Welfare Analysis of State Intervention

EC426 http://darp.lse.ac.uk/ec426 7th October 2013

Introduction • Two key questions

• 1. Why Public Economics? • 2. What role for government in the economy?

• Answers to 1: • economic issues involving cooperative rather than individualistic approach • interrelation with social and political analysis

• Answers to 2: • management of economic mechanisms • manipulation of environment in which mechanisms operate

• This lecture: • 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

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Management of mechanisms • Where the private model doesn’t “work”

• sometimes called “market failure” • useful to look at the separate reasons why

• A typology of difficulties: 1.Market deficiency 2.Nonconvexities 3.Externalities 4.Public consumption

• What do we mean by “failure”? • violations of first or second “welfare theorems” • informational problems

• All 1,…,4 provide a normative role for public economics • characterisation issue (how solution differs from private –sector outcome) • implementation issue (how to design a mechanism)

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Management of environment • Standard micro model takes as given:

• resource allocation • system of rights • institutions

• Raises several questions • can the government modify the above? • motive for doing this? • mechanism for accomplishing it? • costs involved?

• In this lecture • focus on resource allocation • what is basis for interfering with it? • how to formulate a set of principles?

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Framework of analysis

Basis for redistribution

Responsibility & redistribution

Welfare Analysis of Public Economics

Roots in welfare economics

Basis for values

Overview...

An efficiency-equity “trade-off” • What is efficiency?

• 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

• What is equity? • raises issues of definition • also of the case for egalitarianism

• No trade-off if can redistribute without transactions cost • but this is only possible with lump-sum transfers • encounter informational problems

• Use welfare economics to give meaning to the trade-off

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Welfare approaches • The constitution

• the fundamental approach to deriving “social preferences” • uses peoples’ orderings of social state including attitude to redistribution • runs into problem of Arrow theorem • a constitution satisfying (1) Unrestricted domain, (2) Pareto unanimity and

(3) Independence of Irrelevant Alternatives … must be dictatorial (Yu 2012)

• Is the approach hopelessly indecisive? • 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

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Welfarism • Welfarism: a more restrictive view of welfare comparisons

• requires that evaluation of states ignore all non-utility information • an implication of Unrestricted domain, Pareto unanimity, Independence

of Irrelevant Alternatives

• Usually a strong informational structure is imposed • cardinally measurable • interpersonally comparable

• Provides the basis for a coherent model • widely used in modern approaches to compensation and responsibility

(Fleurbaey and Maniquet 2011) • problems if you drop welfarism (Kaplow and Shavell 2001)

• Welfarism usually based on a simple model of individual utility • utility based on resources? • need to examine the basic building blocks…

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Models of resources • Resources allocated among individuals

• n individuals • n = 2 (Irene and Janet) works for many welfare problems • need n ≥ 3 persons for the inequality problem

• Models 1,2: cake-sharing • 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

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Welfare and utility... • What properties does utility have?

• is it (cardinally) measurable? • is it comparable?

• Use income as a proxy for utility? • cardinally measurable and comparable • more on this in lecture 2

• Model 1: υ = U(y; a) • individualistic utility depends on income y and attributes a • may not be comparable, depends on information about a

• Models 2,3: υ = U(y, F) • F: distribution function of income • concern for distribution as a kind of externality • people care about relative incomes (Ferrer-i-Carbonell 2005, Senik 2008)

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Utility and income?

υ

U(y)

income

utili

ty

y

Û(y)

The simple function U Change preferences: φ is a concave function of U.

Risk aversion increases.

More concave φ implies higher risk aversion Example: the iso-elastic form:

y1 – δ – 1 U(y) = ———— , δ ≥ 0 1 – δ index of risk aversion, δ, may take on a welfare significance income and utility equivalent where δ = 0

lower risk aversion

higher risk aversion

Û= φ(U)

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Two persons

Utility-possibility set 1

Jane

t’s in

com

e

Irene’s income 0 45°

Cake-sharing income-possibility set

υi

U is strictly concave Same U for Irene and Janet

Case 1: cake sharing, independent. υ = U(y)

Utility-possibility set 2

Case 2: cake sharing, interdependent. υ = U(y, F)

Utility-possibility set 3

Case 3: production, interdependent. υ = U(y, F)

υj

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1

2 3

Utility-possibility set

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Framework of analysis

Basis for redistribution

Responsibility & redistribution

Welfare Analysis of Public Economics

Philosophies, social welfare and the basis for intervention

Basis for values

Overview...

Entitlement approach • Focus on Nozick (1974) • Answer depends on how status quo came about • Distinguish three key issues:

• fairness in original acquisition • fair transfers • rectification of past injustice

• Little or no role for the State? • “Night watchman”

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End-state • Pareto unanimity criterion is an end-state principle

• Approve the move from status quo to another point… • …if at least one person gains and no-one loses

• Individualistic, based on utilities • utility may have a complicated relationship with income • depend on the income of others?

