Transcript No Slide Title

3 October 2011
Frank Cowell: EC426 Public Economics
MSc Public Economics
2011/12
http://darp.lse.ac.uk/ec426
Welfare Analysis of State Intervention
Frank A. Cowell
Frank Cowell: EC426 Public Economics
Introduction

Two key questions
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Answers to 1:
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economic issues that involve cooperative rather than purely individualistic
approach
interrelation with social and political analysis
Answers to 2:
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1. Why Public Economics?
2. What role for government in the economy?
management of economic mechanisms
manipulation of environment in which mechanisms operate
This lecture:
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focus on the underlying welfare economics to these answers
examine the underlying motivation for concern with redistribution
foundation for lectures on distributional comparisons, on policy design
Frank Cowell: EC426 Public Economics
Management of mechanisms

Where the private model doesn’t “work”

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A typology of difficulties:
1.
2.
3.
4.

Market deficiency
Nonconvexities
Externalities
Public consumption
Perhaps only the first two are really “failure”

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
sometimes called “market failure”
useful to look at the separate reasons why
violations of first or second “welfare theorems”
informational problems
But all 1,…,4 provide a normative role for public economics

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all of these addressed in the coming lectures
characterisation issue (how solution differs from private –sector outcome)
implementation issue (how to design a mechanism)
Frank Cowell: EC426 Public Economics
Manipulation of environment
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Standard micro model takes as given:
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Raises several questions
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resource allocation
system of rights
institutions
can the government modify the above?
motive for doing this?
mechanism for accomplishing it?
costs involved?
In this lecture

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
focus on resource allocation
what is basis for interfering with it?
how to formulate a set of principles?
Frank Cowell: EC426 Public Economics
Overview...
Welfare Analysis of
Public Economics
Framework of
analysis
Roots in welfare
economics
Welfare,
utility, income
The basis for
redistribution
The basis for
values
Responsibility
& redistribution
Frank Cowell: EC426 Public Economics
An efficiency-equity “trade-off”
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What is efficiency?
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What is equity?
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raises issues of definition
also of the case for egalitarianism (Putterman et al. 1998)
Is there necessarily a trade-off?
Not if we can redistribute resources without transactions cost
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PE provides a criterion for the goal of efficiency itself
Pareto criterion gives no guidance away from efficient point
standard approach to gains/losses based on potential efficiency
a criterion for applications in Public Economics such as tax design
but this is only possible with lump-sum transfers
encounter informational problems
Use welfare economics to give meaning to the trade-off:
Frank Cowell: EC426 Public Economics
Welfare approaches
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The constitution
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Is the approach hopelessly indecisive?
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the fundamental approach to deriving “social preferences”
uses peoples’ orderings of social state including attitude to redistribution
runs into problem of Arrow theorem (Arrow 1963, Blau 1972)
a constitution satisfying Unrestricted domain, Pareto unanimity,
Independence of Irrelevant Alternatives must be dictatorial
there’s no clear imperative for action
but will give insight in later lecture on difficulties of implementation
Way forward?

impose more structure on the problem
Frank Cowell: EC426 Public Economics
Welfarism
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Welfarism: a more restrictive view of welfare comparisons
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Usually a strong informational structure is imposed
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cardinally measurable
interpersonally comparable
Provides the basis for a coherent model
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requires that evaluation of social states ignore all non-utility information
an implication of Unrestricted domain, Pareto unanimity, Independence
of Irrelevant Alternatives (Sen 1979)
widely used in modern approaches to compensation and responsibility
(Fleurbaey and Maniquet 2007)
problems if you drop welfarism (Kaplow and Shavell 2001)
Welfarism usually based on a simple model of individual utility

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utility based on resources?
need to examine the basic building blocks…
Frank Cowell: EC426 Public Economics
Overview...
Welfare Analysis of
Public Economics
Framework of
analysis
The basic units
of analysis
Welfare,
utility, income
The basis for
redistribution
The basis for
values
Responsibility
& redistribution
Frank Cowell: EC426 Public Economics
Models of resources
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Resources allocated among individuals
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Models 1,2: cake-sharing
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n individuals
n = 2 (Irene and Janet) works for many welfare problems
need n  3 persons for the inequality problem
fixed total income
but what about economic growth?
costlessly transferable incomes…
…important for first-best welfare economics
Model 3: general case with production


incorporates incentive effects
transfers allow for the “leaky bucket” problem (Okun 1975)
Example 1
Frank Cowell: EC426 Public Economics
Example 2
Welfare and utility...
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.
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.

