uk/ub
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Frank C
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Deprivation, Complaints and Inequality
June 2005 June 2005
Public Economics: University of Barcelona Public Economics: University of Barcelona
Frank CowellFrank Cowell
http://darp.lse.ac.uk/ubhttp://darp.lse.ac.uk/ub
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Overview...
Experimental approaches
Deprivation
Complaints
Claims
Deprivation, complaints, inequality
Background to further work
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Agenda
Begin with a look at some empirical workBegin with a look at some empirical work To what extent are ideas in previous lectures To what extent are ideas in previous lectures
supported?supported? Focus onFocus on
Risk and inequality aversionRisk and inequality aversion The fundamental axiomsThe fundamental axioms The context of distributional comparisonsThe context of distributional comparisons Role of personal characteristicsRole of personal characteristics
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Risk and inequality aversion
Examine preferences for risk and inequality Examine preferences for risk and inequality CarlssonCarlsson et al 2005 et al 2005 Use imagined societies and lotteries.Use imagined societies and lotteries. Willingness to provide for grandchildren? Willingness to provide for grandchildren?
Relative risk aversion is between 2 and 3. Relative risk aversion is between 2 and 3. Social inequality aversion?Social inequality aversion? Most people also individually inequality averseMost people also individually inequality averse
Willing to pay for living in a more equal societyWilling to pay for living in a more equal society Left-wing voters and women are both more risk and Left-wing voters and women are both more risk and
inequality averse than others.inequality averse than others.
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Background
Research programme by Amiel and CowellResearch programme by Amiel and Cowell Several references summarised in Amiel-Cowell (1999)Several references summarised in Amiel-Cowell (1999) Recent work in Recent work in AmielAmiel et al (2005) et al (2005)
Examine the extent to which individual axioms are Examine the extent to which individual axioms are supported.supported.
Also the role of personal characteristicsAlso the role of personal characteristics sexsex ageage economics educationeconomics education political viewspolitical views
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How do the axioms compare?
Source: Amiel and Cowell (1999)
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Recent work Part of a research programme that focuses on the Part of a research programme that focuses on the
way people perceive issuesway people perceive issues Lesson 1 from the past: individuals consistently Lesson 1 from the past: individuals consistently
reject some of the core principlesreject some of the core principles Pareto principlePareto principle Transfer principleTransfer principle
Lesson 2 from the past: context may be importantLesson 2 from the past: context may be important InequalityInequality Welfare…Welfare…
Can we pin down the context effect?Can we pin down the context effect?
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Beginnings of an approach Set up a joint “questionnaire experiment”Set up a joint “questionnaire experiment” Simultaneously use a variety of ethical settingsSimultaneously use a variety of ethical settings
Same experiment in different flavourSame experiment in different flavour Should the “flavouring” matter?Should the “flavouring” matter?
Systematic differences across settings?Systematic differences across settings? Special personal characteristics predispose a Special personal characteristics predispose a
particular set of attitudes? particular set of attitudes? Throw light on the ethical basis for concern with Throw light on the ethical basis for concern with
distributional issues?distributional issues? What issues?What issues?
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Distributional issues Could look at questions of monotonicity / Pareto Could look at questions of monotonicity / Pareto
principleprinciple Transfer principleTransfer principle Close relation to mean-preserving spread Close relation to mean-preserving spread
principleprinciple Serious question here at heart of inequality and Serious question here at heart of inequality and
risk analysisrisk analysis Recall the transfer principle example…Recall the transfer principle example…
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Which group seems to have the more unequal distribution?
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 1 2 3 4 5 6 7 8 9 10 11 12 13
$
$
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Mrs Amiel’s Answer
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 1 2 3 4 5 6 7 8 9 10 11 12 13
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The “Truth”
0 1 2 3 4 5 6 7 8 9 10 11 12 13
0 1 2 3 4 5 6 7 8 9 10 11 12 13
$
$
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What if we had used a different distributional criterion?
