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Frank Cowell: UB Public Economics Deprivation, Complaints and Inequality June 2005 Public Economics: University of Barcelona Frank Cowell http://darp.lse.ac.uk/ub

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Frank Cowell: UB Public Economics Overview... Experimental approaches Deprivation Complaints Claims Deprivation, complaints, inequality Background to further work

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Frank Cowell: UB Public Economics Agenda Begin with a look at some empirical work Begin with a look at some empirical work To what extent are ideas in previous lectures supported? To what extent are ideas in previous lectures supported? Focus on Focus on Risk and inequality aversion The fundamental axioms The context of distributional comparisons Role of personal characteristics

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Frank Cowell: UB Public Economics Risk and inequality aversion Examine preferences for risk and inequality Examine preferences for risk and inequality Carlsson et al 2005 Carlsson et al 2005 Carlsson et al 2005 Use imagined societies and lotteries. 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 averse Most people also individually inequality averse Willing to pay for living in a more equal society Left-wing voters and women are both more risk and inequality averse than others.

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Frank Cowell: UB Public Economics Background Research programme by Amiel and Cowell Research programme by Amiel and Cowell Several references summarised in Amiel-Cowell (1999) Recent work in Amiel et al (2005) Amiel et al (2005)Amiel et al (2005) Examine the extent to which individual axioms are supported. Examine the extent to which individual axioms are supported. Also the role of personal characteristics Also the role of personal characteristics sex age economics education political views

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Frank Cowell: UB Public Economics How do the axioms compare? Source: Amiel and Cowell (1999)

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Frank Cowell: UB Public Economics Recent work Part of a research programme that focuses on the way people perceive issues Part of a research programme that focuses on the way people perceive issues Lesson 1 from the past: individuals consistently reject some of the core principles Lesson 1 from the past: individuals consistently reject some of the core principles Pareto principle Transfer principle Lesson 2 from the past: context may be important Lesson 2 from the past: context may be important Inequality Welfare… Can we pin down the context effect? Can we pin down the context effect?

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Frank Cowell: UB Public Economics Beginnings of an approach Set up a joint “questionnaire experiment” Set up a joint “questionnaire experiment” Simultaneously use a variety of ethical settings Simultaneously use a variety of ethical settings Same experiment in different flavour Should the “flavouring” matter? Systematic differences across settings? Systematic differences across settings? Special personal characteristics predispose a particular set of attitudes? Special personal characteristics predispose a particular set of attitudes? Throw light on the ethical basis for concern with distributional issues? Throw light on the ethical basis for concern with distributional issues? What issues? What issues?

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Frank Cowell: UB Public Economics Distributional issues Could look at questions of monotonicity / Pareto principle Could look at questions of monotonicity / Pareto principle Transfer principle Transfer principle Close relation to mean-preserving spread principle Close relation to mean-preserving spread principle Serious question here at heart of inequality and risk analysis Serious question here at heart of inequality and risk analysis Recall the transfer principle example… Recall the transfer principle example…

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Frank Cowell: UB Public Economics Which group seems to have the more unequal distribution? 0123456789 10111213 0123456789 10111213 $ $

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Frank Cowell: UB Public Economics Mrs Amiel’s Answer 0123456789 10111213 0123456789 10111213 $ $

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Frank Cowell: UB Public Economics The “Truth” 0123456789 10111213 0123456789 10111213 $ $

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Frank Cowell: UB Public Economics What if we had used a different distributional criterion? Following Atkinson, inequality rankings should derive from social welfare rankings Following Atkinson, inequality rankings should derive from social welfare rankings Likewise risk rankings should derive from preference rankings Likewise risk rankings should derive from preference rankings What would have happened if we changed the context of the question? What would have happened if we changed the context of the question? Should just be a matter of changing the flavour Not the substance Consider the risk-inequality relation Consider the risk-inequality relation

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Frank Cowell: UB Public Economics 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 utilitarianism Nevertheless, an important foundation of modern utilitarianism Should be susceptible of investigation as with the inequality questionnaire experiments Should be susceptible of investigation as with the inequality questionnaire experiments