What properties does utility have?
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Model 1: u = U(y; a)
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individualistic utility depends on income y and attributes a
may not be comparable, depends on information about a
Models 2,3: u = U(y, F)
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Is it (cardinally) measurable?
Is it comparable?
(properties are independent)
F: distribution function of income
Concern for distribution as a kind of externality
Evidence that people are concerned about relative incomes
(Ferrer-i-Carbonell 2005, Senik 2008)
Could we use income as a proxy for utility?
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Is it unique and well-defined?
How comprehensive should it be?
What is the relevant receiving unit?
The simple function U
u
Change preferences: φ is a
concave function of U.
utility
Frank Cowell: EC426 Public Economics
Utility and income: cardinality
 Risk aversion increases.
U(y)
lower risk
aversion
Û(y)
higher risk
aversion
Û= φ(U)
More concave f implies higher risk aversion
Example: the iso-elastic form:
y1 – d – 1
U(y) = ———— , d
1 –d
index of risk aversion, d, may take on a welfare
significance
income and utility only equivalent where d = 0
y
income

Adjust for needs using an equivalence scale: x = c ( y, a)
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Special case – income-independent equivalence scale
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x = y / n(a) where nis number of equivalent adults
s
Where does the function c come from?
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a: personal attributes (identity, needs, abilities…)
y: conventionally defined real income
x: equivalised income (money-metric utility)
official government sources
bodies such as OECD
models of household budgets
food
proxy for “need”
Frank Cowell: EC426 Public Economics
Utility and income: comparability
childless
couple
xr  yr
Example: adjusting for need

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
From budget
studies
plot share of food in budget against income
a reference household type…
Engel Equivalence Scale
couple with
children
x, y
0
xi
yi
income
Frank Cowell: EC426 Public Economics
Overview...
Welfare Analysis of
Public Economics
Framework of
analysis
Philosophies,
social welfare
and the basis for
intervention
Welfare,
utility, income
The basis for
redistribution
The basis for
values
Responsibility
& redistribution
 Two persons
 Cake-sharing income-possibility set
 Utility-possibility set 1
uj
 Utility-possibility set 2
 Utility-possibility set 3
Janet’s income
Frank Cowell: EC426 Public Economics
Utility-possibility set
 U is strictly concave
 Same U for Irene and Janet
 Case 1: cake sharing, independent.
u = U(y)
 Case 2: cake sharing, interdependent.
u = U(y, F)
45°
0
ui
Irene’s income
 Case 3: production, interdependent.
u = U(y, F)
Frank Cowell: EC426 Public Economics
Entitlement approach
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Focus on Nozick (1974)
Answer depends on how status quo came about
Distinguish three key issues:
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fairness in original acquisition
fair transfers
rectification of past injustice
Little or no role for the State?

“Night watchman”
Frank Cowell: EC426 Public Economics
End-state
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Pareto unanimity criterion is an end-state principle
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Individualistic, based on utilities
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alternatively, use a social welfare function
what principles should this embody?
Bentham: “Seek the greatest good of the greatest number”
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utility may have a complicated relationship with income
depend on the income of others?
Pareto criterion can be indecisive

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Approve the move from status quo to another point…
…if at least one person gains and no-one loses
interpreted as max sum of individual welfare
u1 +u2 +...+un
Much of public economics uses utilitarianism

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efficiency criteria
sacrifice theories in taxation
a basis for egalitarian transfers?
Frank Cowell: EC426 Public Economics
Nozick, Pareto, Bentham
 The status quo


uj
N
 Pareto improvements
C'

 Feasible points that Pareto-dominate N
C

B
 A possible voluntary solution
 The set of 2-person voluntary solutions
 Benthamite solution
 Will cooperative parties act as Paretians?
 Leads to multiple solutions
 Is this what would happen under Nozick?
 No case for state intervention?
 Benthamite contours are 45º lines
 Benthamite solution is unique
 But (in this case) not equal
 Maybe outside set of cooperative solutions
45°
0
ui
Frank Cowell: EC426 Public Economics
Nozick, Pareto, Bentham:
discussion
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A motive for changing distribution?
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Implementation
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Private voluntary action might not be able to implement C
Could rise if there were many individuals
Case for egalitarianism?
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Nozickians might insist that no move from N is justified
unless it came through private voluntary action
applies even to C
Bentham approach not usually imply egalitarian outcome
Consider two further alternative approaches:

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Concern for the least advantaged (Rawls)
Egalitarianism
Frank Cowell: EC426 Public Economics
The Rawls approach

Rawls’ (1971) distributional philosophy based on two principles:
1. each person has equal right to the most extensive scheme of equal basic
liberties compatible with a similar scheme of liberties for all
2. society should so order its decisions as to secure the best outcome for the
least advantaged

