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Welfare Analysis of Distribution

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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The role of public economics

What is the motivation for our subject?What is the motivation for our subject? What is the reason for intervention by public sector What is the reason for intervention by public sector

in private economic activity?in private economic activity? This is a main purpose of this lectureThis is a main purpose of this lecture We will:We will:

Examine the rationale of the public sectorExamine the rationale of the public sector Analyse alternative philosophical bases for interventionAnalyse alternative philosophical bases for intervention Develop a simple model of welfare Develop a simple model of welfare

First: how to characterise the role of the public First: how to characterise the role of the public sector?sector?

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Economic rôle of government...?

Regulator and enforcerRegulator and enforcer Enforcement of property rightsEnforcement of property rights Prices, quantity, quality standardsPrices, quantity, quality standards

SpenderSpender Public goodsPublic goods Public provision of private goodsPublic provision of private goods

Revenue raiserRevenue raiser Taxes, user charges...Taxes, user charges...

RedistributorRedistributor Taxes, and spending...Taxes, and spending... A brief

agenda....

A brief agenda....

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Agenda

Previous classification is Previous classification is ad hocad hoc..

We seek a reasoned basis for the rWe seek a reasoned basis for the rôôle of public le of public sector.sector.

Use the standard microeconomic model as context.Use the standard microeconomic model as context.

Find the rFind the rôôle for the public sector in this context.le for the public sector in this context.

Examine “Equity-efficiency trade-off”.Examine “Equity-efficiency trade-off”.

Incorporate social values.Incorporate social values.

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Overview...

A model of intervention

Income, welfare, utility

The basis for redistribution

Risk and welfare

Welfare Analysis of Public Economics

Roots in basic microeconomics

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Finding room for public economics We want to ground the public sector within We want to ground the public sector within

conventional economics.conventional economics. The public sector should not be seen as a The public sector should not be seen as a

kind of alien invader.kind of alien invader. It should follow naturally from the model of It should follow naturally from the model of

the economic system.the economic system. In effect we “find room” for the public In effect we “find room” for the public

sector within sector within microeconomics .microeconomics . We begin with a standard paradigm.We begin with a standard paradigm.

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A simple model of the economy

The basics:The basics: A collection of personsA collection of persons A collection of resourcesA collection of resources A collection of firmsA collection of firms

Private ownership:Private ownership: Entitlement to the resourcesEntitlement to the resources Shares in the firmsShares in the firms

A market allocation:A market allocation: Consumption basket for each personConsumption basket for each person Output/input programme for each firmOutput/input programme for each firm A set of pricesA set of prices CompetitiveCompetitive if everyone is maximising if everyone is maximising

A complete description of the economy?

A complete description of the economy?

Determines incomes in market allocationDetermines incomes in market allocation

A complete description of a social state?

A complete description of a social state?

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Market economy: operation Assumptions:Assumptions:

Given property distributionGiven property distribution informed optimisationinformed optimisation Free contractingFree contracting Known pricesKnown prices

Implications:Implications: Incomes are automatically generated Incomes are automatically generated Equilibrium (CE) under fairly general conditionsEquilibrium (CE) under fairly general conditions

Equilibrium system: a fundamental mappingEquilibrium system: a fundamental mapping

property distribution

goodsallocation

individual welfare

Is this a means of steering the economy?Is this a means of steering the economy?

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Market economy: basic results Using the mapping seems a powerful argument. Using the mapping seems a powerful argument. It is strengthened by appeal to It is strengthened by appeal to welfare theoremswelfare theorems::

1.1. Any CE is Pareto Efficient (PE)Any CE is Pareto Efficient (PE)2.2. Any PE allocation can be “supported” by a CEAny PE allocation can be “supported” by a CE

Implications:Implications: Decide on the type of efficient outcome you want.Decide on the type of efficient outcome you want. Use political system to get resource distribution rightUse political system to get resource distribution right Use the competitive system as a delivery vehicleUse the competitive system as a delivery vehicle

But could there be trouble in this competitive But could there be trouble in this competitive paradise?paradise?

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Problems with the market ?