Following Atkinson, inequality rankings should Following Atkinson, inequality rankings should derive from social welfare rankingsderive from social welfare rankings
Likewise risk rankings should derive from Likewise risk rankings should derive from preference rankingspreference rankings
What would have happened if we changed the What would have happened if we changed the context of the question?context of the question? Should just be a matter of changing the flavourShould just be a matter of changing the flavour Not the substanceNot the substance
Consider the risk-inequality relationConsider the risk-inequality relation
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Harsanyi: the two models There may be conceptual problems There may be conceptual problems Are the models actually distinct?Are the models actually distinct? Nevertheless, an important foundation of modern Nevertheless, an important foundation of modern
utilitarianismutilitarianism Should be susceptible of investigation as with the Should be susceptible of investigation as with the
Questionnaire responses of international group of Questionnaire responses of international group of over 1000 studentsover 1000 students
Questionnaire experiments were run during 2003Questionnaire experiments were run during 2003
Each session run during lecture/class timeEach session run during lecture/class time
Questionnaire consisted of a combination of Questionnaire consisted of a combination of (related) numerical problems and a verbal question(related) numerical problems and a verbal question
Experiment was anonymous, but individuals were Experiment was anonymous, but individuals were asked about personal characteristicsasked about personal characteristics
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The setting
An imaginary country: AlfalandAn imaginary country: Alfaland Consists of 5 regionsConsists of 5 regions
equality of income within each regionequality of income within each region income of each region depends on policy chosen.income of each region depends on policy chosen.
One of two policies A, B is to be implementedOne of two policies A, B is to be implemented distributional consequences are knowndistributional consequences are known
What is respondent’s judgment on the outcomes?What is respondent’s judgment on the outcomes? Do this for six scenariosDo this for six scenarios Allow for indifferenceAllow for indifference
An example…An example…
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The Questionnaire
INEQUALITY QUESTIONNAIRE
This questionnaire concerns people's attitude to inequality. We would be interested in yourview, based on hypothetical situations. Because it is about attitudes there are no "right"answers. Some of the possible answers correspond to assumptions consciously made byeconomists: but these assumptions may not be good ones. Your responses will help to shedsome light on this, and we would like to thank you for your participation. The questionnaireis anonymous.
Alfaland consists of five regions that are identical in every respect other thanthe incomes of their inhabitants. Everyone within a given region receives thesame income, but personal incomes differ from region to region.
Two economic policy proposals A and B are being considered forimplementation in Alfaland next year. It is known that - apart from theirimpact on personal incomes - the two policies would have the same effect onthe population. The impact upon the regions’ incomes would depend uponthe particular state of the Alfaland economy at the time the policy (A or B) isto be introduced.
In each of questions (1) to (6) two alternative lists of incomes A and B (inAlfaland local currency) are given. Each of these pairs represents theoutcomes of the A-policy and the B-policy on the five regions in each of sixdifferent situations in which Alfaland might find itself next year. In eachcase please state which policy you consider would result in higherinequality in Alfaland by circling A or B. If you consider that the twopolicies will result in the same inequality then circle both A and B.
RISK QUESTIONNAIRE
This questionnaire concerns people's attitude to risk. We would be interested in your view,based on hypothetical situations. Because it is about attitudes there are no "right" answers.Some of the possible answers correspond to assumptions consciously made by economists: butthese assumptions may not be good ones. Your responses will help to shed some light on this,and we would like to thank you for your participation. The questionnaire is anonymous.
Alfaland consists of five regions that are identical in every respect other thanthe incomes of their inhabitants. Everyone within a given region receives thesame income, but personal incomes differ from region to region. An immigrantto Alfaland would be assigned at random, with equal probability, to any one ofthese five regions. Such a person would therefore have a 20% chance of beingon any one of five income levels.
Two economic policy proposals A and B are being considered forimplementation in Alfaland next year. It is known that - apart from their impacton personal incomes - the two policies would have the same effect on thepopulation. The impact upon the regions’ incomes would depend upon theparticular state of the Alfaland economy at the time the policy (A or B) is to beintroduced.
In each of questions (1) to (6) two alternative lists of incomes A and B (in Alfalandlocal currency) are given. Each of these pairs represents the outcomes of the A-policy and theB-policy on the five regions in each of six different situations in which Alfaland might find itselfnext year. In each case please state which policy you consider would result in higher risk for aperson immigrating to Alfaland by circling A or B. If you consider that the two policies willresult in the same risk to a potential immigrant then circle both A and B.
