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MSc Public Economics 2011/12

http://darp.lse.ac.uk/ec426

Equity, Social Welfare and TaxationEquity, Social Welfare and Taxation

Frank A. Cowell Frank A. Cowell

10 October 2011

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Welfare and distributional analysis

We’ve seen welfare-economics basis for redistribution as a We’ve seen welfare-economics basis for redistribution as a policy objectivepolicy objective

how to assess the impact and effectiveness of such policy?how to assess the impact and effectiveness of such policy? need appropriate criteria for comparing distributions of incomeneed appropriate criteria for comparing distributions of income issues of distributional analysis (issues of distributional analysis (Cowell 2008, 2011)

Distributional analysis covers broad class of economic problemsDistributional analysis covers broad class of economic problems inequalityinequality social welfaresocial welfare povertypoverty

Similar techniquesSimilar techniques rankingsrankings measuresmeasures

Four basic components need to be clarifiedFour basic components need to be clarified ““income” conceptincome” concept ““income receiving unit” conceptincome receiving unit” concept a distributiona distribution method of assessment or comparisonmethod of assessment or comparison

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1: “Irene and Janet” approach

0Irene's income

Jan

et's

inco

me

Karen's income

ix

kx

xj

ray of e

quality

A representation with 3 incomes Income distributions with given total X

xi + xj + xk = Xxi + xj + xk = X

Feasible income distributions given X

Equal income distributions

particularly appropriate in particularly appropriate in approaches to the subject approaches to the subject based primarily upon based primarily upon individualistic welfare criteriaindividualistic welfare criteria

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2: The parade

x

0.2 0.8 10

x0.8

q

"in

com

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hei

ght)

proportion of the population

x0.2

especially useful in cases especially useful in cases where it is appropriate to where it is appropriate to adopt a parametric model adopt a parametric model of income distributionof income distribution

Pen (1971)Pen (1971)

0

1

x

F(x)

x0

F(x0)distribution function F(∙)

Plot income against proportion of population

Parade in ascending order of "income" / height Related to familiar statistical concept

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Overview...Welfare axioms

Rankings

Equity and social welfare

Taxation and sacrifice

Equity, Social Welfare, Taxation

Basic principles of distributional comparisons

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Social-welfare functions

A standard approach to a method of assessmentA standard approach to a method of assessment Basic tool is a Basic tool is a social welfare functionsocial welfare function (SWF) (SWF)

Maps set of distributions into the real lineMaps set of distributions into the real line I.e. for each distribution we get one specific numberI.e. for each distribution we get one specific number In Irene-Janet notation In Irene-Janet notation W = WW = W((xx11, , xx22,…,,…,xxnn ) )

Properties will depend on economic principlesProperties will depend on economic principles Simple example of a SWF:Simple example of a SWF:

Total income in the economy Total income in the economy WW = = xxii

Perhaps not very interestingPerhaps not very interesting Consider principles on whichConsider principles on which SWF could be basedSWF could be based

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The approach

There is no such thing as a “right” or “wrong” axiomThere is no such thing as a “right” or “wrong” axiom However axioms could be appropriate or inappropriateHowever axioms could be appropriate or inappropriate

Need some standard of “reasonableness”Need some standard of “reasonableness” For example, how do people view income distribution comparisons?For example, how do people view income distribution comparisons?

Use a simple framework to list some of the basic axiomsUse a simple framework to list some of the basic axioms Assume a fixed population of size Assume a fixed population of size nn Assume that individual utility can be measured by Assume that individual utility can be measured by xx Income normalised by equivalence scalesIncome normalised by equivalence scales Rules out utility interdependenceRules out utility interdependence Welfare is just a function of the vector Welfare is just a function of the vector xx := ( := (xx11, , xx22,…,,…,xxnn ) )

Follow the approach of Follow the approach of Amiel-Cowell (1999) Appendix A Appendix A

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SWF axioms

Anonymity. Suppose x′ is a permutation of x. Then: W(x′) = W(x)

Population principle. W(x) W(y) W(x,x,…,x) W(y,y,…,y)

Decomposability. Suppose x' is formed by joining x with z and y' is formed by joining y with z. Then :

W(x) W(y) W(x') W(y')

Monotonicity. W(x1,x2..., xi+,..., xn) > W(x1,x2,..., xi,..., xn)

Transfer principle. (Dalton 1920) Suppose xi< xj then for small :