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Frank Cowell: UB Public Economics Outline of Approach Questionnaire responses of international group of over 1000 students Questionnaire responses of international group of over 1000 students Questionnaire experiments were run during 2003 Questionnaire experiments were run during 2003 Each session run during lecture/class time Each session run during lecture/class time Questionnaire consisted of a combination of (related) numerical problems and a verbal question Questionnaire consisted of a combination of (related) numerical problems and a verbal question Experiment was anonymous, but individuals were asked about personal characteristics Experiment was anonymous, but individuals were asked about personal characteristics

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Frank Cowell: UB Public Economics The setting An imaginary country: Alfaland An imaginary country: Alfaland Consists of 5 regions Consists of 5 regions equality of income within each region income of each region depends on policy chosen. One of two policies A, B is to be implemented One of two policies A, B is to be implemented distributional consequences are known What is respondent’s judgment on the outcomes? What is respondent’s judgment on the outcomes? Do this for six scenarios Allow for indifference An example… An example…

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Frank Cowell: UB Public Economics The Questionnaire

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Frank Cowell: UB Public Economics Seven flavours In each case please state which policy you consider… 1. would result in higher inequality in Alfaland 2. would result in higher risk for a person immigrating to Alfaland 3. would result in higher risk for you as an immigrant to Alfaland 4. would result in a better situation in Alfaland 5. would result in a better situation in Alfaland 6. as more just for Alfaland 7. would result in a fairer situation in 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, but you do not know which one.

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Frank Cowell: UB Public Economics Features of Questionnaire: 1 Seven questionnaires for the price of one Seven questionnaires for the price of one For example risk questionnaire generated from inequality by Ctrl-H For example risk questionnaire generated from inequality by Ctrl-H Others in the same way. Others in the same way. Students ranked six pairs of income vectors (A and B) in terms of risk and inequality Students ranked six pairs of income vectors (A and B) in terms of risk and inequality For each question B obtained from A by an equalising income transfer from a rich to a poor region For each question B obtained from A by an equalising income transfer from a rich to a poor region Transfer Principle (mps principle) implies that A is riskier/more unequal than B in all six questions Transfer Principle (mps principle) implies that A is riskier/more unequal than B in all six questions

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Frank Cowell: UB Public Economics Numerical Questions

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Frank Cowell: UB Public Economics Features of Questionnaire 2 Check the numerical responses with a verbal question Check the numerical responses with a verbal question Using the same story we present the issue of the principle of transfers Using the same story we present the issue of the principle of transfers Then see if they want to change their minds on the numerical problems Then see if they want to change their minds on the numerical problems

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Frank Cowell: UB Public Economics Questionnaire: Verbal Part risk …and for risk

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Frank Cowell: UB Public Economics Questionnaire: A Check

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Frank Cowell: UB Public Economics The Questionnaire: Personal Characteristics

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Frank Cowell: UB Public Economics The respondents Drawn from three countries: Drawn from three countries: Germany: 344 Israel: 362 UK: 309 Balance of male/female respondents Balance of male/female respondents males: 561 females: 426 (some unknown!) Both economists and non-economists Both economists and non-economists

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Frank Cowell: UB Public Economics Responses to numerical questions Could examine each numerical question separately Could examine each numerical question separately Or (more appropriately?) as a collection of 6 Or (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 AAAAAA for inequality/risk BBBBBB for welfare, justice fairness What is the proportion of orthodox individual-Q responses? What is the proportion of orthodox individual-Q 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 inequality and risk. First a look at results from a previous study involving just inequality and risk. Respondents from Argentina, Belgium, Germany, Israel, UK.

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Frank Cowell: UB Public Economics Probit Regression of 6 x Response A P > 2 16 56 60 58 90 74 15 Coef P > |z| 0.121 0.10 9 0.0090 0.0254 -0.0145 0.0088 0.0221Inequality VariableMale Economic Subject Age Employment Political opinion Income 1990 Income Change 2010 Number of observations 1153. Explanatory variables include dummy variables for countries. male and economic subject lead to higher share of A responses, especially for risk Coef P > |z| 0.210 0.141 0.0141 -0.0188 -0.0133 0.0076 -0.0148Risk Equality of coefficients across subgroups. Equality of coefficients across subgroups.

