Welfare Analysis for Public Economicsdarp.lse.ac.uk/pdf/EC426/EC426_15_01_H.pdfReinterpreted by...

$: Welfare Analysis for Public Economicsdarp.lse.ac.uk/pdf/EC426/EC426_15_01_H.pdfReinterpreted by Meade (1976) \Superegalitarianism" Welfare is perceived in terms of pairwise di erences:j˛$
Ethical basis Welfare and values Ranking distributions Conclusion References

Welfare Analysis for Public Economics

Frank Cowell

EC426http://darp.lse.ac.uk/ec426

26 September 2016

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


Outline

Ethical basisFundamentalsPhilosophies compared

Welfare and valuesSWF: Axiomatic approachValues

Ranking distributionsDominance and welfareDominance and inequality

Conclusion


Welfare approaches

The Constitution: an approach to deriving “socialpreferences”

• uses peoples’ orderings of social states

• including attitudes to redistribution

• constitution satisfying Unrestricted domain, Paretounanimity, Independence of Irrelevant Alternatives:

• must be dictatorial (Yu 2012)

• constitution hopelessly indecisive?

Welfarism: a more restrictive view of welfare comparisons

• Evaluation of states ignore all non-utility information

• an implication of U, P, I

• Usually a strong informational structure is imposed

• Problems if you drop welfarism (Kaplow and Shavell 2001)


Entitlement vs End-state

Entitlement: Nozick focuses on how status quo arose:

• fairness in original acquisition

• fair transfers

• rectification of past injustice

End-state: Pareto suggests unanimity criterion

• Approve the move from status quo if at least one persongains and no-one loses

• Individualistic, based on utilities

• May have a complicated relationship with income

End-state: Bentham suggests aggregative criterion

• Greatest good of the greatest number

• interpreted as max υ1 + υ2 + ...+ υn


Utility-possibility sets


Nozick, Pareto, Bentham


Rawls

Rawls(1971,1999) distributional philosophy based on twoprinciples:

1. each person has equal right to the most extensive scheme ofequal basic liberties compatible with a similar scheme ofliberties for all

2. society should so order its decisions as to secure the bestoutcome for the least advantaged

Economic focus has usually been on 2• based on reasoning behind a “veil of ignorance”• “don’t know my position when I’m making social

judgment”• avoid confusion with probabilistic approach

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


Egalitarianism

Pure Egalitarianism

• Origin goes back to Plato

• Reinterpreted by Meade (1976)

“Superegalitarianism”

• Welfare is perceived in terms of pairwisedifferences:|υi − υj |, ...,

• Welfare might not be expressible as a neat additiveexpression involving individual utilities

• Finds an echo in more recent welfare developments

• Related to concepts of deprivation


Max-min and superegalitarianism


General SWF


Social-welfare functions

Characterise structure of SWFA standard approach to welfare assessment

• individual utility as equivalised income: υ = x = y/ν(a)

• income distributions x := (x1, x2, . . . , xn) (fixed populationof n )

SWF evaluates all possible distributions

• for each distribution x:

• get one specific number W = W (x) = W (x1, x2, . . . , xn)

Properties will depend on economic principles

• similar principles used in other measurement problems

• inequality, poverty, mobility


SWF axioms

Axiomatic approach (Amiel and Cowell 1999 Appendix A)

Anonymity If x′ is a permutation of x then W (x′) = W (x)

Population principleW (x′) ≥W (x)⇒W (x′,...,x′) ≥W (x,...,x)

Decomposability W (x′) ≥W (x)⇒W (x′,x∗) ≥W (x,x∗)

MonotonicityW (x1, x2, ..., xi + δ, . . . , xn) ≥W (x1, x2, ..., xi, . . . , xn)

Transfer principle (Dalton 1920) If xi < xj then, for small δ,W (x1, ..., xi + δ, . . . , xj − δ, . . . , xn) ≥W (x1, . . . , xn)

Scale invariance W (x′) ≥W (x)⇒W (λx′) ≥W (λx)


Classes of SWF

Anonymity and pop principle: SWF in terms of distributionfunctionIntroduce decomposability: get class of additive SWFs• W : W (x) =

∑ni=1 ζ (xi)

• ζ is “social utility” or social evaluation function• however W excludes some well-known welfare criteria

Impose monotonicity: get W1⊂W, ζ increasing• subclass where marginal social utility always positive

Impose transfer principle: get W2⊂W1, ζ increasing &concave• subclass where marginal social utility is positive and

decreasing

Impose scale invariance: get isoelastic evaluation function:

ζ (x) =x1−ε − 1

1− ε


Evaluation function


Welfare-based inequality

Equally Distributed Equivalent income ξ:

• W (x) = W (ξ1) = W (ξ, ξ, ..., ξ)

• EDE depends on income distribution:ξ (x) = ξ (x1, x2, · · · , xn)

Measure inequality as “shortfall” from mean µ (x) (Atkinson

1970):

I (x) = 1− ξ (x)

µ (x)

• In the case of isoelastic evaluation function

I (x) = 1−

[1

n

n∑i=1

[xiµ (x)

]1−ε] 11−ε

Trade-off in SWF: W (x) = Ω(µ (x) , I (x)) (Ebert and Welsch

2009)


SWF and inequality


Where do values in SWF come from?

