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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

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$

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Mrs Amiel’s Answer

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The “Truth”

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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

inequality questionnaire experimentsinequality questionnaire experiments

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Outline of Approach

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:

Germany: 344Germany: 344 Israel: 362Israel: 362 UK: 309UK: 309

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)

6) A = (2, 5, 9, 20, 30) B = (2, 6, 9, 19, 30)

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Response patterns overall

Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q6Q6

joint joint Q1-Q1-Q6Q6

IneqIneq 37.8%37.8% 71.3%71.3% 59.4%59.4% 57.3%57.3% 73.4%73.4% 46.2%46.2% 14.7%14.7%

RiskRisk 41.4%41.4% 57.9%57.9% 57.1%57.1% 56.4%56.4% 57.9%57.9% 48.6%48.6% 14.3%14.3%

Risk iRisk i 41.5%41.5% 54.9%54.9% 50.7%50.7% 47.2%47.2% 56.3%56.3% 42.3%42.3% 12.0%12.0%

Hars Hars 58.9%58.9% 80.9%80.9% 72.3%72.3% 61.0%61.0% 80.9%80.9% 56.0%56.0% 26.2%26.2%

Hars iHars i 55.0%55.0% 78.5%78.5% 65.8%65.8% 57.0%57.0% 76.5%76.5% 53.7%53.7% 24.8%24.8%

JustJust 60.9%60.9% 89.4%89.4% 78.8%78.8% 62.9%62.9% 77.5%77.5% 76.2%76.2% 32.5%32.5%

FairFair 51.7%51.7% 83.9%83.9% 71.8%71.8% 61.1%61.1% 74.5%74.5% 58.4%58.4% 26.2%26.2%

AllAll 49.8%49.8% 74.1%74.1% 65.3%65.3% 57.7%57.7% 71.2%71.2% 54.7%54.7% 21.7%21.7%

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

orthodox responsesorthodox responses Involvement?Involvement?

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Involvement

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

detachment…detachment…

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Males-females risk

Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q6Q6

joint joint Q1-Q1-Q6Q6

MalesMales RiskRisk 44.4%44.4% 66.7%66.7% 59.3%59.3% 60.5%60.5% 65.4%65.4% 58.0%58.0% 18.5%18.5%

FemalesFemales RiskRisk 37.7%37.7% 45.3%45.3% 54.7%54.7% 49.1%49.1% 50.9%50.9% 35.8%35.8% 9.4%9.4%

MalesMales Risk iRisk i 42.3%42.3% 53.5%53.5% 50.7%50.7% 46.5%46.5% 62.0%62.0% 43.7%43.7% 11.3%11.3%

FemalesFemales Risk iRisk i 46.0%46.0% 55.6%55.6% 52.4%52.4% 50.8%50.8% 52.4%52.4% 41.3%41.3% 14.3%14.3%

Non-involved risk. Males more orthodox Non-involved risk. Males more orthodox Does not hold for involved risk. Does not hold for involved risk.

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Males-females Harsanyi

Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q6Q6

joint joint Q1-Q1-Q6Q6

MalesMales Hars Hars 63.2%63.2% 81.6%81.6% 72.4%72.4% 61.8%61.8% 85.5%85.5% 61.8%61.8% 27.6%27.6%

FemalesFemales Hars Hars 54.8%54.8% 79.0%79.0% 72.6%72.6% 59.7%59.7% 74.2%74.2% 51.6%51.6% 25.8%25.8%

MalesMales Hars iHars i 51.2%51.2% 74.4%74.4% 70.7%70.7% 64.6%64.6% 81.7%81.7% 56.1%56.1% 28.0%28.0%

FemalesFemales Hars iHars i 60.9%60.9% 84.4%84.4% 59.4%59.4% 45.3%45.3% 70.3%70.3% 50.0%50.0% 20.3%20.3%

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

51 H1 flavour (outside observer)51 H1 flavour (outside observer) 50 H2 flavour (involved observer)50 H2 flavour (involved observer)

Again look at breakdown by questionsAgain look at breakdown by questions

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Israel 2005: H2 dominates again

Q1Q1 Q2Q2 Q3Q3 Q4Q4 Q5Q5 Q6Q6

joint joint Q1- Q1-Q6Q6

Hars Hars (H1)(H1) 5151 54.9%54.9% 80.4%80.4% 70.6%70.6% 68.6%68.6% 68.6%68.6% 64.7%64.7% 21.6%21.6%

Hars i Hars i (H2)(H2) 5050 62.0%62.0% 86.0%86.0% 78.0%78.0% 76.0%76.0% 78.0%78.0% 66.0%66.0% 32.0%32.0%

AllAll 101101 58.4%58.4% 83.2%83.2% 74.3%74.3% 72.3%72.3% 73.3%73.3% 65.3%65.3% 26.7%26.7%

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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

II constant constant

0

1•

x*

•

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Individual deprivation The Yitzhaki (QJE 1979) definitionThe Yitzhaki (QJE 1979) definition

Equivalent formEquivalent form

In present notationIn present notation

Use the conditional mean Use the conditional mean

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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

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Deprivation: Axiomatic approach 2 NormalisationNormalisation

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

Chakravarty-Mukherjee (TD 1999)Chakravarty-Mukherjee (TD 1999)

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-

middle class” complaint: middle class” complaint: xxnn––xxn-n-1 1 . .

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

lines.lines.

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Cumulative complaints Define cumulative complaintsDefine cumulative complaints

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

welfare-economic framework:welfare-economic framework:

Linear approximation:Linear approximation:

Total incomeTotal incomeInequalityInequality

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Welfare contours (φ=1)

A’s income

B’s

inco

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Welfare contours (φ<1)

A’s income

B’s

inco

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Welfare contours (φ>1)

A’s income

B’s

inco

me

Meade’s “superegalitarianism”

Meade’s “superegalitarianism”

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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

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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

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Claims vector

xi

xj

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Feasible set

y: CEA rule

d: Disagreement point

d

z: TCP rule v: CEL rule

v

c

z

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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.