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Frank Cowell: UB Public Economics From previous studies Consistent violations of standard distributional axioms Consistent violations of standard distributional axioms Both special subject and male/female were important Both special subject and male/female were important More male than female students view equalising transfer as risk/inequality reducing, on each question separately More male than female students view equalising transfer as 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 inequality Male/female differences are larger for risk than inequality Respondents are more likely to view equalising transfers as risk/inequality reducing when occurring from upper to lower end of distribution rather than ‘within’ the distribution Respondents are more likely to view equalising transfers as risk/inequality reducing when occurring from upper to lower end of distribution rather than ‘within’ the distribution The transfer type matters more for female and for risk The transfer type matters more for female and for risk

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Frank Cowell: UB Public Economics Numerical Questions: Detail

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Frank Cowell: UB Public Economics Response patterns overallQ1Q2Q3Q4Q5Q6 joint Q1- Q6 Ineq37.8%71.3%59.4%57.3%73.4%46.2%14.7% Risk41.4%57.9%57.1%56.4%57.9%48.6%14.3% Risk i 41.5%54.9%50.7%47.2%56.3%42.3%12.0% Hars58.9%80.9%72.3%61.0%80.9%56.0%26.2% Hars i 55.0%78.5%65.8%57.0%76.5%53.7%24.8% Just60.9%89.4%78.8%62.9%77.5%76.2%32.5% Fair51.7%83.9%71.8%61.1%74.5%58.4%26.2% All49.8%74.1%65.3%57.7%71.2%54.7%21.7% Strict adherence to axiom is very low “Negative” questions get fewer orthodox answers Cases involving extremes get more support H1 dominates H2?

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Frank Cowell: UB Public Economics Overall results Responses violate transfer (mps) principle Responses violate transfer (mps) principle Question pattern similar to previous studies Question pattern similar to previous studies Extremes produce orthodox responses Extremes produce orthodox responses Positive flavours exhibit higher proportion of orthodox responses Positive flavours exhibit higher proportion of orthodox responses Involvement? Involvement?

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Frank Cowell: UB Public Economics 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 detachment… Yes if we are looking from Olympian detachment…

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Frank Cowell: UB Public Economics Males-females riskQ1Q2Q3Q4Q5Q6 joint Q1- Q6 MalesRisk44.4%66.7%59.3%60.5%65.4%58.0%18.5% FemalesRisk37.7%45.3%54.7%49.1%50.9%35.8%9.4% Males Risk i 42.3%53.5%50.7%46.5%62.0%43.7%11.3% Females 46.0%55.6%52.4%50.8%52.4%41.3%14.3% Non-involved risk. Males more orthodox Does not hold for involved risk.

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Frank Cowell: UB Public Economics Males-females HarsanyiQ1Q2Q3Q4Q5Q6 joint Q1- Q6 MalesHars63.2%81.6%72.4%61.8%85.5%61.8%27.6% FemalesHars54.8%79.0%72.6%59.7%74.2%51.6%25.8% Males Hars i 51.2%74.4%70.7%64.6%81.7%56.1%28.0% Females 60.9%84.4%59.4%45.3%70.3%50.0%20.3% Outside observer. Males more orthodox? Does not hold for involved observer

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Frank Cowell: UB Public Economics Regression Approach Consider equation of the form: Prob(answer B)= b1x1 +b2x2 +…+bnxn Estimate this using probit if is standard normal Personal characteristics can be used as dummies Also flavours… Also country subsamples