Why might the delivery system not work?Why might the delivery system not work? Classic issues in market failure:Classic issues in market failure:

externalitiesexternalities public goodspublic goods non-existence of equilibriumnon-existence of equilibrium

Informational problems in redistributionInformational problems in redistribution unobservable resourcesunobservable resources uncertainty about prices uncertainty about prices

Opens up natural discussion of role for public sectorOpens up natural discussion of role for public sector

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Rôle for government?

Facilitate the economic systemFacilitate the economic system Enforce property rightsEnforce property rights

Correct “market failure”Correct “market failure” ExternalitiesExternalities Public goodsPublic goods Information problemsInformation problems

Change the resource distributionChange the resource distribution But may not be possible without excessive costBut may not be possible without excessive cost

Change the relationship between resources and Change the relationship between resources and allocationsallocations A policy trade-off…?A policy trade-off…?

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Policy options

Often depicted as a trade-off.Often depicted as a trade-off. But what kind of trade-off?But what kind of trade-off? Is a trade-off actually necessary?Is a trade-off actually necessary? And how to make the choice from the trade-off And how to make the choice from the trade-off

options?options?

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An standard approach?

equity

effi

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A classic trade-off

Social values

An optimum?

Need to define terms...What is “efficiency”? What is “equity”?

Need to define terms...What is “efficiency”? What is “equity”?

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Efficiency-equity trade-off Is there necessarily a trade-off?Is there necessarily a trade-off?

Not if we can redistribute resources without transactions cost.Not if we can redistribute resources without transactions cost.

What is efficiency?What is efficiency? PE provides a criterion for the goal of efficiency itself.PE provides a criterion for the goal of efficiency itself. Pareto criterion gives no guidance away from efficient point.Pareto criterion gives no guidance away from efficient point.

Standard approach to efficiency gains and losses:Standard approach to efficiency gains and losses: A criterion for Public Economics applications such as tax design.A criterion for Public Economics applications such as tax design.

What is equity?What is equity? Raises issues of definition.Raises issues of definition. Also of the case for egalitarianism (Also of the case for egalitarianism (PuttermanPutterman et al. - JEL98 et al. - JEL98).).

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Components of the policy problem Specification of the technologySpecification of the technology

Production of private and public goodsProduction of private and public goods Enables precise definition of efficiencyEnables precise definition of efficiency

A definition of equityA definition of equity Also related concepts such as inequality Also related concepts such as inequality See later lecturesSee later lectures

An analysis of the nature of the trade-offAn analysis of the nature of the trade-off Informational problemsInformational problems See lecture on design issuesSee lecture on design issues

A statement of social preferencesA statement of social preferences What is the basis for concern with distribution?What is the basis for concern with distribution? We deal with this in the current lectureWe deal with this in the current lecture

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Welfare approaches

Ordinal approaches to welfare Ordinal approaches to welfare These are of little useThese are of little use Run into the Arrow (1953) problemRun into the Arrow (1953) problem Hence are hopelessly indecisiveHence are hopelessly indecisive

Welfarism Welfarism Uses a cardinally measurable and interpersonally Uses a cardinally measurable and interpersonally

comparable approach to welfare.comparable approach to welfare. Usually based on individualismUsually based on individualism Provides the basis for a coherent modelProvides the basis for a coherent model

Need to examine the basic building blocks…Need to examine the basic building blocks…

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Overview...

A model of intervention

Income, welfare, utility

The basis for redistribution

Risk and welfare

Welfare Analysis of Public Economics

The basic units of analysis

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Ingredients of an approach

A model of individual resourcesA model of individual resources

A measure of individual welfareA measure of individual welfare

A basis for interpersonal comparisonsA basis for interpersonal comparisons

An intellectual base for state interventionAn intellectual base for state intervention

We will deal with the first three of these now.We will deal with the first three of these now.

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Individual resources and distribution We adopt two simple paradigms concerning We adopt two simple paradigms concerning

resources:resources: The cake-sharing problemThe cake-sharing problem The general case with productionThe general case with production

Often distributional analysis can be conducted Often distributional analysis can be conducted in terms of typical individuals in terms of typical individuals ii and and jj. .