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Seven flavours
In each case please state which policy you In each case please state which policy you consider… consider…
1.1. would result in higher inequality in Alfaland would result in higher inequality in Alfaland 2.2. would result in higher risk for a person would result in higher risk for a person
immigrating to Alfaland immigrating to Alfaland 3.3. would result in higher risk for you as an would result in higher risk for you as an
immigrant to Alfaland immigrant to Alfaland 4.4. would result in a better situation in Alfaland would result in a better situation in Alfaland 5.5. would result in a better situation in Alfaland would result in a better situation in Alfaland 6.6. as more just for Alfaland as more just for Alfaland 7.7. would result in a fairer situation in Alfalandwould result in a fairer situation in Alfaland
Imagine that you are invited to be an outside observer of Alfaland.
Imagine that you are invited to be an outside observer of Alfaland.
Imagine that you have been assigned to one of the regions in Alfaland with an equal chance of
being in any one of the five regions.
Imagine that you have been assigned to one of the regions in Alfaland with an equal chance of
being in any one of the five regions.
Imagine that you have been assigned to one of the regions in Alfaland, but you do not know
which one.
Imagine that you have been assigned to one of the regions in Alfaland, but you do not know
which one.
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Features of Questionnaire: 1 Seven questionnaires for the price of oneSeven questionnaires for the price of one
For example risk questionnaire generated from For example risk questionnaire generated from inequality by Ctrl-Hinequality by Ctrl-H
Others in the same way.Others in the same way.
Students ranked six pairs of income vectors (A Students ranked six pairs of income vectors (A and B) in terms of risk and inequalityand B) in terms of risk and inequality
For each question B obtained from A by an For each question B obtained from A by an equalising income transfer from a rich to a poor equalising income transfer from a rich to a poor regionregion
Transfer Principle (mps principle) implies that A Transfer Principle (mps principle) implies that A is riskier/more unequal than B in all six questionsis riskier/more unequal than B in all six questions
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Numerical Questions
1) A = (2, 5, 9, 20, 30) B = (2, 6, 8, 20, 30)
2) A = (2, 5, 9, 20, 30) B = (3, 5, 9, 20, 29)
3) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 20, 29)
4) A = (2, 5, 9, 20, 30) B = (2, 10, 9, 15, 30)
5) A = (10, 10, 10, 10, 30) B = (10, 10, 10, 20, 20)
6) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 19, 30)
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Features of Questionnaire 2
Check the numerical responses with a verbal Check the numerical responses with a verbal questionquestion
Using the same story we present the issue of the Using the same story we present the issue of the principle of transfersprinciple of transfers
Then see if they want to change their minds on Then see if they want to change their minds on the numerical problemsthe numerical problems
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Questionnaire: Verbal Part
risk
risk
risk
risk
…and for risk
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Questionnaire: A Check
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The Questionnaire: Personal Characteristics
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The respondents Drawn from three countries:Drawn from three countries:
Balance of male/female respondentsBalance of male/female respondents males: 561males: 561 females: 426females: 426 (some unknown!)(some unknown!)
Both economists and non-economistsBoth economists and non-economists
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Responses to numerical questions Could examine each numerical question separatelyCould examine each numerical question separately Or (more appropriately?) as a collection of 6Or (more appropriately?) as a collection of 6 To be consistent with the theory should have the pattern To be consistent with the theory should have the pattern
AAAAAAAAAAAA for inequality/risk for inequality/risk BBBBBBBBBBBB for welfare, justice fairness for welfare, justice fairness
What is the proportion of orthodox individual-What is the proportion of orthodox individual-Q Q responses?responses?
What is the proportion of orthodox patterns?What is the proportion of orthodox patterns? Do they differ by flavour?Do they differ by flavour? First a look at results from a previous study involving just First a look at results from a previous study involving just
inequality and risk. inequality and risk. Respondents from Argentina, Belgium, Germany, Israel, UK.Respondents from Argentina, Belgium, Germany, Israel, UK.