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Frank Cowell: UB Public Economics Specification 1 q1q2q3q4q5q6r sex0.06300.13080.19250.18800.11550.21030.1019 age0.0063-0.0097-0.0225-0.01660.0012-0.01400.0129 emp-0.1448-0.1191-0.0315-0.13810.0013-0.08350.0598 pol0.0243-0.0855-0.0449-0.0009-0.0848-0.0226-0.0941 ssecon0.05890.27470.05440.02340.10780.0307-0.0084 inc90-0.0471-0.04680.0349-0.00480.00100.0070-0.0013 inc10-0.01860.0374-0.04740.01230.01850.02730.0379 negquest-0.3862-0.3841-0.3720-0.2860-0.2671-0.34070.9435 ukd-0.2478-0.4373-0.4345-0.1894-0.4056-0.2259-0.0883 deutd0.0797-0.1557-0.0630-0.0134-0.01580.13710.2285 significant at 10% level significant at 5% level significant at 1% level

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Frank Cowell: UB Public Economics Specification 2 q1q2q3q4q5q6r sex0.05690.13450.19930.16940.11150.20880.1006 age0.0066-0.0099-0.0232-0.01430.0010-0.01510.0126 emp-0.1135-0.0828-0.0286-0.11290.0262-0.06820.0850 pol0.0256-0.0795-0.0419-0.0138-0.0792-0.0160-0.0965 ssbroad0.04050.2219-0.06650.18490.0693-0.0752-0.0705 inc90-0.0555-0.04700.0361-0.0093-0.00180.00750.0010 inc10-0.01050.0373-0.04180.01340.02070.03140.0380 negquest-0.3949-0.3764-0.3596-0.2991-0.2636-0.34270.9567 ukd-0.1995-0.4225-0.3774-0.2079-0.3633-0.1554-0.0599 deutd0.1000-0.1250-0.0277-0.05340.00680.17090.2529 significant at 5% level significant at 10% level significant at 1% level

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Frank Cowell: UB Public Economics 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 significant Perhaps political views are significant But two things come through clearly But two things come through clearly Importance of flavour (neg/pos) Role of country dummies Look more closely at subsamples Look more closely at subsamples

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Frank Cowell: UB Public Economics UK subsample: H1 dominates?

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Frank Cowell: UB Public Economics Germany subsample: H1 dominates

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Frank Cowell: UB Public Economics Israel subsample: H2 dominates!

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Frank Cowell: UB Public Economics A second go Results from Israel were truly remarkable Results 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 later Try a second sample 18 months later Just focus on the Harsanyi flavours Just focus on the Harsanyi flavours 51 H1 flavour (outside observer) 50 H2 flavour (involved observer) Again look at breakdown by questions Again look at breakdown by questions

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Frank Cowell: UB Public Economics Israel 2005: H2 dominates again Q1Q2Q3Q4Q5Q6 joint Q1- Q6 Hars (H1) 5154.9%80.4%70.6%68.6%68.6%64.7%21.6% Hars i (H2) 5062.0%86.0%78.0%76.0%78.0%66.0%32.0% All10158.4%83.2%74.3%72.3%73.3%65.3%26.7%

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Frank Cowell: UB Public Economics Conclusions Move beyond simple question of transfer/mps principle Move beyond simple question of transfer/mps principle Importance of cultural background? Importance of cultural background? H1 and H2 not the same H1 and H2 not the same In some ways reflect response patterns on risk In some ways reflect response patterns on risk

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Frank Cowell: UB Public Economics Overview... Experimental approaches Deprivation Complaints Claims Deprivation, complaints, inequality An economic interpretation of a sociological concept

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Frank Cowell: UB Public Economics A way forward We will look at recent theoretical developments in distributional analysis We will look at recent theoretical developments in distributional analysis Focus on alternative approaches to inequality Focus on alternative approaches to inequality Use ideas from sociology and philosophy Use ideas from sociology and philosophy Adopt the same axiomatic approach as was used for Poverty Adopt the same axiomatic approach as was used for Poverty

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Frank Cowell: UB Public Economics “Structural” axioms Take some social evaluation function Take some social evaluation function Continuity Continuity Linear homogeneity Linear homogeneity Translation invariance Translation invariance