W(x1,x2..., xi+ ,..., xj ,..., xn) > W(x1,x2,..., xi,..., xn)

Scale invariance. W(x) W(y) W(x) W(y)

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Classes of SWFs (1)

Use axioms to characterise important Use axioms to characterise important classesclasses of SWF of SWF AnonymityAnonymity and and populationpopulation principle imply we can principle imply we can

write SWF in either Irene-Janet form or write SWF in either Irene-Janet form or F F formform most modern approaches use these assumptionsmost modern approaches use these assumptions but may need to standardise for needs etc but may need to standardise for needs etc

Introduce Introduce decomposabilitydecomposability and you get class of and you get class of Additive SWFs Additive SWFs WW : : WW((xx) = ) = uu((xxii) ) or equivalently in or equivalently in FF-form -form WW((FF) = ) = uu((xx) d) dFF((xx)) think of think of uu((••) as ) as social utilitysocial utility or or social evaluationsocial evaluation function function

The class The class WW is of great importance is of great importance But But WW excludes some well-known welfare criteria excludes some well-known welfare criteria

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Classes of SWFs (2)

From W we get important subclasses

If we impose monotonicity we get W1 W : u(•) increasing subclass where marginal social utility always positive

If we further impose the transfer principle we get W2 W1: u(•) increasing and concave subclass where marginal social utility is positive and

decreasing

We often need to use these special subclasses Illustrate their properties with a simple example…

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Overview...Welfare axioms

Rankings

Equity and social welfare

Taxation and sacrifice

Equity, Social Welfare, Taxation

Classes of SWF and distributional comparisons

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Ranking and dominance Consider problem of comparing distributionsConsider problem of comparing distributions Introduce two simple conceptsIntroduce two simple concepts

first illustrate using the Irene-Janet representationfirst illustrate using the Irene-Janet representation take income vectors take income vectors xx and and yy for a given for a given nn

First-order dominance:First-order dominance: yy(1) (1) > > xx(1)(1), y, y(2) (2) > > xx(2)(2), y, y(3) (3) > > xx(3)(3)

Each ordered income in Each ordered income in yy larger than that in larger than that in xx Second-order dominance:Second-order dominance:

yy(1) (1) > > xx(1)(1), y, y(1)(1)+y+y(2) (2) > > xx(1)(1)+x+x(2)(2), y, y(1)(1)+y+y(2) (2) +…+ y+…+ y((nn) ) > > xx(1)(1)+x+x(2) (2) …+ x…+ x((nn))

Each cumulated income sum in Each cumulated income sum in yy larger than that in larger than that in xx Weaker than first-order dominanceWeaker than first-order dominance

Need to generalise this a littleNeed to generalise this a little given anonymity, population principle can represent distributions in given anonymity, population principle can represent distributions in FF-form-form qq: population proportion (0 : population proportion (0 ≤≤ qq ≤≤ 1) 1) FF((xx): proportion of population with incomes ): proportion of population with incomes ≤≤ xx ((FF): mean of distribution ): mean of distribution FF

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1st-Order approach

Basic tool is the Basic tool is the quantilequantile, expressed as, expressed asQQ((FF; ; qq) := inf {) := inf {x x || F F((xx) ) qq} = } = xxqq

““smallest income such that cumulative frequency is at least as great as smallest income such that cumulative frequency is at least as great as qq””

Use this to derive a number of intuitive conceptsUse this to derive a number of intuitive concepts interquartile range, decile-ratios, semi-decile ratiosinterquartile range, decile-ratios, semi-decile ratios graph of graph of QQ is Pen’s Parade is Pen’s Parade

Also to characterise 1Also to characterise 1stst-order (quantile) dominance:-order (quantile) dominance: ““G G quantile-dominates quantile-dominates FF””meansmeans: :

for every for every qq,, Q Q((GG;;qq) ) QQ((FF;;qq), ), for some for some qq,, Q Q((GG;;qq) > ) > QQ((FF;;qq))

A fundamental result:A fundamental result: G G quantile-dominates quantile-dominates F F iff iff WW((GG) > ) > W W((FF) for all ) for all WWWW11

Illustrate using Parade:

Illustrate using Parade:

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Parade and 1st-order dominance

F

G

Q(.; q)

10 q

Plot quantiles against proportion of population

Parade for distribution F again

Parade for distribution G

In this case In this case GG clearly clearly quantile-dominates quantile-dominates FFBut (as often happens) But (as often happens) what if it doesn’t?what if it doesn’t?Try second-order methodTry second-order method