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Probit Regression of 6 x Response A
P P > > 22
1616
5656
6060
5858
9090
7474
1515
CoefCoef P P > |> |zz||
0.120.12 11
0.100.10 99
0.000.00 9090
0.020.02 5454
-0.01-0.01 4545
0.000.00 8888
0.020.02 2121
InequalityInequalityVariableVariable
MaleMale
Economic SubjectEconomic Subject
AgeAge
EmploymentEmployment
Political opinionPolitical opinion
Income 1990Income 1990
Income Change 2010Income Change 2010
Number of observations 1153.Number of observations 1153.Explanatory variables include dummy variables for countries.Explanatory variables include dummy variables for countries.
male and economic subject lead to higher share of A male and economic subject lead to higher share of A responses, especially for riskresponses, especially for risk
CoefCoef P P > |> |zz||
0.210.21 00
0.140.14 11
0.010.01 4141
-0.01-0.01 8888
-0.01-0.01 3333
0.000.00 7676
-0.01-0.01 4848
RiskRisk
Equality of coefficients
across subgroups.
Equality of coefficients
across subgroups.
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From previous studies Consistent violations of standard distributional axiomsConsistent violations of standard distributional axioms
Both special subject and male/female were importantBoth special subject and male/female were important
More male than female students view equalising transfer More male than female students view equalising transfer as risk/inequality reducing, on each question separatelyas risk/inequality reducing, on each question separately
Also true for consistency with Transfer Principle Also true for consistency with Transfer Principle
Male/female differences are larger for risk than Male/female differences are larger for risk than inequalityinequality
Respondents are more likely to view equalising transfers Respondents are more likely to view equalising transfers as risk/inequality reducing when occurring from upper to as risk/inequality reducing when occurring from upper to lower end of distribution rather than ‘within’ the lower end of distribution rather than ‘within’ the distributiondistribution
The transfer type matters more for female and for risk The transfer type matters more for female and for risk
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Numerical Questions: Detail
1) A = (2, 5, 9, 20, 30) B = (2, 6, 8, 20, 30)
2) A = (2, 5, 9, 20, 30) B = (3, 5, 9, 20, 29)
3) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 20, 29)
4) A = (2, 5, 9, 20, 30) B = (2, 10, 9, 15, 30)
5) A = (10, 10, 10, 10, 30) B = (10, 10, 10, 20, 20)
Strict adherence to axiom is very lowStrict adherence to axiom is very low“Negative” questions get fewer orthodox answers
“Negative” questions get fewer orthodox answers
Cases involving extremes get more support
Cases involving extremes get more support
H1 dominates H2?H1 dominates H2?
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Overall results
Responses violate transfer (mps) principleResponses violate transfer (mps) principle Question pattern similar to previous studiesQuestion pattern similar to previous studies Extremes produce orthodox responsesExtremes produce orthodox responses Positive flavours exhibit higher proportion of Positive flavours exhibit higher proportion of
Same issues for risk and for welfare?Same issues for risk and for welfare? Is there a male/female effect?Is there a male/female effect? Yes if we are looking from Olympian Yes if we are looking from Olympian
Outside observer. Males more orthodox? Outside observer. Males more orthodox? Does not hold for involved observerDoes not hold for involved observer
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Regression Approach
Consider equation of the form: Consider equation of the form: ProbProb(answer (answer BB))= = bb11xx1 1 +b+b22xx2 2 +…+b+…+bnnxxnn Estimate this using probit if Estimate this using probit if is standard normal is standard normal Personal characteristics can be used as dummiesPersonal characteristics can be used as dummies Also flavours…Also flavours… Also country subsamplesAlso country subsamples
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Specification 1q1q1 q2q2 q3q3 q4q4 q5q5 q6q6 rr