In some cases one needs a more general In some cases one needs a more general distributional notationdistributional notation

Fixed total incomeFixed total income

Incorporates incentive effectsIncorporates incentive effects

Irene and JanetIrene and Janet

The F-form approachThe F-form approach

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A simple model for the distributional problem

Two persons

The interesting distributions

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Income distributionswith given totalIncome distributionswith given total

The basic cake-sharing income-distribution problem

The feasible set

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Limitations of this basic model

Just 2 personsJust 2 persons nn 3 persons for the inequality problem 3 persons for the inequality problem

Fixed-size cakeFixed-size cake Economic growth?Economic growth? Waste through distortion?Waste through distortion?

Costlessly transferable incomesCostlessly transferable incomes The “leaky bucket” problemThe “leaky bucket” problem Analysed further in discussion of incentivesAnalysed further in discussion of incentives

Incomes or utilities?Incomes or utilities?

Essential to first-bestwelfare economicsEssential to first-bestwelfare economics

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For welfare purposes we are concerned with utility...

What is the relationship of utility to What is the relationship of utility to income?income?

What properties does utility have?What properties does utility have?

Is it measurable?Is it measurable? Is it comparable?Is it comparable?

These properties are independentThese properties are independent

We usually need bothWe usually need both

Measurability without comparability:

Imagine a world where utility is proportional to income, but the constant of proportionality is known to depend on family characteristics which may be unobservable.

Double a family’s income and you double each member’s utility; but you cannot compare utilities of persons from different families.

Measurability without comparability:

Imagine a world where utility is proportional to income, but the constant of proportionality is known to depend on family characteristics which may be unobservable.

Double a family’s income and you double each member’s utility; but you cannot compare utilities of persons from different families.

Example 1Example 1

Comparability without measurability :

Imagine a world where access to public services determines utility and the following ordering is recognised:•Gas+Electricity•Electricity only•Gas only•Neither

It makes no sense to say “U(G+E) =2U(E)”, but you could still compare individuals.

Comparability without measurability :

Imagine a world where access to public services determines utility and the following ordering is recognised:•Gas+Electricity•Electricity only•Gas only•Neither

It makes no sense to say “U(G+E) =2U(E)”, but you could still compare individuals.

Example 2Example 2

We need a simple model

of utility....

We need a simple model

of utility....

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Ingredients aa: personal attributes: personal attributes

IdentityIdentity NeedsNeeds AbilitiesAbilities Special “merit” or “desert”Special “merit” or “desert”

yy: income: income Could be exogenousCould be exogenous Or you can model as a function of attributes: Or you can model as a function of attributes: yy==yy((aa))

: individual utility: individual utility Several ways of modelling this…Several ways of modelling this… ……see belowsee below

xx: “equivalised” income: “equivalised” income Dollar/Pound/Euro units…Dollar/Pound/Euro units… Can be treated as a version of “utility”Can be treated as a version of “utility”

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Ingredients (2)

FF : distribution function : distribution function Standard tool borrowed from statisticsStandard tool borrowed from statistics

UU : utility function : utility function A variety of specifications – see belowA variety of specifications – see below Gives indicator of how “well-off” a person of given Gives indicator of how “well-off” a person of given

attributes isattributes is

: equivalisation function : equivalisation function A simple way of accounting for differences in needsA simple way of accounting for differences in needs Perhaps too simple?Perhaps too simple? We will try something different in the next lectureWe will try something different in the next lecture

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Basic questions about income

Is it unique?Is it unique?

How comprehensive should it be?How comprehensive should it be?

What is the relevant receiving unit?What is the relevant receiving unit?

Is it comparable between persons?Is it comparable between persons?

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Income: Uniqueness? Should we use univariate or multivariate analysis?Should we use univariate or multivariate analysis?

income and expenditure?income and expenditure? income and wealth?income and wealth? income over time?income over time?

A relationship between different types of “income”?A relationship between different types of “income”? covariance of earnings and asset income?covariance of earnings and asset income? conditional transfers?conditional transfers?

Several definitions may be relevant?Several definitions may be relevant? gross income?gross income? disposable income?disposable income? other concepts?other concepts?

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Income: comprehensiveness? Is income “full income”?Is income “full income”?

final income +final income + value of leisure +...?value of leisure +...?

Is income a proxy for economic welfare?Is income a proxy for economic welfare? discount for risk?discount for risk? valuation over time?..valuation over time?..

Can income be zero?Can income be zero? rental income?rental income?