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2nd-Order approach

Basic tool is the Basic tool is the income cumulantincome cumulant, expressed as, expressed asCC((FF; ; qq) := ) := ∫∫ QQ((FF; ; qq)) x x ddFF((xx))

““The sum of incomes in the Parade, up to and including position The sum of incomes in the Parade, up to and including position qq””

Use this to derive a number of intuitive conceptsUse this to derive a number of intuitive concepts the “shares” ranking, Gini coefficientthe “shares” ranking, Gini coefficient graph of graph of CC is is the the generalised Lorenz curvegeneralised Lorenz curve

Also to characterise the idea of 2Also to characterise the idea of 2ndnd-order (cumulant) -order (cumulant) dominance:dominance: ““G G cumulant-dominates cumulant-dominates FF””meansmeans: :

for every for every qq,, C C((GG;;qq) ) CC((FF;;qq), ), for some for some qq,, C C((GG;;qq) > ) > CC((FF;;qq))

A fundamental result (A fundamental result (Shorrocks 1983):): G G cumulant-dominates cumulant-dominates F F iff iff WW((GG) > ) > W W((FF) for all ) for all WWWW22

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GLC and 2nd-order dominance

10

0

C(G; . )

C(F; . )

C(.; q)

(F)

(G)

q

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Plot cumulations against proportion of population

GLC for distribution F

GLC for distribution G

Intercept on vertical axis Intercept on vertical axis is at mean incomeis at mean income

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2nd-Order approach (continued)

A useful tool: the A useful tool: the shareshare of the proportion of the proportion qq of of distribution distribution FF is is LL((FF;;qq) := ) := CC((FF;;qq) / ) / ((FF))

““income cumulation at divided income cumulation at divided qq by total income” by total income”

Yields Lorenz dominance, or the “shares” ranking:Yields Lorenz dominance, or the “shares” ranking: ““G G Lorenz-dominates Lorenz-dominates FF””meansmeans: :

for every for every qq,, L L((GG;;qq) ) LL((FF;;qq), ), for some for some qq,, L L((GG;;qq) > ) > LL((FF;;qq))

Another fundamental result (Another fundamental result (Atkinson 1970):): For given For given ,, G G Lorenz-dominates Lorenz-dominates F F iff iff WW((GG) > ) > W W((FF) for ) for

all all W W WW22

Illustrate using Lorenz curve:

Illustrate using Lorenz curve:

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Lorenz curve and ranking

0 0.2 0.4 0.6 0.8 10

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1

prop

orti

on o

f in

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proportion of population

L(G;.)

L(F;.)

L(.; q)

q

Plot shares against proportion of population

Lorenz curve for distribution F

Lorenz curve for distribution G

In this case In this case GG clearly clearly Lorenz-dominates Lorenz-dominates FFSo So FF displays more displays more inequality than inequality than GGBut (as often happens) But (as often happens) what if it doesn’t?what if it doesn’t?No clear statement about No clear statement about inequality (or welfare) is inequality (or welfare) is possible without further possible without further informationinformation

Perfect equality

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Overview...Welfare axioms

Rankings

Equity and social welfare

Taxation and sacrifice

Equity, Social Welfare, Taxation

Quantifying social values

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Equity and social welfare So far we have just general principlesSo far we have just general principles

may lead to ambiguous resultsmay lead to ambiguous results need a tighter description of social-welfare?need a tighter description of social-welfare?

Consider “reduced form” of social welfareConsider “reduced form” of social welfare WW = = ((, I, I) ) ((FF) is mean of distribution ) is mean of distribution FF IIII((FF) is inequality of distribution ) is inequality of distribution FF embodies trade-off between objectivesembodies trade-off between objectives

II can be taken as an “equity” criterion can be taken as an “equity” criterion from same roots as SWF?from same roots as SWF? or independently determined?or independently determined?

Consider a “natural” definition of inequalityConsider a “natural” definition of inequality

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0 1

1

L(.; q)

q

Gini coefficient

Redraw Lorenz diagramRedraw Lorenz diagram A “natural” inequality measure…?A “natural” inequality measure…?

normalised area above Lorenz curvenormalised area above Lorenz curve can express this also in I-J termscan express this also in I-J terms

Also (equivalently) represented as Also (equivalently) represented as normalised difference between income pairs:normalised difference between income pairs:

In In FF-form:-form:

In Irene-Janet terms:In Irene-Janet terms:

Intuition is neat, butIntuition is neat, but inequality index is clearly arbitraryinequality index is clearly arbitrary can we find one based on welfare criteria?can we find one based on welfare criteria?