sexsex0.0630.063
000.1300.130
880.1920.192
550.1880.188
000.1150.115
550.2100.210
330.1010.101
99
ageage0.0060.006
33
--0.0090.009
77
--0.0220.022
55
--0.0160.016
660.0010.001
22
--0.0140.014
000.0120.012
99
empemp
--0.1440.144
88
--0.1190.119
11
--0.0310.031
55
--0.1380.138
110.0010.001
33
--0.0830.083
550.0590.059
88
polpol0.0240.024
33
--0.0850.085
55
--0.0440.044
99
--0.0000.000
99
--0.0840.084
88
--0.0220.022
66
--0.0940.094
11
sseconssecon0.0580.058
990.2740.274
770.0540.054
440.0230.023
440.1070.107
880.0300.030
77
--0.0080.008
44
inc90inc90
--0.0470.047
11
--0.0460.046
880.0340.034
99
--0.0040.004
880.0010.001
000.0070.007
00
--0.0010.001
33
inc10inc10
--0.0180.018
660.0370.037
44
--0.0470.047
440.0120.012
330.0180.018
550.0270.027
330.0370.037
99
negquesnegquestt
--0.3860.386
22
--0.3840.384
11
--0.3720.372
00
--0.2860.286
00
--0.2670.267
11
--0.3400.340
770.9430.943
55
ukdukd
--0.2470.247
88
--0.4370.437
33
--0.4340.434
55
--0.1890.189
44
--0.4050.405
66
--0.2250.225
99
--0.0880.088
33
deutddeutd0.0790.079
77
--0.1550.155
77
--0.0630.063
00
--0.0130.013
44
--0.0150.015
880.1370.137
110.2280.228
55
significant at 10% levelsignificant at 5% level
significant at 1% level
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Specification 2q1q1 q2q2 q3q3 q4q4 q5q5 q6q6 rr
sexsex0.0560.056
990.1340.134
550.1990.199
330.1690.169
440.1110.111
550.2080.208
880.1000.100
66
ageage0.0060.006
66
--0.0090.009
99
--0.0230.023
22
--0.0140.014
330.0010.001
00
--0.0150.015
110.0120.012
66
empemp
--0.1130.113
55
--0.0820.082
88
--0.0280.028
66
--0.1120.112
990.0260.026
22
--0.0680.068
220.0850.085
00
polpol0.0250.025
66
--0.0790.079
55
--0.0410.041
99
--0.0130.013
88
--0.0790.079
22
--0.0160.016
00
--0.0960.096
55
ssbroadssbroad0.0400.040
550.2210.221
99
--0.0660.066
550.1840.184
990.0690.069
33
--0.0750.075
22
--0.0700.070
55
inc90inc90
--0.0550.055
55
--0.0470.047
000.0360.036
11
--0.0090.009
33
--0.0010.001
880.0070.007
550.0010.001
00
inc10inc10
--0.0100.010
550.0370.037
33
--0.0410.041
880.0130.013
440.0200.020
770.0310.031
440.0380.038
00
negquenegquestst
--0.3940.394
99
--0.3760.376
44
--0.3590.359
66
--0.2990.299
11
--0.2630.263
66
--0.3420.342
770.9560.956
77
ukdukd
--0.1990.199
55
--0.4220.422
55
--0.3770.377
44
--0.2070.207
99
--0.3630.363
33
--0.1550.155
44
--0.0590.059
99
deutddeutd0.1000.100
00
--0.1250.125
00
--0.0270.027
77
--0.0530.053
440.0060.006
880.1700.170
990.2520.252
99
significant at 5% level
significant at 10% level significant at 1% level
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Regression results
For regressions on the whole set of flavours…For regressions on the whole set of flavours… Get different picture of personal characteristics:Get different picture of personal characteristics:
Sex and economics not significantSex and economics not significant Perhaps political views are significantPerhaps political views are significant
But two things come through clearlyBut two things come through clearly Importance of flavour (neg/pos)Importance of flavour (neg/pos) Role of country dummiesRole of country dummies
Look more closely at subsamplesLook more closely at subsamples
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UK subsample: H1 dominates?
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Germany subsample: H1 dominates
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Israel subsample: H2 dominates!
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A second go Results from Israel were truly remarkableResults from Israel were truly remarkable Were they a fluke from the specific sample?Were they a fluke from the specific sample? Try a second sample 18 months laterTry a second sample 18 months later Just focus on the Harsanyi flavoursJust focus on the Harsanyi flavours
Conclusions Move beyond simple question of transfer/mps Move beyond simple question of transfer/mps
principleprinciple Importance of cultural background?Importance of cultural background? H1 and H2 not the sameH1 and H2 not the same In some ways reflect response patterns on riskIn some ways reflect response patterns on risk
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Overview...