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Frank Cowell: UB Public Economics Structural axioms: illustration x1x1 x3x3 x2x2 D for n=3 D for n=3 An income distribution An income distribution Perfect equality Perfect equality Contours of “Absolute” Gini Contours of “Absolute” Gini Continuity Continuity Continuous approach to I = 0 Linear homogeneity Linear homogeneity Proportionate increase in I Translation invariance Translation invariance I constant D for n=3 D for n=3 An income distribution An income distribution Perfect equality Perfect equality Contours of “Absolute” Gini Contours of “Absolute” Gini Continuity Continuity Continuous approach to I = 0 Linear homogeneity Linear homogeneity Proportionate increase in I Translation invariance Translation invariance I constant 0 1 x *

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Frank Cowell: UB Public Economics Individual deprivation The Yitzhaki (QJE 1979) definition The Yitzhaki (QJE 1979) definition Equivalent form Equivalent form In present notation In present notation Use the conditional mean Use the conditional mean

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Frank Cowell: UB Public Economics Deprivation: Axiomatic approach 1 The Better-than set for i The Better-than set for i Focus Focus works like the poverty concept

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Frank Cowell: UB Public Economics Deprivation: Axiomatic approach 2 Normalisation Normalisation Additivity Additivity works like the independence axiom

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Frank Cowell: UB Public Economics Bossert-D’Ambrosio (2004) This is just the Yitzhaki individual deprivation index This is just the Yitzhaki individual deprivation index There is an alternative axiomatisation There is an alternative axiomatisation Ebert-Moyes (Economics Letters 2000) Different structure of reference group

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Frank Cowell: UB Public Economics Aggregate deprivation Simple approach: just sum individual deprivation Simple approach: just sum individual deprivation Could consider an ethically weighted variant Could consider an ethically weighted variant Chakravarty-Chakraborty (EL 1984) Chakravarty-Mukherjee (SIR 1999) As with poverty consider relative as well as absolute indices… As with poverty consider relative as well as absolute indices…

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Frank Cowell: UB Public Economics Aggregate deprivation (2) An ethically weighted relative index An ethically weighted relative index Chakravarty-Mukherjee (TD 1999) One based on the generalised-Gini One based on the generalised-Gini Duclos-Gregoire (RIW 2002)

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Frank Cowell: UB Public Economics Overview... Experimental approaches Deprivation Complaints Claims Deprivation, complaints, inequality Reference groups and distributional judgments Model Inequality results Rankings and welfare

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Frank Cowell: UB Public Economics The Temkin approach Larry Temkin (1986, 1993) approach to inequality Larry Temkin (1986, 1993) approach to inequality Unconventional Not based on utilitarian welfare economics But not a complete “outlier” Common ground with other distributional analysis Common ground with other distributional analysis Poverty deprivation Contains the following elements: Contains the following elements: Concept of a complaint The idea of a reference group A method of aggregation

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Frank Cowell: UB Public Economics What is a “complaint?” Individual’s relationship with the income distribution Individual’s relationship with the income distribution The complaint exists independently The complaint exists independently does not depend on how people feel does not invoke “utility” or (dis)satisfaction Requires a reference group Requires a reference group effectively a reference income a variety of specifications

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Frank Cowell: UB Public Economics Types of reference point BOP BOP The Best-Off Person Possible ambiguity if there is more than one By extension could consider the best-off group AVE AVE The AVErage income Obvious tie-in with conventional inequality measures A conceptual difficulty for those above the mean? ATBO ATBO All Those Better Off A “conditional” reference point

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Frank Cowell: UB Public Economics Aggregation The complaint is an individual phenomenon. The complaint is an individual phenomenon. How to make the transition from this to society as a whole? How to make the transition from this to society as a whole? Temkin makes two suggestions: Temkin makes two suggestions: Simple sum Simple sum Just add up the complaints Weighted sum Weighted sum Introduce distributional weights Then sum the weighted complaints

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Frank Cowell: UB Public Economics The BOP Complaint Let r(x) be the first richest person you find in N. Let r(x) be the first richest person you find in N. Person r (and higher) has income x n. Person r (and higher) has income x n. 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 “p” with “r” Now we replace “p” with “r”

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Frank Cowell: UB Public Economics BOP-Complaint: Axiomatisation Use same structural axioms as before. Plus… Use same structural axioms as before. Plus… Monotonicity: income increments reduce complaint Monotonicity: income increments reduce complaint Independence Independence Normalisation Normalisation