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SWF and inequality

O xi

xj

The Irene &Janet diagram A given distribution Distributions with same mean Contours of the SWF

•E

(F) (F)

•F

Construct an equal distribution E such that W(E) = W(F) Equally-Distributed Equivalent income

Social waste from inequality

Curvature of contour indicates society’s willingness to tolerate “efficiency loss” in pursuit of greater equality

contour: x values such that W(x) = const

do this for special case

do this for special case

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An important family of SWF

Take the Take the W2 subclass and impose subclass and impose scale invariance. scale invariance. Get the family of SWFs where Get the family of SWFs where uu is iso-elastic: is iso-elastic:

xx1 – – 1 u(xx) = ————— , 1 – has same form as CRRA utility functionhas same form as CRRA utility function

Parameter Parameter captures society’s inequality aversion. captures society’s inequality aversion. Similar interpretation to individual risk aversionSimilar interpretation to individual risk aversion See See Atkinson (1970)Atkinson (1970)

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Welfare-based inequality

From the concept of social waste From the concept of social waste Atkinson (1970) suggested an inequality measure:suggested an inequality measure:

((FF))II((FF)) = 1 = 1 –– —— ——

((FF)) Atkinson further assumed Atkinson further assumed

additive SWF, additive SWF, WW((FF)) = = uu((xx) d) dFF((xx)) isoelastic isoelastic uu

So inequality takes the formSo inequality takes the form

But what value of inequality aversion parameter But what value of inequality aversion parameter

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Values: the issues

SWF is central to public policy makingSWF is central to public policy making Practical example in Practical example in HM Treasury (2003) pp 93-94 pp 93-94 We need to fWe need to focus on two questions…ocus on two questions…

FirstFirst: do people care about distribution?: do people care about distribution? Experiments suggest they do – Experiments suggest they do – Carlsson et al (2005) Do social and economic factors make a difference?Do social and economic factors make a difference?

SecondSecond: What is the shape of : What is the shape of uu? ? ((Cowell-Gardiner 2000)) Direct estimates of inequality aversion Direct estimates of inequality aversion Estimates of risk aversion as proxy for inequality aversionEstimates of risk aversion as proxy for inequality aversion Indirect estimates of risk aversionIndirect estimates of risk aversion Indirect estimates of inequality aversion from choices made by Indirect estimates of inequality aversion from choices made by

governmentgovernment

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Preferences, happiness and welfare?

Ebert, U. and Welsch, H. (2009) Evaluate subjective well being as a function of personal and

environmental data using form Examine which inequality index seems to fit preferences best

Alesina et al (2004) Use data on happiness from social surveyUse data on happiness from social survey Construct a model of the determinants of happinessConstruct a model of the determinants of happiness Use this to see if income inequality makes a differenceUse this to see if income inequality makes a difference

Seems to be a difference in priorities between US and EuropeSeems to be a difference in priorities between US and EuropeUSUS Continental EuropeContinental Europe

Share of government in GDP Share of government in GDP 30% 30% 45%45%Share of transfers in GDP Share of transfers in GDP 11% 11% 18%18%

Do people in Europe care more about inequality?Do people in Europe care more about inequality?

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The Alesina et al model

Ordered logit model Ordered logit model ““Happy” is categorical: “Happy” is categorical: “not too happy”, “fairly happy”, “very happy”not too happy”, “fairly happy”, “very happy” iindividual, ndividual, sstate, tate, ttime, ime, ggroup. roup. Macro variables include inflation, unemployment rateMacro variables include inflation, unemployment rate Micro variables include personal characteristicsMicro variables include personal characteristics are state, time dummiesare state, time dummies

ResultsResults People declare lower happiness levels when inequality is high. People declare lower happiness levels when inequality is high. Strong negative effect of inequality on happiness of the European poor Strong negative effect of inequality on happiness of the European poor

and leftistsand leftists No effects of inequality on happiness of US poor and left-wingersNo effects of inequality on happiness of US poor and left-wingers Negative effect of inequality on happiness of US richNegative effect of inequality on happiness of US rich No differences across the American right and the European right. No differences across the American right and the European right. No differences between the American rich and the European richNo differences between the American rich and the European rich