... or less than zero?... or less than zero? business losses?business losses?

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Income: Comparability? Price adjustmentPrice adjustment

Normalise by price indicesNormalise by price indices Adjustment for needs and household sizeAdjustment for needs and household size

Usual approach is to introduce equivalence scalesUsual approach is to introduce equivalence scales The equivalence transformation isThe equivalence transformation is

x = ( y, a )

Usually a simplifying assumption is made.Usually a simplifying assumption is made. Write transformation as an income-independent Write transformation as an income-independent

equivalence scale:equivalence scale:

x = y / (a)

nominal incomenominal incomepersonal attributespersonal attributes

Equivalised incomeEquivalised income

Number of equivalent adultsNumber of equivalent adults

Where does the function Where does the function come from? come from?

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Equivalence Scales We will assume that there is an agreed We will assume that there is an agreed

method of determining equivalence scales.method of determining equivalence scales.

But there is a variety of possible sources of But there is a variety of possible sources of information for equivalence scales:information for equivalence scales: From official government sourcesFrom official government sources

From international bodies such as OECDFrom international bodies such as OECD

From econometric models of household budgets.From econometric models of household budgets.

Consider an example of the last of these:Consider an example of the last of these:

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A model of income and need

childless couple

couple with children

x, yyixi

sfood

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pro

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“ne

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From budget studiesFrom budget studies

Plot share of food in budget against household income A reference household type... Engel Equivalence Scale

xr yrxr yr

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Alternative models of utility = U (y)

Inter-personally comparable utilityInter-personally comparable utility = U (y; a)

Individualistic utilityIndividualistic utility May not be comparable, depending on information about May not be comparable, depending on information about a..

= U (y, F) Concern for distribution as a kind of externality Need not be benevolent concern Evidence that people are

Concerned about relative incomes “upward looking” in their comparisons. Ferrar-i-Carbonell (2005)

x= (y ; a) = y / (a) A comparable money-metric utility?A comparable money-metric utility?

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The relationship between utility and income:

= U(y)

y

= U(y)^

Increase concavityIncrease concavity

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A simple model

As an example take the As an example take the iso-elasticiso-elastic form: form:

y1 – – 1 U(y) = ———— , 1 –

We can think of We can think of as risk aversion as risk aversion But it may take on an additional welfare significanceBut it may take on an additional welfare significance

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What to do with this information?

We need a method of appraising either the We need a method of appraising either the distribution of utilities…distribution of utilities…

……or, the system by which they were or, the system by which they were producedproduced

This involves fundamentally different This involves fundamentally different approaches to welfare judgments.approaches to welfare judgments.

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Overview...

A model of intervention

Income, welfare, utility

The basis for redistribution

Risk and welfare

Welfare Analysis of Public Economics

Philosophies, social welfare and the basis for intervention

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Five intellectual bases for public action ……and five social philosophersand five social philosophers

Entitlement theoriesEntitlement theories NozickNozick

UnanimityUnanimity ParetoPareto

UtilitarianismUtilitarianism Bentham Bentham

Concern with the least advantagedConcern with the least advantaged Rawls Rawls

EgalitarianismEgalitarianism PlatoPlato

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A distributional outcome Standard cake-sharing model

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N stands for “Nozick”

N

implications for utility

possibilities

implications for utility

possibilities

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N N

Utility-possibility set

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…and that U is the same function for both Irene and Janet.

…and that U is the same function for both Irene and Janet.

Plot utility on the axes

The effect of utility interdependence

Simple cake-sharing

Assuming that U is strictly concave...Assuming that U is strictly concave...

0 i

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Should we move from N?

What is the case for shifting from the status-quo What is the case for shifting from the status-quo point?point?