Consensus?

• Again the problem of the Arrow Theorem

Personal concern for distribution υi = u(xi,x)

• 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?

Base on individual rationality under uncertainty

• 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)


Harsanyi: Impartial observer theorem

Based on individual preferences Vi over lotteries

• Lottery of Life

• each lottery is a vector of probabilities p

• Vi satisfy EU axioms i = 1, . . . , n

Impartial observer j imagines self as person i (objectivecircumstances, preferences )

• j imagines an equal chance of being anyone in 1, ..., n• calculates average EU of each p using weights 1/n, ..., 1/n• Vj (p) = 1

n

∑ni=1 Vi (p)

Reinterpret the sum-of-utilities approach

• equivalent to: 1nυ1 + 1

nυ2 + ...+ 1nυn

• reinterpreted as p1υ1 + p2υ2 + ...+ pnυn, where pi = 1n


Harsanyi: some difficulties

Preferences known behind the “Veil of ignorance”?

• not in the Rawls approach

• Harsanyi assumes representative person knows others’utilities

Model assumes equal probability

• do people have prior information?

• subjective probabilities may be inconsistent

View risk and distributional choices in the same way? (Cowelland Schokkaert 2001, Kroll and Davidovitz 2003, Carlsson et al. 2005)

• concerned only with expected utility?

• take account of more information?


Values: the issues

SWF is central to public policy making

• practical example in H. M. Treasury (2011), pp 93-94

• focus on two questions

First: do people care about distribution?

• experiments suggest they do (Carlsson et al. 2005)

• evidence from “happiness”literature?

• do social and economic factors make a difference?

Second: What is the shape of ζ? (Cowell and Gardiner 2000)

• direct estimates of inequality aversion

• estimates of risk aversion as proxy for inequality aversion

• indirect estimates of risk aversion

• indirect estimates from choices made by government


Preferences, happiness and welfare

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

Determinants of happiness: inequality important? (Alesina et al.

2004)

• people declare lower happiness levels when inequality ishigh

• negative effect of inequality on European poor and leftists• negative effect of inequality on happiness of US rich

What value for ε?• from happiness studies 1.0 to 1.5 (Layard et al. 2008)

• related to extent of inequality in the country? (Lambert et al.

2003)

• affected by way the question is put? (Pirttila and Uusitalo

2010)

• from tax schedules 1.2 to 1.4 (Cowell and Gardiner 2000)

Evidence from risk aversion on ε is mixed• direct survey evidence: 3.8 to 4.3 (Barsky et al. 1997)

• from life-cycle consumption : 0.4 to 1.4 (Blundell et al. 1994)

• in each case depends on how well-off people are


Dominance criteria

F (x): proportion of population with incomes ≤ x• qth quantile, defined as xq := inf x|F (x) ≥ q where

(0 ≤ q ≤ 1)

• qth cumulant, defined as cq :=∫ xqx0xdF (x)

• qth share, defined as sq := cq/c1 = cq/µ

1st-order dominance:

• x′q ≥ xq for all q, with “>” for some q

• if both are n-vectors: x′(i) ≥ x(i), for all i, with “>” forsome i

• each ordered income in x′ larger than that in x

2nd-order dominance:

• c′q ≥ cq for all q, with “>” for some q

• if n-vectors:∑i

j=1 x′(j) ≥

∑ij=1 x(j), for all i, with “>” for

some i

• each cumulated income sum in x′ larger than that in x


Welfare and 1st-order dominance

W (x′) > W (x) for all W ∈W1 if and only if x′ 1st-orderdominates x


Welfare and 2nd-order dominance

W (x′) > W (x) for all W ∈W2 if and only if x′ 2nd-orderdominates x (Shorrocks 1983)


Lorenz dominance

Lorenz dominance: x′ L x if s′q ≥ sq for all q, with “>” for

some q

• If µ(x′) = µ(x): W (x′) > W (x) for all W ∈W2 iff x′ L x(Atkinson 1970)

• If x′ L x then I (x′) < I (x) for all I satisfying transfer principle

• Includes all Atkinson indices and Gini coefficient1

2n2µ(x)

∑ni=1

∑nj=1 |xi − xj | =

1nµ(x)

∑ni=1 x(i)

[2i−1n − 1

]


Lorenz ranking and tax/benefit

Tax and benefit system maps one distribution into another• ypost = ypre − T (ypre)• characterise progression of T in welfare terms• interested in this because of ability-to-pay criterion of

taxation (Atkinson 2015)

Use concept of Lorenz dominance• T is progressive if ypost Lorenz-dominates ypre (Jakobsson

1976)

What ranking would we expect for these 5 concepts in UK?

original income+cash benefits

gross income- direct taxes

disposable income- indirect taxes

post-tax income+non-cash benefits

final income


Lorenz ranking: UK taxes and benefits

Source: Jones (2008)


Summary and key reading

• Alternative philosophies support redistributive arguments

• base these arguments on private tastes?• base on personal attitudes to risk? (Cowell and Schokkaert

2001)

• To model welfare need just a few axioms (Cowell 2016)

• anonymity• population principle• decomposability• monotonicity• principle of transfers

• Ranking criteria can be used to provide broad judgments

• (Cowell 2011,Chapter 3)

• may be indecisive, so specific SWFs could be used• ranking criteria connected to taxation principles


Coming up...