• Pareto criterion can be indecisive • alternatively, use a social welfare function • what principles should this embody?

• Bentham: “Seek the greatest good of the greatest number” • interpreted as max sum of individual welfare • υ1 + υ2 + ...+ υn

• Much of public economics uses utilitarianism • efficiency criteria • sacrifice theories in taxation • a basis for egalitarian transfers?

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Nozick, Pareto, Bentham

0 45°

υi

υj

Will cooperative parties act as Paretians? Leads to multiple solutions Is this what would happen under Nozick? No case for state intervention?

l B l N

The status quo

Feasible points that Pareto-dominate N

Pareto improvements

A possible voluntary solution The set of 2-person voluntary solutions Benthamite solution

Benthamite contours are 45º lines Benthamite solution is unique But (in this case) not equal Outside set of cooperative solutions?

l C l C'

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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 • Argument based on reasoning behind a “veil of ignorance” • “I don’t know my position in society when I’m making social judgment”

• Needs careful interpretation • Avoid confusion with probabilistic approach later

• What is meant by the difference principle? • Often interpreted as maximising utility of the worst-off : min {υ1, υ2, ..., υn} • Based on simplistic interpretation of veil of ignorance argument • Rawls interpreted it differently, but rather vaguely

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Egalitarianism? • Origin goes back to Plato… • …but reinterpreted by Meade (1974)

• “Superegalitarianism”

• Welfare is perceived in terms of pairwise differences: [υi − υj]...

• Welfare might not be expressible as a neat additive expression involving individual utilities • Finds an echo in more recent welfare developments • Related to concepts of deprivation

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Max-min & egalitarianism

0 45°

υi

υj

Contours of max-min are L-shaped Max-min optimum at R (not on diagonal) Maxi-min does not imply equality

l N

The status quo

Superegalitarianism

Max-min outcome

Superegalitarian contours are V-shaped May get equality with superegalitarianism But E is Pareto-dominated

l R

l E

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A general class of SWF • We could just use a weaker individualistic form

• W(υ1 , υ2 , ..., υn)

• Specific welfare functions are special cases of this • many (not superegalitarianism) have additive form • u(υ1) + u(υ2) + ... + u(υn) • take u as a ``social utility” or “evaluation” function

• Again useful to take the iso-elastic form of u: υ 1 – ε – 1 u(υ) = ————— , ε ≥ 0 1 – ε

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

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General SWF

l W l R

l E

B. Benthamite (ε = 0) W. Intermediate (ε = 1)

R. 'Rawlsian' ( ε =∞) E. ‘Superegalitarianism' (no ε value)

l B

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Framework of analysis

Basis for redistribution

Responsibility & redistribution

Welfare Analysis of Public Economics

Should we reinvent utilitarianism?

Basis for values

Overview...

Where do values in SWF come from? • Consensus?

• Again the problem of the “Arrow Theorem...”

• Personal concern for distribution υ = U(y, F) • people may have two sets of values, private and public • may treat distribution as a “public good”

• Interest groups • “People Like Us Matter” • will they be consistent?

• Based on individual rationality under uncertainty • 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)

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Harsanyi 1: Aggregation theorem

• Consider preferences over set of lotteries L • 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 αi and β such that, for all p∈L

1 n V(p) = ― Σ αi Vi(p) + β n i=1

• Powerful result • does not assume interpersonal utility comparisons. • αi 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

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Harsanyi 2: Impartial observer theorem

• Observer sympathetic to the interests of each member of society • makes value judgments • assumes interpersonal comparisons of utility

• The observer j is to imagine himself being person i • i’s objective circumstances • i’s preferences

• To get a representative person, continue the thought experiment • 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: 1 n Vj (p) = ― Σ Vi (p) n i=1 • I.e. person j’s expected utility

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Implications of Harsanyi

• The aggregation theorem gives an argument for additivity • Reinterpret the sum-of-utilities approach

• equivalent to: (1/n)υ1 + (1/n)υ2 + ...+ (1/n)υn • reinterpreted as p1υ1 + p2υ2 + ...+ pnυn , where pi := 1/n • this is simply expected utility

• The “representative person” induces a probabilistic approach • Then social welfare is inherited from individual 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?

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Harsanyi: Some difficulties

• Are preferences known behind the “Veil of ignorance”? • not in the Rawls approach • but Harsanyi assumes that representative person knows others’ utilities

• Model assumes equal probability • do people have prior information? • Subjective probabilities may be inconsistent

• Do people view risk and distributional choices in the same way? • 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? • maybe other aspects of the probability distribution?

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Mobility and opportunity?