Answer differs dramatically according to social Answer differs dramatically according to social philosophy:philosophy:

Entitlement approach is concerned with Entitlement approach is concerned with processprocess

Other approaches concerned with Other approaches concerned with end-statesend-states

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Entitlement approach

Focus on Nozick (Focus on Nozick (Anarchy, State and UtopiaAnarchy, State and Utopia, 1974, 1974).). Answer depends crucially on how N came aboutAnswer depends crucially on how N came about Distinguish three key issues:Distinguish three key issues:

fairness in original acquisitionfairness in original acquisition fair transfersfair transfers rectification of past injusticerectification of past injustice

Presumption is that there will be little or no role Presumption is that there will be little or no role for the Statefor the State ““Night watchman”Night watchman”

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Pareto Criterion

Pareto unanimity criterion is an end-state principlePareto unanimity criterion is an end-state principle Approve the move from N to another point…Approve the move from N to another point… ……if at least one person gainsif at least one person gains ……and no-one losesand no-one loses

IndividualisticIndividualistic Based on utilitiesBased on utilities

But utility may have a complicated relationship with But utility may have a complicated relationship with incomeincome

May depend on the income of othersMay depend on the income of others

See how Pareto applies in the simple exampleSee how Pareto applies in the simple example

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Pareto improvement: simple case

0 i

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N

No case for intervention?

No case for intervention?

The utility-possibility set again The initial point

Pareto superior points

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End-state approaches: beyond Pareto

Pareto criterion can be indecisivePareto criterion can be indecisive Alternative end state approaches use a social Alternative end state approaches use a social

welfare functionwelfare function Typically get unique solutionTypically get unique solution

What principles should this embody?What principles should this embody? Individualism?Individualism? The Pareto principle?The Pareto principle? Additivity?Additivity?

Take a simple example that combines them all...Take a simple example that combines them all...

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Benthamite approach

General principle is “Seek the greatest good of the General principle is “Seek the greatest good of the greatest number”greatest number”

This is typically interpreted as maximising the This is typically interpreted as maximising the sum of individual welfare.sum of individual welfare.

In Irene-Janet terms: In Irene-Janet terms: 1 2n More generally the SWF is: More generally the SWF is:

WB = dF()

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Distributional implications of utilitarianism Much of public economics uses utilitarianism. Much of public economics uses utilitarianism.

Efficiency criteriaEfficiency criteria Sacrifice theories in taxationSacrifice theories in taxation

But does utilitarianism provide a basis for But does utilitarianism provide a basis for egalitarian transfers?egalitarian transfers? Sen has argued that this is a common fallacySen has argued that this is a common fallacy Sen and Foster (1997)Sen and Foster (1997)

Again look at this within the simple modelAgain look at this within the simple model

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Benthamite redistribution?

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N B

ij = constantij = constant

Take a symmetric utility-possibility set

The initial distribution

Benthamite welfare contour

Maximise welfare

Optimum in this case

Implied tax/transfer

The general case?

The general case?

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Incorporates differential incentive effects etc.

Points that Pareto-dominate N

The general case... N

Anywhere above C might be a candidate

C The voluntary solution?

B. Benthamite solution

Pareto improvements

N. The status quo

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Paretianism leads to multiple solutionsBenthamite utilitarianism leads to a unique, possibly different, solution.

Paretianism leads to multiple solutionsBenthamite utilitarianism leads to a unique, possibly different, solution.

B

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General case: discussion

A motive for changing distribution?A motive for changing distribution? Nozickians might still insist that no move from N is justifiedNozickians might still insist that no move from N is justified unless it came through private voluntary actionunless it came through private voluntary action Applies even to C Applies even to C

Implementation:Implementation: Private voluntary action might not be able to implement CPrivate voluntary action might not be able to implement C Could rise if there were many individualsCould rise if there were many individuals

Case for egalitarianism?Case for egalitarianism? Clearly Bentham approach does not usually imply egalitarian Clearly Bentham approach does not usually imply egalitarian

outcome.outcome. Consider two further alternative approaches:Consider two further alternative approaches:

Concern for the least advantaged (Rawls)Concern for the least advantaged (Rawls) EgalitarianismEgalitarianism

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Rawls (1971) Rawls’ distributional philosophy is based on two Rawls’ distributional philosophy is based on two

fundamental principles:fundamental principles:1.1. each person has equal right to the most extensive scheme of each person has equal right to the most extensive scheme of

equal basic liberties compatible with a similar scheme of equal basic liberties compatible with a similar scheme of liberties for allliberties for all

2.2. society should so order its decisions as to secure the best society should so order its decisions as to secure the best outcome for the least advantagedoutcome for the least advantaged

Economic focus has usually been on 2Economic focus has usually been on 2 Argument based on reasoning behind a “veil of ignorance”Argument based on reasoning behind a “veil of ignorance” I do not know which position in society I have when making I do not know which position in society I have when making

social judgmentsocial judgment

Needs careful interpretationNeeds careful interpretation Avoid confusion with a probabilistic approach we consider Avoid confusion with a probabilistic approach we consider

laterlater

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The Rawls approach…?