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Frank Cowell: UB Public Economics Overview... Experimental approaches Deprivation Complaints Claims Deprivation, complaints, inequality A new approach to inequality Model Inequality results Rankings and welfare

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Frank Cowell: UB Public Economics 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. Transfer principles and properties of measures: Transfer principles and properties of measures: use these to characterise ethical nature of measures

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Frank Cowell: UB Public Economics A BOP-complaint class The Cowell-Ebert (SCW 2004) result The Cowell-Ebert (SCW 2004) result Similarity of form to FGT Similarity of form to FGT Characterises a family of distributions … Characterises a family of distributions …

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Frank Cowell: UB Public Economics The transfer principle Do BOP-complaint measures satisfy the transfer principle? Do BOP-complaint measures satisfy the transfer principle? If transfer is from richest, yes But if transfers are amongst hoi polloi, maybe not Cowell-Ebert (SCW 2004): Cowell-Ebert (SCW 2004): Look at some examples that satisfy this Look at some examples that satisfy this

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Frank Cowell: UB Public Economics Inequality contours To examine the properties of the derived indices… To examine the properties of the derived indices… …take the case n = 3 …take the case n = 3 Draw contours of T –inequality Draw contours of T –inequality Note that both the sensitivity parameter and the weights w are of interest… Note that both the sensitivity parameter and the weights w are of interest…

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Frank Cowell: UB Public Economics Inequality contours ( =2) w 1 =0.5 w 2 =0.5 Now change the weights…

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Frank Cowell: UB Public Economics Inequality contours ( =2) w 1 =0.75 w 2 =0.25

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Frank Cowell: UB Public Economics Inequality contours ( = 1) w 1 =0.75 w 2 =0.25

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Frank Cowell: UB Public Economics By contrast: Gini contours

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Frank Cowell: UB Public Economics Inequality contours ( = 0) w 1 =0.5 w 2 =0.5 Again change the weights… Again change the weights…

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Frank Cowell: UB Public Economics Inequality contours ( = –1) w 1 =0.75 w 2 =0.25

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Frank Cowell: UB Public Economics Inequality contours ( = –1) w 1 =0.5 w 2 =0.5

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Frank Cowell: UB Public Economics Special cases If then inequality just becomes the range, x n – x 1. If then inequality just becomes the range, x n – x 1. If – then inequality just becomes the “upper- middle class” complaint: x n –x n-1. If – then inequality just becomes the “upper- middle class” complaint: x n –x n-1. If = 1 then inequality becomes a generalised absolute Gini. If = 1 then inequality becomes a generalised absolute Gini. “triangles” “Y-shapes” Hexagons

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Frank Cowell: UB Public Economics Which is more unequal? 0 2468101214161820222426 2830 A 02468101214161820222426 2830 B

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Frank Cowell: UB Public Economics Focus on one type of BOP complaint 0 2468101214161820222426 2830 A 02468101214161820222426 2830 B

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Frank Cowell: UB Public Economics Orthodox approach 0 2468101214161820222426 2830 A 02468101214161820222426 2830 B

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Frank Cowell: UB Public Economics T – inequality

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Frank Cowell: UB Public Economics The “sequence” Temkin’s seminal contributions offer an intuitive approach to considering changes in inequality. Temkin’s seminal contributions offer an intuitive 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 not. The rungs are fixed, but the numbers on them are 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 rung. Then, one by one, people are transferred to the lower rung. What happens to inequality? What happens to inequality?

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Frank Cowell: UB Public Economics The “sequence” (2) For the case of T –inequality we have For the case of T –inequality we have This is increasing in m if > 0 This is increasing in m if > 0 For other cases there is a degenerate sequence in the same direction For other cases there is a degenerate sequence in the same direction

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Frank Cowell: UB Public Economics 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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Frank Cowell: UB Public Economics Rankings Move beyond simple inequality measures Move beyond simple inequality measures The notion of complaint can also be used to generate a ranking principle that can be applied quite generally. The notion of complaint can also be used to generate a ranking principle that can be applied quite generally. This is rather like the use of Lorenz curves to specify a Lorenz ordering that characterises inequality comparisons. This is rather like the use of Lorenz curves to specify a Lorenz ordering that characterises inequality comparisons. Also similar to poverty rankings with arbitrary poverty lines. Also similar to poverty rankings with arbitrary poverty lines.