• Mobility may be important as well as expected outcome • personal expectations (Ravallion and Lokshin 2000 )

• Associated with equality of opportunity? • wide appeal of EOp? • less so for equality of outcome?

• Redistribution and personal interest • “tunnel effect” • land of opportunity? (Alesina and La Ferrara 2005)

• POUM • Poor may not support redistribution • But POUM dominated by demand for social insurance (Bénabou and Ok

2001)

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Values: other factors

• Why would individuals support redistribution? • Are people just concerned with their own prospects?

• issues beyond self interest • income risk is important Ohtake and Tomioka (2004)

• Consistently find a mixture of motives • see Corneo and Grüner (2002) • attitudes maybe depend on culture (Isaksson and Lindskog 2009)

• Direct concern with fairness distributive justice • see Fong (2001)

• For an overview: • see Alesina and Giuliano (2009)

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Framework of analysis

Basis for redistribution

Responsibility & redistribution

Welfare Analysis of Public Economics

What should be equalised?

Basis for values

Overview...

Responsibility and redistribution

• Role of individual actions – “responsibility cut” ? • affect the case for redistribution • affect the evaluation of redistribution

• 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 given by income function f • f maps attributes into incomes f(ai) • only person i’s attributes involved

• Situation after intervention given by distribution rule F • F maps profile of attributes a into income of each person i • feasible: Σk Fk(a) = Σk f(ak) • anonymous: if ai = aj then Fi(a) = Fj(a)

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Responsibility Principles

• 1. Equal Income for Equal R-attributes • focus on distribution itself • if ai

R = aj

R then Fi(a) = Fj(a)

• 2. Equal Transfers for Equal C-attributes • focus on changes in distribution • if ai

C = aj

C then Fi(a) – f(ai) = Fj(a) – f(aj)

• Problem • EIER and ETEC are incompatible except in the special case • f(ai) = g(ai

R) + h(aiC)

• In this special case, a natural redistribution mechanism • Fi

0(a) = g(aiR) + (1/n) Σk h(ai

C)

• In general case we need a compromise…

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Compromises • 1. Egalitarian-equivalent mechanisms

• FiEE(a) = f(ai

R, a*C) – T • T := (1/n) Σk [ f(ak

R, a*C) – f(ak)] • insist on full adjustment (EIER) but weaken ETEC

• 2. Conditionally-egalitarian mechanisms • Fi

CE(a) = f(ai) – f(a*R, aiC) + G

• G := (1/n) Σk f(a*R, akC)

• insist on strict compensation (ETEC) but weaken EIER • Both compromises use reference characteristics (R or C)

1.Everyone gets income equal to the pre-redistribution earnings given reference characteristics plus uniform transfer

2.Everyone guaranteed average income of a hypothetical economy • Gaertner and Schokkaert (2012) show that there is

considerable support for such intermediate positions

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Concluding remarks

• Model with an individualistic base for welfare comparisons • Alternative social philosophies to 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? • What if people like seeing the poor..?

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

• How should we distinguish between the factors that warrant redistribution and those that don’t?

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References 1

• *Alesina, A, F. and Giuliano, P. (2009) “Preferences for Redistribution,” NBER WP 14825 • Alesina, A. and La Ferrara, E. (2005) “Preferences for redistribution in the land of opportunities”, Journal of

Public Economics, 89, 897-931 • 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. • Bénabou, R. and Ok, E. (2001) “Social Mobility and the Demand for Redistribution: The POUM Hypothesis”,

Quarterly Journal of Economics, 116, 447-487 • Carlsson et al (2005) “Are people inequality averse or just risk averse?” Economica, 72, 375-396 • Corneo, G. Grüner, H.-P. (2002) “Individual preferences for political redistribution”, Journal of Public Economics

83, 83-107 • * 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. (2011) “Compensation and Responsibility,” Handbook of Social Choice, North-Holland, Amsterdam, Section 2.4

• Fong, C. (2001) “Social Preferences, Self-Interest and the Demand for Redistribution,” Journal of Public Economics, 82, 225-246

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References 2 • Gaertner, W. and Schokkaert, E. (2012) Empirical Social Choice: Questionnaire-Experimental Studies on

Distributive Justice, Cambridge University Press, Cambridge. • Harsanyi, J. (1953) “Cardinal utility in welfare economics and in the theory of risk-taking”, 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.

• Harsanyi, J. (1978) “Bayesian decision theory and utilitarian ethics,” American Economic Review, 68, 223-228 Isaksson, A-S and Lindskog, A. (2009) Journal of Economic Behavior & Organization, 72, 884–902

• 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 • 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 • Senik, C. (2008) “Ambition and jealousy: income Interactions in the old Europe versus the new Europe and the

United States,” Economica, 75, 495-513 • Yu, N.N. (2012) “A one-shot proof of Arrow’s impossibility theorem, Economic Theory, 50, 523-525

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