What is meant by the difference principle?What is meant by the difference principle? This is typically interpreted as maximising the welfare of This is typically interpreted as maximising the welfare of

the worst-off person.the worst-off person. Based on simplistic interpretation of veil of ignorance argumentBased on simplistic interpretation of veil of ignorance argument Rawls interpreted it differentlyRawls interpreted it differently But rather vaguelyBut rather vaguely

In Irene-Janet terms: In Irene-Janet terms: min {1 2n}

So the suggested SWF is: So the suggested SWF is:

WR = {min : F()>0}

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Egalitarianism?

Origin goes back to Plato…Origin goes back to Plato… ……but reinterpreted by Meade (1974).but reinterpreted by Meade (1974).

““Superegalitarianism”Superegalitarianism” Welfare is perceived in terms of pairwise Welfare is perceived in terms of pairwise differencesdifferences: :

[[iijj]... ]...

Welfare might not be expressible as a neat additive Welfare might not be expressible as a neat additive expression involving individual utilities.expression involving individual utilities. Finds an echo in more recent welfare developmentsFinds an echo in more recent welfare developments Covered in a later lectureCovered in a later lecture

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0i

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General case (2)

R

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Contours of max min functionContours of max min function

N

ray o

f equali

ty

A 'Rawlsian' solution Superegalitarianism

Maxi-min does not imply equality

Maxi-min does not imply equality

Superegalitaranism implies equality

Superegalitaranism implies equality

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Bergson-Samuelson approach

But why an additive form of the SWF?But why an additive form of the SWF? We could just use a weaker individualistic form.We could just use a weaker individualistic form. This is the basis of the Bergson-Samuelson This is the basis of the Bergson-Samuelson

formulation formulation A generalisation A generalisation Subsumes several welfare conceptsSubsumes several welfare concepts

In Irene-Janet terms: In Irene-Janet terms: W(1 2n)

More generally the SWF is: More generally the SWF is: WBS = W(F)

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General individualistic welfare The specific welfare functions are special cases of The specific welfare functions are special cases of

Bergson-Samuelson.Bergson-Samuelson.

Most satisfy the principle of additivityMost satisfy the principle of additivity Except for the last one (utility differences)Except for the last one (utility differences)

In Irene-Janet terms this means we can write: In Irene-Janet terms this means we can write: uu((1) ) uu((2) ) uu((n) )

More generally the SWF is: More generally the SWF is:

WBSa = uu(()) dF()

This is clear for Bentham where This is clear for Bentham where uu(()=)= But…But…

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General individualistic welfare (2)

……we can say morewe can say more

Again take the Again take the iso-elasticiso-elastic form, this time of the form, this time of the (social) (social) uu-function:-function:

1 – – 1 u() = ————, 1 –

Bentham corresponds to the case Bentham corresponds to the case Max-min (“Rawls”) corresponds to the case Max-min (“Rawls”) corresponds to the case Intermediate cases (0<Intermediate cases (0<) are interesting too) are interesting too

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General case (closeup)

B W

R

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B. Benthamite ( 0)

W. Intermediate ()

R. 'Rawlsian' ( )

‘E. Superegalitarianism' (no e value)

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A brief summary

Entitlement theoriesEntitlement theories Thatcherism? Thatcherism?

UnanimityUnanimity Blairism? Blairism?

UtilitarianismUtilitarianism A basis for egalitarianism? A basis for egalitarianism?

Concern with the least advantagedConcern with the least advantaged How to be interpreted? How to be interpreted?

(Super)-egalitarianism(Super)-egalitarianism Out of fashion in UK. Out of fashion in UK. In Spain...?In Spain...?

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Overview...

A model of intervention

Income, welfare, utility

The basis for redistribution

Risk and welfare

Welfare Analysis of Public Economics

A reinvention of utilitarianism?

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But where do the values in the SWF come from...?