Experimental approaches
Deprivation
Complaints
Claims
Deprivation, complaints, inequality
An economic interpretation of a sociological concept
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A way forward We will look at recent theoretical developments We will look at recent theoretical developments
in distributional analysisin distributional analysis Focus on alternative approaches to inequalityFocus on alternative approaches to inequality Use ideas from sociology and philosophyUse ideas from sociology and philosophy Adopt the same axiomatic approach as was used Adopt the same axiomatic approach as was used
for Povertyfor Poverty
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“Structural” axioms
Take some social evaluation function Take some social evaluation function ContinuityContinuity
Linear homogeneityLinear homogeneity
Translation invarianceTranslation invariance
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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
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
Additivity Additivity works like the independence axiomworks like the independence axiom
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Bossert-D’Ambrosio (2004)
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-Moyes (Economics Letters 2000)Ebert-Moyes (Economics Letters 2000) Different structure of reference groupDifferent structure of reference group
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Aggregate deprivation Simple approach: just sum individual deprivationSimple approach: just sum individual deprivation
Could consider an ethically weighted variantCould consider an ethically weighted variant Chakravarty-Chakraborty (EL 1984)Chakravarty-Chakraborty (EL 1984) Chakravarty-Mukherjee (SIR 1999)Chakravarty-Mukherjee (SIR 1999)
As with poverty consider relative as well as As with poverty consider relative as well as absolute indices…absolute indices…
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Aggregate deprivation (2) An ethically weighted relative indexAn ethically weighted relative index
One based on the generalised-GiniOne based on the generalised-Gini Duclos-Gregoire (RIW 2002)Duclos-Gregoire (RIW 2002)
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Overview...
Experimental approaches
Deprivation
Complaints
Claims
Deprivation, complaints, inequality
Reference groups and distributional judgments
•Model•Inequality results•Rankings and welfare
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The Temkin approach
Larry Temkin (1986, 1993) approach to inequalityLarry Temkin (1986, 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
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What is a “complaint?”
Individual’s relationship with the income Individual’s relationship with the income distributiondistribution
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
Requires a reference groupRequires a reference group effectively a reference incomeeffectively a reference income a variety of specificationsa variety of specifications
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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
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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, natural definition of complaint:For “lower” persons, natural definition of complaint:
Similar to fundamental difference for poverty:Similar to fundamental difference for poverty:
Now we replace “Now we replace “pp” with “” with “rr””
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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
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Overview...
Experimental approaches
Deprivation
Complaints
Claims
Deprivation, complaints, inequality
A new approach to inequality
•Model•Inequality results•Rankings and welfare
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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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A BOP-complaint class The Cowell-Ebert (SCW 2004) resultThe Cowell-Ebert (SCW 2004) 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 the transfer Do BOP-complaint measures satisfy the transfer
principle?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
Cowell-Ebert (SCW 2004):Cowell-Ebert (SCW 2004):
Look at some examples that satisfy thisLook at some examples that satisfy this
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Inequality contours
To examine the properties of the derived indices…To examine the properties of the derived indices… ……take the case take the case nn = 3 = 3 Draw contours of Draw contours of TT––inequality inequality
Note that both the sensitivity parameter Note that both the sensitivity parameter and the weights and the weights ww are of interest… are of interest…
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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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Inequality contours (= 1)
w1=0.75 w2=0.25
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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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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––xx1 1
.. If If –– then inequality just becomes the “upper- then inequality just becomes the “upper-
If If = 1 then inequality becomes a generalised = 1 then inequality becomes a generalised absolute Gini.absolute Gini.
“triangles”“triangles”
“Y-shapes”“Y-shapes”
HexagonsHexagons
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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
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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
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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
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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
ineq
ualit
y
A: (2,5,9,20,30)B: (2,6,9,19,30)
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The “sequence”
Temkin’s seminal contributions offer an intuitive Temkin’s seminal contributions offer an intuitive approach to considering changes in inequality.approach to considering changes 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 The rungs are fixed, but the numbers on them are
not.not. Initially everyone is on the upper rung. Initially everyone is on the upper rung. Then, one by one, people are transferred to the lower Then, one by one, people are transferred to the lower
rung.rung. What happens to inequality? What happens to inequality?
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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
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Overview...
Experimental approaches
Deprivation
Complaints
Claims
Deprivation, complaints, inequality
A replacement for the Lorenz order?