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Frank Cowell: UB Public Economics Cumulative complaints Define cumulative complaints Define cumulative complaints Gives the CCC Gives the CCC cumulative-complaint contour Just like TIP / Poverty profile Use this to get a ranking principle Use this to get a ranking principle i/n r(x)r(x) K(x)K(x)

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Frank Cowell: UB Public Economics Complaint-ranking The class of BOP-complaint indices The class of BOP-complaint indices Define complaint ranking Define complaint ranking Like the generalised-Lorenz result Like the generalised-Lorenz result

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Frank Cowell: UB Public Economics Social welfare again Temkin’s complaints approach to income distribution was to be viewed in terms of “better” or “worse” Temkin’s complaints approach to income distribution was to be viewed in terms of “better” or “worse” Not just “less” or “more” inequality. Not just “less” or “more” inequality. Can incorporate the complaint-inequality index in a welfare-economic framework: Can incorporate the complaint-inequality index in a welfare-economic framework: Linear approximation: Linear approximation: Total income Inequality

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Frank Cowell: UB Public Economics Welfare contours (φ=1) A’s income B’s income

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Frank Cowell: UB Public Economics Welfare contours (φ<1) A’s income B’s income

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Frank Cowell: UB Public Economics Welfare contours (φ>1) A’s income B’s income Meade’s “superegalitarianism”

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Frank Cowell: UB Public Economics 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 class Use this complaint in the Temkin class Get a form similar to Chakravarty deprivation Get a form similar to Chakravarty deprivation

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Frank Cowell: UB Public Economics Summary: complaints “Complaints” provide a useful basis for inequality analysis. “Complaints” provide a useful basis for inequality analysis. Intuitive links with poverty and deprivation as well as conventional inequality. Intuitive links with poverty and deprivation as well as conventional inequality. BOP extension provides an implementable inequality measure. BOP extension provides an implementable inequality measure. CCCs provide an implementable ranking principle CCCs provide an implementable ranking principle

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Frank Cowell: UB Public Economics Overview... Experimental approaches Deprivation Complaints Claims Deprivation, complaints, inequality New insight on old rules

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Frank Cowell: UB Public Economics The approach Settling “claims” by concerned parties Settling “claims” by concerned parties Long historical precedent Long historical precedent Discussed in the Talmud The disputed garment story Applies to a variety of civil disputes Applies to a variety of civil disputes All have a similar structure Recently extended to Public Economics Recently extended to Public Economics “Claims” as the basis for social justice “Claims” as the basis for social justice

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Frank Cowell: UB Public Economics The setting Issue usually outlined in terms of parables Issue usually outlined in terms of parables Bankruptcy Bankruptcy A firm goes bust Value of the failed firm is E Collection of creditors N with claims c i, i N, If E falls short of sum of c i, how do you settle? Estate division Estate division A person leaves estate worth E. Collection of beneficiaries N with claims c i on the estate i N If E falls short of sum of c i, how do you treat the beneficiaries? If there is a surplus, how do you treat the beneficiaries? Taxation Taxation Government’s plans create a social dividend Citizens have claims on this How should tax burden be allocated? A 2-person example

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Frank Cowell: UB Public Economics Two persons: Concede and divide Irene and Janet each have a claim on an object Irene and Janet each have a claim on an object Irene claims c i Janet claims c i Object is worth E Transform this in terms of “concessions” Transform this in terms of “concessions” Irene is conceding max {E − c i, 0} to Janet Janet is conceding max {E − c j, 0} to Irene Define surplus S 0 as sum of concessions Define surplus S 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… …plus half the surplus