ConsensusConsensus Runs into the “Arrow Theorem...”Runs into the “Arrow Theorem...”

High-minded idealismHigh-minded idealism Social and private values...?Social and private values...?

The PLUM principleThe PLUM principle ““People Like Us Matter” – a cynical approachPeople Like Us Matter” – a cynical approach

The Harsanyi approachThe Harsanyi approach Based on individual rationality under uncertaintyBased on individual rationality under uncertainty

take another look...

take another look...

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High-minded idealism?

Do people care about inequality or other distributional Do people care about inequality or other distributional issues?issues?

Multiple values argumentMultiple values argument Suppose that people are “schizophrenic”Suppose that people are “schizophrenic” They have two sets of values, private and public.They have two sets of values, private and public.

Externality argumentExternality argument People treat the income distribution as a “public good”People treat the income distribution as a “public good” HochmanHochman and Rodgers (AER 1969 and Rodgers (AER 1969))

Motivates the formulation Motivates the formulation = = UU ( (y, Fy, F)) Individuals care about the income distribution Individuals care about the income distribution FF

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The PLUM principle

Interest groups may determine what the SWF isInterest groups may determine what the SWF is Champernowne and Cowell (1998)Champernowne and Cowell (1998)

No reason to suppose that it has a direct No reason to suppose that it has a direct connection with individual utilitiesconnection with individual utilities

However we may still be able to say something However we may still be able to say something about how values are/should be determinedabout how values are/should be determined

For example they should at least be consistentFor example they should at least be consistent

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An approach based on risk analysis

Social welfare is based individual utility Social welfare is based individual utility Utility is of a representative person Utility is of a representative person Harsanyi Harsanyi (Journal of Political Economy 1953, 1955)

Each citizen ranks social states on the basis of expected Each citizen ranks social states on the basis of expected utilityutility

These utilities concern life prospectsThese utilities concern life prospects made behind a “veil of ignorance” similar to Rawlsmade behind a “veil of ignorance” similar to Rawls Ignorance concerns income, wealth, social position etcIgnorance concerns income, wealth, social position etc But what of personal values?But what of personal values?

We need to reconsider and reinterpret the sum-of-utilities We need to reconsider and reinterpret the sum-of-utilities approach.approach.

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Reinterpret sum-of-utilities

The Irene-Janet version: The Irene-Janet version: 1 2n

This is equivalent to:This is equivalent to:

(1/n)1 + (1/n)2(1/n)n

Reinterpreted as: Reinterpreted as:

p11 + p22pnn, where , where pi := 1/:= 1/nn

Which is simply Which is simply EEi

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Reinterpret sum-of-utilities (2)

The formal utility function: The formal utility function: dF()

This is equivalent to: This is equivalent to: U(y) f(y)dy

Reinterpreted as: Reinterpreted as: U(y(a)) p(a) da

Which is simply Which is simply EEU(y(a))

How do we reach this conclusion…?

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Welfare and Risk? Expect links between welfare and risk analysisExpect links between welfare and risk analysis

Argument by analogy Argument by analogy Atkinson (JET 1970) on inequalityAtkinson (JET 1970) on inequality

The Harsanyi paradigm (The Harsanyi paradigm (J.Pol.E. J.Pol.E. 1953, 1955) 1953, 1955)

Harsanyi’s contribution is fundamentalHarsanyi’s contribution is fundamental Consists of two strands.Consists of two strands.

See Amiel et al (2005)See Amiel et al (2005)

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Harsanyi 1 Aggregation theoremAggregation theorem Consider preferences over set of lotteries Consider preferences over set of lotteries LL Individuals’ preferences Individuals’ preferences VVii satisfy EU axioms satisfy EU axioms ii=1,=1,

…,…,nn Social preference Social preference VV satisfies EU axioms satisfies EU axioms Assume Pareto indifference is satisfiedAssume Pareto indifference is satisfied Then there are numbers Then there are numbers aaii and and bb such that, for all such that, for all

ppLL

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Harsanyi 1 (contd) Powerful resultPowerful result Does not assume interpersonal utility comparisons. Does not assume interpersonal utility comparisons. If such comparisons ruled out, the If such comparisons ruled out, the aaii are based on are based on

the evaluator’s value judgments the evaluator’s value judgments (Harsanyi 1978, p. 227)(Harsanyi 1978, p. 227) personal?personal? arbitrary?arbitrary? the evaluator?the evaluator?