• We have the first component of design problem

• individualistic SWF• based on end-state principle

• Consider alternative approaches to evaluation ofdistributions

• equality of opportunity• mobility• [lectures 2 and 3]

• Need to complete the design model

• introduce other components• methods of solution• [lectures 4 and 5]


Bibliography I

Alesina, A., R. Di Tella, and R. MacCulloch (2004). Inequality and happiness: areEuropeans and Americans different? Journal of Public Economics 88, 2009–2042.

Amiel, Y. and F. A. Cowell (1999). Thinking about Inequality. Cambridge: CambridgeUniversity Press.

Amiel, Y., F. A. Cowell, L. Davidovitz, and A. Polovin (2008). Preference reversals and theanalysis of income distributions. Social Choice and Welfare 30, 305–330.

Amiel, Y., F. A. Cowell, and W. Gaertner (2009). To be or not to be involved: Aquestionnaire-experimental view on Harsanyi’s utilitarian ethics. Social Choice andWelfare 32, 299–316.

Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory 2,244–263.

Atkinson, A. B. (2015). Inequality: What can be done? London: Harvard University Press.

Barsky, R. B., F. T. Juster, M. S. Kimball, and M. D. Shapiro (1997). Preferenceparameters and behavioral heterogeneity : An experimental approachin the health andretirement survey. Quarterly Journal of Economics 112, 537–579.

Blundell, R., M. Browning, and C. Meghir (1994). Consumer demand and the life-cycleallocation of household expenditures. Review of Economic Studies 61, 57–80.


Bibliography II

Carlsson, F., D. Daruvala, and O. Johansson-Stenman (2005). Are people inequality averseor just risk averse? Economica 72, 375–396.

Cowell, F. A. (2011). Measuring Inequality (Third ed.). Oxford: Oxford University Press.

Cowell, F. A. (2016). Inequality and poverty measures. In M. D. Adler and M. Fleurbaey(Eds.), Oxford Handbook of Well-Being And Public Policy, Chapter 4. Oxford UniversityPress.

Cowell, F. A. and K. A. Gardiner (2000). Welfare weights. OFT Economic Research Paper202, Office of Fair Training, Salisbury Square, London.

Cowell, F. A. and E. Schokkaert (2001). Risk perceptions and distributional judgments.European Economic Review 42, 941–952.

Dalton, H. (1920). Measurement of the inequality of incomes. The Economic Journal 30,348–361.

Ebert, U. and H. Welsch (2009). How do Europeans evaluate income distributions? anassessment based on happiness surveys. Review of Income Wealth 55, 803–819.

H. M. Treasury (2011). The Green Book: Appraisal and Evaluation in Central Government.London: HMSO.

Harsanyi, J. C. (1953). Cardinal utility in welfare economics and in the theory ofrisk-taking. Journal of Political Economy 61, 434–435.


Bibliography III

Harsanyi, J. C. (1955). Cardinal welfare, individualistic ethics and interpersonalcomparisons of utility. Journal of Political Economy 63, 309–321.

Jakobsson, U. (1976). On the measurement of the degree of progression. Journal of PublicEconomics 5, 161–168.

Jones, F. (2008). The effects of taxes and benefits on household income, 2006/07. Economicand Labour Market Review 2, 37–47.

Kaplow, L. and S. Shavell (2001). Any non-welfarist method of policy assessment violatesthe Pareto principle. Journal of Political Economy 109, 281–286.

Kroll, Y. and L. Davidovitz (2003). Inequality aversion versus risk aversion. Economica 70,19 – 29.

Lambert, P. J., D. L. Millimet, and D. J. Slottje (2003). Inequality aversion and the naturalrate of subjective inequality. Journal of Public Economics 87, 1061–1090.

Layard, R., S. Nickell, and G. Mayraz (2008). The marginal utility of income. Journal ofPublic Economics 92, 1846–1857.

Meade, J. E. (1976). The Just Economy, Chapter VII: Measurement and patterns ofinequality. Allen and Unwin.

Pirttila, J. and R. Uusitalo (2010). A ‘leaky bucket’ in the real world: Estimating inequalityaversion using survey data. Economica 77, 60–76.


Bibliography IV

Rawls, J. (1971). A Theory of Justice. Cambridge, Massachusetts: Harvard University Press.

Rawls, J. (1999). A Theory of Justice (Revised ed.). Cambridge, Massachusetts: HarvardUniversity Press.

Shorrocks, A. F. (1983). Ranking income distributions. Economica 50, 3–17.

Yu, N. N. (2012). A one-shot proof of Arrow’s impossibility theorem. Economic Theory 50,523–525.

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