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Inequality aversion and Elasticity of MU

Consistent inequality preferences?Consistent inequality preferences? Preference reversals (Preference reversals (Amiel et al 2008))

What value for What value for ?? from happiness studies 1.0 to 1.5 (from happiness studies 1.0 to 1.5 (Layard et al 2008)) related to extent of inequality in the country? (related to extent of inequality in the country? (Lambert et al 2003)) affected by way the question is put? (affected by way the question is put? (Pirttilä and Uusitalo 2010))

Evidence on Evidence on risk aversionrisk aversion is mixed is mixed direct survey evidence suggests estimated relative risk-aversion direct survey evidence suggests estimated relative risk-aversion

3.8 to 4.3 (3.8 to 4.3 (Barsky et al 1997) ) indirect evidence (from estimated life-cycle consumption model) indirect evidence (from estimated life-cycle consumption model)

suggests 0.4 to 1.4 (suggests 0.4 to 1.4 (Blundell et al 1994)) in each case depends on how well-off people arein each case depends on how well-off people are

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Overview...Welfare axioms

Rankings

Equity and social welfare

Taxation and sacrifice

Equity, Social Welfare, Taxation

Does structure of taxation make sense in welfare terms?

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Another application of ranking Tax and benefit system maps one Tax and benefit system maps one

distribution into anotherdistribution into another cc = = yy TT((yy)) yy: pre-tax income : pre-tax income cc: post-tax income : post-tax income

Use ranking tools to assess the impact of Use ranking tools to assess the impact of this in welfare termsthis in welfare terms

Typically this uses one or other concept of Typically this uses one or other concept of Lorenz dominanceLorenz dominance

Linked to Linked to effective tax progressioneffective tax progression TT is progressive if is progressive if c c Lorenz-dominatesLorenz-dominates y y see see Jakobsson (1976)

What Lorenz ranking would we expect to What Lorenz ranking would we expect to apply to these 5 concepts?apply to these 5 concepts?

original income+ cash benefits

gross income- direct taxes

disposable income- indirect taxes

post-tax income+ non-cash benefits

final income

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Proportion of population

Pro

po

rtio

n o

f In

co

me

(Equality Line)

Original Income

Gross Income

Disposable Income

After Tax Income

Final Income

Impact of Taxes and Benefits. UK 2006/7. Lorenz Curve

+ cash benefits

direct taxes

indirect taxes

+ noncash benefits

Big effect from benefits sideBig effect from benefits sideModest impact of taxesModest impact of taxesDirect and indirect taxes work Direct and indirect taxes work in opposite directionsin opposite directions

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1998/9

2006/7

indirect 1992

1998/9

2006/7

Implied tax rates in Economic and Labour Market Review

Formerly Formerly Economic Trends. Economic Trends. Taxes as proportion of gross income – see Taxes as proportion of gross income – see Jones, (2008)

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Tax-benefit example: implications

We might have guessed the outcome of exampleWe might have guessed the outcome of example In most countries:In most countries:

income tax progressiveincome tax progressive so are public expendituresso are public expenditures but indirect tax is regressivebut indirect tax is regressive so Lorenz-dominance is not surprising.so Lorenz-dominance is not surprising.

In many countries there is a move toward greater reliance on In many countries there is a move toward greater reliance on indirect taxationindirect taxation

political convenience?political convenience? administrative simplicity? administrative simplicity?

Structure of taxation should not be haphazardStructure of taxation should not be haphazard How should the How should the yy →→ cc mapping be determined? mapping be determined?

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Tax Criteria

What broad principles should tax reflect?What broad principles should tax reflect? ““benefit received:” pay for benefits you get through public sectorbenefit received:” pay for benefits you get through public sector ““sacrifice:” some principle of equality applied across individualssacrifice:” some principle of equality applied across individuals see see Neill (2000)Neill (2000) for a reconciliation of these twofor a reconciliation of these two

The sacrifice approachThe sacrifice approach Reflect views on equity in society.Reflect views on equity in society. Analyse in terms of income distributionAnalyse in terms of income distribution Compare distribution of Compare distribution of yy with distribution of with distribution of y y T T??

Three types of question:Three types of question:1.1. what’s a “fair” or “neutral” way to reduce incomes…?what’s a “fair” or “neutral” way to reduce incomes…?

2.2. when will a tax system induce when will a tax system induce LL-dominance?-dominance?