““Judges and other public officials” Judges and other public officials” (1978, p. 226)(1978, p. 226)

Need not be a member of the societyNeed not be a member of the society Must satisfy some consistency requirementsMust satisfy some consistency requirements

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Harsanyi 2 Impartial observer theorem.Impartial observer theorem. Basic idea already in Vickrey (1945).Basic idea already in Vickrey (1945). Assumes interpersonal comparisons of utility.Assumes interpersonal comparisons of utility. An impartial observer sympathetic to the interests of An impartial observer sympathetic to the interests of

each member of society makes value judgments. each member of society makes value judgments. The observer is to imagine himself being person The observer is to imagine himself being person ii..

ii’s objective circumstances’s objective circumstances ii’s preferences’s preferences

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Harsanyi 2 (contd) How to get a representative person?How to get a representative person? Thought experimentThought experiment

Evaluator imagines he has an equal chance of being any Evaluator imagines he has an equal chance of being any person in societyperson in society

Equal consideration to each person’s interests.Equal consideration to each person’s interests.

Impartial observer calculates average expected Impartial observer calculates average expected utility of each lottery in utility of each lottery in L:L:

I.e. person I.e. person jj’s expected utility’s expected utility

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Implications of Harsanyi approach

The aggregation theorem gives an argument for The aggregation theorem gives an argument for additivityadditivity

The “representative person” induces a The “representative person” induces a probabilistic approachprobabilistic approach

Then Then socialsocial welfare is found to be inherited from welfare is found to be inherited from individualindividual expected utility expected utility

But on what basis do we get the probabilities But on what basis do we get the probabilities here? here?

And is “expectations” an appropriate basis for And is “expectations” an appropriate basis for social choice?social choice?

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Harsanyi: Some difficulties

Are preferences known behind the “Veil of ignorance”?Are preferences known behind the “Veil of ignorance”? Not in the Rawls approachNot in the Rawls approach But Harsanyi assumes that representative person knows others But Harsanyi assumes that representative person knows others

utilitiesutilities

Is it useful to suppose equal ignorance?Is it useful to suppose equal ignorance? Subjective probabilities may be inconsistentSubjective probabilities may be inconsistent Should we be concerned only with expected utility?Should we be concerned only with expected utility? It is not clear that individuals view risk-choices and It is not clear that individuals view risk-choices and

distributional choices in the same way distributional choices in the same way Cowell and Schokkaert (EER 2001)Cowell and Schokkaert (EER 2001).. Carlsson et al (Economica 2005)Carlsson et al (Economica 2005)

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Identitypr

obab

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identity |

n

the veil of ignorance

the cynical approach

i

a general view

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1

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2

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3

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A difficulty with expected utility? Suppose the outcomes depend on uncertain eventsSuppose the outcomes depend on uncertain events

probabilities of Events 1,2 are (p, 1 p) Payoffs for persons (Payoffs for persons (i,ji,j) under two policies are) under two policies are

Policy Event 1 Event 2

Consider choice between policies Consider choice between policies and and Expected payoffs are:

Under : (1,0) Under : (p, 1 p)

Should society be indifferent between and ? Mobility may be important as well as expected outcome

See Diamond (Journal of Political Economy 1967)..

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Views on redistribution

Source: Ravallion and Lokshin (JPubE 2000) Clearly views on distribution depend on (i) your current

position and (ii) your expectations

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Concluding remarks We can construct a model with an individualistic base for We can construct a model with an individualistic base for

welfare comparisons.welfare comparisons. The alternative social philosophies may give support to The alternative social philosophies may give support to

redistributive arguments, redistributive arguments, But it raises some awkward questions...But it raises some awkward questions... Should the Should the socialsocial basis for redistribution rest on basis for redistribution rest on privateprivate

tastes for equality or aversion to misery? tastes for equality or aversion to misery? What if people What if people likelike seeing the poor..? seeing the poor..?

Should it rest on individual attitudes to risk?Should it rest on individual attitudes to risk? What if people are not risk-averse?What if people are not risk-averse?

We will come back to consider the implications of these We will come back to consider the implications of these questionsquestions