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Frank Cowell: UB Public Economics Questions Natural extension beyond two persons? Natural extension beyond two persons? Handle S > 0 case differently? Handle S > 0 case differently? What if individual claim exceeds E? What if individual claim exceeds E? Basis for claims? Basis for claims? Usually assumed exogenous What is the economic rationale for this precedent? What is the economic rationale for this precedent? Connection with game-theoretic approaches

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Frank Cowell: UB Public Economics Division rules 1 Constrained Equal Awards Constrained Equal Awards Assign equal amounts to all No-one must receive more than his claim Proportionality Proportionality Scale all the claims such that the sum of all scaled claims equals the dividend Truncated Claims Proportionality Truncated Claims Proportionality First truncate claims (if necessary) by the dividend Then apply proportionality to the truncated claims Constrained Equal Losses Constrained Equal Losses Equalise losses subject to no-one getting a negative amount

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Frank Cowell: UB Public Economics The role of rules Find equivalent outcome from the solution to a game Find equivalent outcome from the solution to a game Transferable utility Fixed number of players Two main types Two main types Bargaining Coalitional games Results Results Show that fairness rules can be rationalised as equilibria “ X ~ Y ” means “rule X corresponds to solution Y”

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Frank Cowell: UB Public Economics Bargaining solutions CEA ~ Nash bargaining CEA ~ Nash bargaining Nash solution maximises sum of log utility gains from d Dagan and Volij (1993) CEA ~ lexicographic egalitarian CEA ~ lexicographic egalitarian Gains are maximal in maximin order P ~ weighted Nash P ~ weighted Nash A natural extension of Nash solution but with weighted sum TCP ~ Kalai-Smorodinsky TCP ~ Kalai-Smorodinsky Each gets max u subject to the others getting at least d CEL ~ extended equal losses CEL ~ extended equal losses Illustrate in 2- person example

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Frank Cowell: UB Public Economics Claims problems (1) Cake to be divided 0 45° ray of equality Claims vector ll cll c xixi xjxj ll yll y Feasible set CEA rule Disagreement point d TCP rule ll zll z CEL rule ll vll v ll ll

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Frank Cowell: UB Public Economics Claims problems (2) Cake to be divided 0 45° ray of equality Claims vector xixi xjxj ll yll y Feasible set y: CEA rule d: Disagreement point d z: TCP rule v: CEL rule ll vll v ll ll ll cll c ll zll z

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Frank Cowell: UB Public Economics Division rules 2 Random arrival Random arrival Imagine claimants arriving one at a time Each person is compensated fully Goes on until money runs out O’Neill (1982) Talmud Talmud If dividend ≥ half-sum of claims… …award min {half claim, share of dividend} Otherwise award claim − min {half claim, share of dividend}

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Frank Cowell: UB Public Economics Coalitional games Random arrival ~ Shapley value Random arrival ~ Shapley value Expected amount that arrival of new member changes worth of coalition O’Neill (1982) Talmud ~ prenucleolus Talmud ~ prenucleolus Dissatisfaction := difference between worth and sun of payouts Then minimise dissatisfaction for most dissatisfied Then for next most... Aumann and Maschler (1985) CEA ~ Dutta-Ray solution CEA ~ Dutta-Ray solution Core-vector that is Lorenz-maximal Dutta and Ray (1989) Adjusted proportional ~ -value Adjusted proportional ~ -value Calculate maximum and minimum for each player Choose efficient vector that lies on line joining (max,min) Curiel et al (1987)

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Frank Cowell: UB Public Economics Empirical investigation (1) Ponti et al (2002) Ponti et al (2002) Focus on three rules Focus on three rules CEA Proportional CEL Subjects play four games Subjects play four games For games k = 1,2,3... ...equilibrium outcome of game k coincides with rule k. Coordination game 4... ...strategy profiles where agree on the same rule are a NE.

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Frank Cowell: UB Public Economics Empirical investigation (2) Ponti et al (2002) results Ponti et al (2002) results Games 1...3: Games 1...3: Play converges to the unique equilibrium rule Confirms that claims rules are rational? Game 4: Game 4: proportional rule prevails as a coordination device.

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Chapter 1: Expressions, Equations, & Inequalities

Chapter 1: Expressions, Equations, & Inequalities

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