3.3. what is implication of imposing uniformity of sacrifice?what is implication of imposing uniformity of sacrifice?

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Amiel-Cowell (1999) approach

Irene's income

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equa

lity

The Irene &Janet diagram Initial distribution Possible directions for a “fair” tax

An iso-inequality path?

1 Scale-independent iso-inequality

1 Proportionate reductions are “fair”

2 Translation-independent iso-inequality

2 Absolute reductions are “fair”

3 “Intermediate” iso-inequality

3 Affine reductions are “fair”

4 No iso-inequality direction

4 Amiel-Cowell showed that individuals perceive inequality comparisons this way.

Based on Dalton (1920) conjecture

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Tax and the Lorenz curve

Assume a tax function Assume a tax function TT((∙∙) based on income) based on income a person with income a person with income yy, pays an amount , pays an amount TT((yy)) disposable income given by disposable income given by c c := := y y TT((yy))

Compare distribution of Compare distribution of yy with that of with that of cc will will cc be more equally distributed than be more equally distributed than yy?? will will TT((∙∙) produce more equally distributed ) produce more equally distributed cc than than T*T*((∙∙)? )? if so under what conditions?if so under what conditions?

Define Define residual progressionresidual progression of of TT [d[dcc/d/dyy][][y/cy/c] = [1] = [1 TT((yy)] /[1)] /[1 yy / /TT((yy)])]

Disposable income under Disposable income under T*T* L-dominates that under L-dominates that under T*T* iff iff residual progression of residual progression of TT is higher than that of is higher than that of T*…T*… ……for all for all yy see see JakobssonJakobsson (1976) (1976)

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A sacrifice approach

Suppose utility function Suppose utility function UU is continuous and increasing is continuous and increasing Definition of absolute sacrifice:Definition of absolute sacrifice:

((yy, , TT) displays at least as much (absolute) sacrifice as () displays at least as much (absolute) sacrifice as (yy**, , TT**)…)… ……if if UU((yy) ) UU((yyTT) ) ≥ ≥ UU((yy**) ) UU((yy**TT**))

Equal absolute sacrifice is scale invariant iffEqual absolute sacrifice is scale invariant iff y1 – – 1

U(y) = ———— 1 – ……or a linear transformation of thisor a linear transformation of this ((Young 1987Young 1987)

Apply sacrifice criterion to actual tax schedules Apply sacrifice criterion to actual tax schedules TT((∙∙)) Young (1990) does this for US tax system does this for US tax system Consider a UK applicationConsider a UK application

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Applying sacrifice approach

Assume simple form of social welfare functionAssume simple form of social welfare function social welfare defined in terms of incomesocial welfare defined in terms of income drop distinction between drop distinction between UU and and uu

Use the equal absolute sacrifice principle Use the equal absolute sacrifice principle uu((yy) ) uu((y y TT((yy)) = const)) = const

If insist on scale invariance If insist on scale invariance uu is isoelastic is isoelastic yy1 1 –– [ [y y TT((yy)])]1 1 –– = const = const is again inequality aversionis again inequality aversion

Differentiate and rearrange: Differentiate and rearrange: yy –– [1[1 TT((yy)] [)] [y y TT((yy)])]–– = 0 = 0 log[1log[1 TT((yy)] = )] = log ([ log ([ y y TT((yy) / ) / yy])])

Estimate Estimate from actual structure from actual structure TT((∙∙) ) get implied inequality aversionget implied inequality aversion For income tax (1999/2000): For income tax (1999/2000): = = For IT and NIC (1999/2000): For IT and NIC (1999/2000): = = see see Cowell-Gardiner (2000)

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Conclusion Axiomatisation of welfare needs just a few basic principlesAxiomatisation of welfare needs just a few basic principles

anonymityanonymity population principlepopulation principle decomposabilitydecomposability monotonicity monotonicity principle of transfersprinciple of transfers

Basic framework of distributional analysis can be extended to Basic framework of distributional analysis can be extended to related problems:related problems:

for example inequality and poverty…for example inequality and poverty… ……in second termin second term

Ranking criteria can be used to provide broad judgmentsRanking criteria can be used to provide broad judgments These may be indecisive, so specific SWFs could be usedThese may be indecisive, so specific SWFs could be used

scale invariant?scale invariant? perhaps a value for perhaps a value for of around 0.7 – 2of around 0.7 – 2

Welfare criteria can be used to provide taxation principlesWelfare criteria can be used to provide taxation principles

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