•Model•Inequality results•Rankings and welfare
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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 generally.ranking 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 comparisons.Lorenz ordering that characterises inequality comparisons. Also similar to poverty rankings with arbitrary poverty Also similar to poverty rankings with arbitrary poverty
Gives the CCC Gives the CCC cumulative-complaint contourcumulative-complaint contour Just like TIP / Poverty profileJust like TIP / Poverty profile
Use this to get a ranking Use this to get a ranking principleprinciple
i/n
r(x)
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 again Temkin’s complaints approach to income Temkin’s complaints approach to income
distribution was to be viewed in terms of “better” distribution was to be viewed in terms of “better” or “worse”or “worse”
Not just “less” or “more” inequality. Not just “less” or “more” inequality. Can incorporate the complaint-inequality index in a Can incorporate the complaint-inequality index in a
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
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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
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Overview...
Experimental approaches
Deprivation
Complaints
Claims
Deprivation, complaints, inequality
New insight on old rules
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The approach
Settling “claims” by concerned partiesSettling “claims” by concerned parties Long historical precedentLong historical precedent
Discussed in the TalmudDiscussed in the Talmud The disputed garment storyThe disputed garment story
Applies to a variety of civil disputesApplies to a variety of civil disputes All have a similar structureAll have a similar structure
Recently extended to Public EconomicsRecently extended to Public Economics ““Claims” as the basis for social justiceClaims” as the basis for social justice
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The setting Issue usually outlined in terms of parablesIssue usually outlined in terms of parables BankruptcyBankruptcy
A firm goes bustA firm goes bust Value of the failed firm is Value of the failed firm is EE Collection of creditors Collection of creditors NN with claims with claims ccii, , iiNN,, If If EE falls short of sum of falls short of sum of ccii, how do you settle?, how do you settle?
Estate divisionEstate division A person leaves estate worth A person leaves estate worth EE.. Collection of beneficiaries Collection of beneficiaries NN with claims with claims cci i on the estate on the estate iiNN If If EE falls short of sum of falls short of sum of ccii, how do you treat the beneficiaries?, how do you treat the beneficiaries? If there is a surplus, how do you treat the beneficiaries?If there is a surplus, how do you treat the beneficiaries?
TaxationTaxation Government’s plans create a social dividendGovernment’s plans create a social dividend Citizens have claims on thisCitizens have claims on this How should tax burden be allocated?How should tax burden be allocated?
A 2-person example
A 2-person example
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Two persons: Concede and divide
Irene and Janet each have a claim on an objectIrene and Janet each have a claim on an object Irene claims Irene claims ccii
Janet claims Janet claims ccii
Object is worth Object is worth EE
Transform this in terms of “concessions”Transform this in terms of “concessions” Irene is conceding max {Irene is conceding max {EE − − ccii, 0} to Janet, 0} to Janet
Janet is conceding max {Janet is conceding max {EE − − ccjj, 0} to Irene , 0} to Irene
Define surplus Define surplus SS 0 as sum of concessions 0 as sum of concessions The fairness rule gives each person a “package”The fairness rule gives each person a “package”
The concession from the other person…The concession from the other person… ……plus half the surplusplus half the surplus
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Questions
Natural extension beyond two persons?Natural extension beyond two persons? Handle Handle S S > 0 case differently?> 0 case differently? What if individual claim exceeds What if individual claim exceeds EE?? Basis for claims? Basis for claims?