Economic focus has usually been on 2
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Needs careful interpretation
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Argument based on reasoning behind a “veil of ignorance”
I do not know which position in society I have when making social
judgment
Avoid confusion with probabilistic approach later
What is meant by the difference principle?
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Often interpreted as maximising utility of the worst-off : min {u1,u2 ,...,un}
Based on simplistic interpretation of veil of ignorance argument
Rawls interpreted it differently, but rather vaguely
Frank Cowell: EC426 Public Economics
Egalitarianism?
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Origin goes back to Plato…
…but reinterpreted by Meade (1974)
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“Superegalitarianism”
Welfare is perceived in terms of pairwise differences:
[ui - uj]...

Welfare might not be expressible as a neat additive
expression involving individual utilities

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Finds an echo in more recent welfare developments
Related to concepts of deprivation
Frank Cowell: EC426 Public Economics
Max-min & egalitarianism
 The status quo
 Max-min outcome

uj
 Superegalitarianism
N

R
 Contours of max-min are L-shaped
 Max-min optimum at R (not on diagonal)
 Maxi-min does not imply equality

45°
0
E
 Superegalitarian contours are V-shaped
 May get equality with superegalitarianism
 But E is Pareto-dominated
ui
Frank Cowell: EC426 Public Economics
A general class of SWF

We could just use a weaker individualistic form
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Specific welfare functions are special cases of this
many (not superegalitarianism) have additive form
 u(u1) +u(u2) +...+u(un)
 take u as a ``social utility” or “evaluation” function
Again useful to take the iso-elastic form of u:
u 1–e – 1
u(u) = ————— , e
1–e
 Bentham corresponds to the case e=
 Max-min (“Rawls”) corresponds to the case e=
 Intermediate cases (0 <e<) are interesting too

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Bergson-Samuelson formulation (Bergson 1938, Samuelson 1947)
W(u1 ,u2 ,...,un)
Frank Cowell: EC426 Public Economics
General SWF
 B. Benthamite (e= 0)
 W. Intermediate (e=1)
 R. 'Rawlsian' ( e=)
 E. ‘Superegalitarianism' (no e value)


E
B
 W
 R
Frank Cowell: EC426 Public Economics
Overview...
Welfare Analysis of
Public Economics
Framework of
analysis
A reinvention of
utilitarianism?
Welfare,
utility, income
The basis for
redistribution
The basis for
values
Responsibility
& redistribution
Frank Cowell: EC426 Public Economics
Where do values in SWF come from?

Consensus?


Personal concern for distribution u = U(y, F)

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people may have two sets of values, private and public
may treat distribution as a “public good” (Hochman and Rodgers 1969)
The PLUM principle
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Again the problem of the “Arrow Theorem...”
“People Like Us Matter” – (Champernowne and Cowell 1998)
interest groups determine SWF – will they be consistent?
Based on individual rationality under uncertainty
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argument by analogy between welfare and risk analysis (Atkinson 1970)
social welfare based on individual utility (Harsanyi 1953, 1955)
argument consists of two strands (Amiel et al 2009)
Frank Cowell: EC426 Public Economics
Harsanyi 1: Aggregation theorem

Consider preferences over set of lotteries L
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think of lotteries concerning life prospects
individuals’ preferences Vi satisfy EU axioms i =1,…,n
social preference V satisfies EU axioms
Assume Pareto indifference is satisfied
Then there are numbers ai and b such that, for all pL
V(p) =

1 n
― S ai Vi(p) + b
n i=1
Powerful result
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does not assume interpersonal utility comparisons.
ai are based on “the evaluator’s” value judgments (Harsanyi 1978, p. 227)
evaluator: “Judges and other public officials” (1978, p. 226)
need not be a member of the society
Frank Cowell: EC426 Public Economics
Harsanyi 2: Impartial observer theorem

Observer sympathetic to the interests of each member of society
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The observer j is to imagine himself being person i

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
i’s objective circumstances
i’s preferences
To get a representative person, continue the thought experiment

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
makes value judgments
assumes interpersonal comparisons of utility (Vickrey 1945)
j imagines he has an equal chance of being any person in society
equal consideration to each person’s interests.
Impartial observer j calculates average EU of each lottery in L:
Vj (p) =

1
―
n
n
S
i=1
Vi (p)
I.e. person j’s expected utility
Frank Cowell: EC426 Public Economics
Implications of Harsanyi