Usually assumed exogenousUsually assumed exogenous
What is the economic rationale for this precedent?What is the economic rationale for this precedent? Connection with game-theoretic approachesConnection with game-theoretic approaches
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Division rules 1
CConstrained onstrained EEqual qual AAwardswards Assign equal amounts to all Assign equal amounts to all No-one must receive more than his claimNo-one must receive more than his claim
PProportionalityroportionality Scale all the claims such that the sum of all scaled claims equals Scale all the claims such that the sum of all scaled claims equals
the dividendthe dividend TTruncated runcated CClaims laims PProportionalityroportionality
First truncate claims (if necessary) by the dividendFirst truncate claims (if necessary) by the dividend Then apply proportionality to the truncated claimsThen apply proportionality to the truncated claims
CConstrained onstrained EEqual qual LLosses osses Equalise losses subject to no-one getting a negative amountEqualise losses subject to no-one getting a negative amount
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The role of rules
Find equivalent outcome from the solution to a gameFind equivalent outcome from the solution to a game Transferable utilityTransferable utility Fixed number of playersFixed number of players
Two main typesTwo main types BargainingBargaining Coalitional gamesCoalitional games
ResultsResults Show that fairness rules can be rationalised as equilibriaShow that fairness rules can be rationalised as equilibria “ “ X ~ Y ”X ~ Y ” means “rule X means “rule X corresponds to solution Y” corresponds to solution Y”
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Bargaining solutions
CEA CEA ~ ~ Nash bargainingNash bargaining Nash solution maximises sum of log utility gains from Nash solution maximises sum of log utility gains from dd Dagan and Volij (1993)Dagan and Volij (1993)
CEA CEA ~~ lexicographic egalitarianlexicographic egalitarian Gains are maximal in maximin orderGains are maximal in maximin order
P P ~ ~ weighted Nashweighted Nash A natural extension of Nash solution but with weighted sumA natural extension of Nash solution but with weighted sum
TCP TCP ~ ~ Kalai-SmorodinskyKalai-Smorodinsky Each gets max Each gets max uu subject to the others getting at least subject to the others getting at least dd
CEL CEL ~~ extended equal losses extended equal losses Illustrate in 2-
person example
Illustrate in 2-person
example
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Claims problems (1) Cake to be divided
045°
ray o
f equali
ty
Claims vector
c
xi
xj
y
Feasible set
CEA rule
Disagreement point
d
TCP rule
z
CEL rule
v
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Claims problems (2) Cake to be divided
045°
ray o
f equali
ty
Claims vector
xi
xj
y
Feasible set
y: CEA rule
d: Disagreement point
d
z: TCP rule v: CEL rule
v
c
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Division rules 2
Random arrivalRandom arrival Imagine claimants arriving one at a timeImagine claimants arriving one at a time Each person is compensated fullyEach person is compensated fully Goes on until money runs outGoes on until money runs out O’Neill (1982)O’Neill (1982)
TalmudTalmud If dividend If dividend ≥≥ half-sum of claims… half-sum of claims… ……award min {half claim, share of dividend}award min {half claim, share of dividend} Otherwise award claim Otherwise award claim − − min {half claim, share of dividend}min {half claim, share of dividend}
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Coalitional games Random arrival Random arrival ~~ Shapley valueShapley value
Expected amount that arrival of new member changes worth of coalitionExpected amount that arrival of new member changes worth of coalition O’Neill (1982)O’Neill (1982)
Talmud Talmud ~ ~ prenucleolusprenucleolus Dissatisfaction := difference between worth and sun of payoutsDissatisfaction := difference between worth and sun of payouts Then minimise dissatisfaction for most dissatisfiedThen minimise dissatisfaction for most dissatisfied Then for next most...Then for next most... Aumann and Maschler (1985)Aumann and Maschler (1985)
CEA ~ CEA ~ Dutta-Ray solutionDutta-Ray solution Core-vector that is Lorenz-maximalCore-vector that is Lorenz-maximal Dutta and Ray (1989)Dutta and Ray (1989)
Adjusted proportional ~ Adjusted proportional ~ -value-value Calculate maximum and minimum for each playerCalculate maximum and minimum for each player Choose efficient vector that lies on line joining (max,min)Choose efficient vector that lies on line joining (max,min) Curiel et al (1987)Curiel et al (1987)
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Empirical investigation (1)
Ponti et al (2002)Ponti et al (2002) Focus on three rulesFocus on three rules
CEACEA ProportionalProportional CELCEL
Subjects play four games Subjects play four games For games For games kk = 1,2,3... = 1,2,3... ...equilibrium outcome of game ...equilibrium outcome of game kk coincides with rule coincides with rule kk.. Coordination game 4...Coordination game 4... ...strategy profiles where agree on the same rule are a NE....strategy profiles where agree on the same rule are a NE.
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Empirical investigation (2)
Ponti et al (2002) resultsPonti et al (2002) results Games 1...3:Games 1...3:
Play converges to the unique equilibrium rulePlay converges to the unique equilibrium rule Confirms that claims rules are rational?Confirms that claims rules are rational?
Game 4: Game 4: proportional rule prevails as a coordination device.proportional rule prevails as a coordination device.