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The aggregation theorem gives an argument for additivity
Reinterpret the sum-of-utilities approach
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The “representative person” induces a probabilistic approach
Then social welfare is inherited from individual expected utility


equivalent to: (1/n)u1 + (1/n)u2 +...+(1/n)un
reinterpreted as p1u1 + p2u2 +...+pnun , where pi := 1/n
this is simply expected utility
…the analysis of impersonal value judgments concerning social welfare
seems to suggest a close affinity between the cardinal utility concept of
welfare economics and the cardinal utility concept of theory of choices
involving risk (Harsanyi 1953)
Some questions:


on what basis do we get the probabilities here?
is “expectations” an appropriate basis for social choice?
Frank Cowell: EC426 Public Economics
Harsanyi: Some difficulties

Are preferences known behind the “Veil of ignorance”?
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Model assumes equal probability

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
independent of income, wealth, social position etc
do people have prior information?
Subjective probabilities may be inconsistent
Do people view risk and distributional choices in the same way?

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

not in the Rawls approach
but Harsanyi assumes that representative person knows others’ utilities
Cowell and Schokkaert (2001)
Carlsson et al (2005)
Kroll and Davidovitz (2003)
Should we be concerned only with expected utility?

Should we take account of more information
Frank Cowell: EC426 Public Economics
A difficulty with expected utility?

Suppose the outcomes depend on uncertain events


probabilities of events 1,2 are (p, 1- p)
Payoffs for persons (i,j) under two policies are
Policy
a
b




Event 2
(1,)
(,1)
Consider choice between policies a and b(Diamond 1967)
Expected payoffs are:


Event 1
(1,)
(1,)
under a: (1,0)
under b: (p, 1- p)
Should society be indifferent between a and b?
Mobility may be important as well as expected outcome
Frank Cowell: EC426 Public Economics
Views on redistribution

Views on distribution depend on (i) your current position and (ii)
your expectations (Ravallion and Lokshin 2000)

Alesina and Giuliano (2009) confirm this for US (GSS) and show
importance of perceived fairness
Income may not be over-riding concern (Ohtake and Tomioka 2004)
But more than self-interest is at work (Fong 2001)


Frank Cowell: EC426 Public Economics
Overview...
Welfare Analysis of
Public Economics
Framework of
analysis
What should be
equalised?
Welfare,
utility, income
The basis for
redistribution
The basis for
values
Responsibility
& redistribution
Frank Cowell: EC426 Public Economics
Responsibility and redistribution

Take account of individual responsibility?





Each person i has a vector of attributes ai:




Attributes partitioned into two classes
R-attributes: responsibility characteristics
C-attributes: compensation characteristics
Situation before intervention determined by income function f



role of individual actions – “responsibility cut”
affect the case for redistribution
affect the evaluation of redistribution
differentiate between characteristics for which people can be held responsible and
others
f maps attributes into incomes f(ai)
only person i’s attributes involved
Situation after intervention determined by distribution rule F



F maps profile of attributes a into income of each person i
feasible: Sk Fk(a) = Sk f(ak)
anonymous: if ai = aj then Fi(a) = Fj(a)
Frank Cowell: EC426 Public Economics
Responsibility Principles

1. Equal Income for Equal R-attributes



2. Equal Transfers for Equal C-attributes




EIER and ETEC are incompatible except in the special case
f(ai) = g(aiR) + h(aiC)
In this special case, a natural redistribution mechanism


focus on changes in distribution
if aiC = ajC then Fi(a) – f(ai) = Fj(a) – f(aj)
Problem (Bossert and Fleurbaey 1996):


focus on distribution itself
if aiR = ajR then Fi(a) = Fj(a)
Fi0(a) = g(aiR) +
(1/n)
Sk h(aiC)
In general case we need a compromise…
Frank Cowell: EC426 Public Economics
Compromises

1. Egalitarian-equivalent mechanisms




2. Conditionally-egalitarian mechanisms




FiCE(a) = f(ai) – f(a*R, aiC) + G
G := (1/n) Sk f(a*R, akC)
insist on strict compensation (ETEC) but weaken EIER
Both compromises use reference characteristics (R or C)
1.
2.

FiEE(a) = f(aiR, a*C) – T
T := (1/n) Sk [ f(akR, a*C) – f(ak)]
insist on full adjustment (EIER) but weaken ETEC
Everyone gets income equal to the pre-redistribution earnings
given reference characteristics plus uniform transfer
Everyone guaranteed average income of a hypothetical
economy
Gaertner and Schokkaert (2012) show that there is
considerable support for such intermediate positions
Frank Cowell: EC426 Public Economics
Concluding remarks




A model with an individualistic base for welfare comparisons
Alternative social philosophies may support redistributive
arguments
But it raises some awkward questions...
Should the social basis for redistribution rest on private tastes
for equality or aversion to misery?


Should it rest on individual attitudes to risk?



What if people like seeing the poor..?
What if people are not risk-averse?
How should we distinguish between the factors that warrant
redistribution and those that don’t?
We will come back to consider the implications of these
questions
Frank Cowell: EC426 Public Economics
References 1











*Alesina, A, F. and Giuliano, P. (2009) “Preferences for Redistribution,” NBER
Working paper 14825
Amiel, Y., Cowell, F. A. and Gaertner, W. (2009) “To Be or not To Be Involved: A
Questionnaire-Experimental View on Harsanyi's Utilitarian Ethics, Social Choice and
Welfare , 32, 299-316.
Arrow, K. J. (1963) Social Choice and Individual Values ,Wiley, 2nd edition
Blau, J. H. (1972) “A direct proof of Arrow's theorem,” Econometrica, 40, 61-67.
Bergson, A. (1938) “A reformulation of certain aspects of welfare economics,” The
Quarterly Journal of Economics, 52, 310-334.
* Bossert, W. and Fleurbaey, M. (1996) “Redistribution and compensation,” Social
Choice and Welfare, 13, 343-355.
Carlsson et al (2005) “Are people inequality averse or just risk averse?” Economica,
72, 375-396
* Cowell, F. A. and Schokkaert, E. (2001), “Risk Perceptions and Distributional
Judgments”, European Economic Review, 42, 941-952.
Diamond, P.A. (1967) “Cardinal welfare, individualistic ethics and interpersonal
comparison of utility: comment,” Journal of Political Economy, 75, 765-766.
Ferrer-i-Carbonell, A. (2005) “Income and well-being: an empirical analysis of the
comparison income effect”, Journal of Public Economics, 89, 997-1019
Fleurbaey, M. and Maniquet, F. (2007) “Compensation and Responsibility,”
Handbook of Social Choice, North-Holland, Amsterdam
Frank Cowell: EC426 Public Economics
References 2
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

Fong, C. (2001) “Social Preferences, Self-Interest and the Demand for
Redistribution,” Journal of Public Economics, 82, 225-246
Gaertner, W. and Schokkaert, E. (2012) Empirical Social Choice: QuestionnaireExperimental Studies on Distributive Justice, Cambridge University Press, Cambridge.
Harsanyi, J. (1953) “Cardinal utility in welfare economics and in the theory of risktaking”, Journal of Political Economy, 61, 434-435

Harsanyi, J. (1955) “Cardinal welfare, individualistic ethics and interpersonal
comparison of utility,” Journal of Political Economy, 63, 309-321.
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Harsanyi, J. (1978) Bayesian decision theory and utilitarian ethics, American
Economic Review, 68, 223-228

Hochman, H. and Rodgers, J.D. (1969) Pareto-optimal redistribution, American
Economic Review, 59, 542-557
Kaplow, L. and Shavell, S. (2001), “Any Non-Welfarist Method of Policy
Assessment Violates the Pareto Principle,” The Journal of Political Economy, 109,
281-286.
Kroll, Y. and Davidovitz, L. (2003) “Inequality aversion versus risk aversion.”
Economica, 70, 19-29
Meade, J.E. (1976) The Just Economy, Allen and Unwin, London
Nozick, R. (1974) Anarchy, State and Utopia, Basic Books, New York
Ohtake, F. and Tomioka, J. (2004) “Who Supports Redistribution?” The Japanese
Economic Review, 55, 333-354





Frank Cowell: EC426 Public Economics
References 3








Okun, A. M. (1975) Equality and Efficiency: the Big Trade-off, Brookings
Institution, Washington.
Putterman, L. and Roemer, J. and Silvestre, J. (1998) “Does egalitarianism have
a future?”, Journal of Economic Literature, 36, 861-902 .
Ravallion, M. and Lokshin, M. (2000) “Who wants to redistribute? The tunnel
effect in 1990s Russia,” Journal of Public Economics, 76, 87-104@@.
Rawls, J. (1971) A Theory of Justice, Harvard University Press
Samuelson, P. A. (1947) Foundations of Economic Analysis, Harvard
University Press, Cambridge, Massachusetts
Sen, A. K. (1979) “Personal utilities and public judgements: or what's wrong
with welfare economics?” The Economic Journal, 89, 537-558.
Senik, C. (2008) “Ambition and jealousy: income Interactions in the old Europe
versus the new Europe and the United States,” Economica, 75, 495-513
Vickrey, W.S. (1945) “Measuring marginal utility by reaction to risk,”
Econometrica, 13, 319-333.