Welfare Analysis for Public Economics EC426

Transcription

1 Welfare Analysis for Public Economics Frank Cowell EC September 2015

2 Outline Ethical basis Fundamentals Philosophies compared Welfare and values SWF: Axiomatic approach Values Ranking distributions Dominance and welfare Dominance and inequality Conclusion

3 Welfare approaches The Constitution: an approach to deriving social preferences uses peoples orderings of social states including attitudes to redistribution constitution satisfying Unrestricted domain, Pareto unanimity, 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)

4 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 person gains 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 υ 1 + υ υ n

5 Utility-possibility sets

6 Nozick, Pareto, Bentham

7 Rawls Rawls(1971,1999) 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 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{υ 1,υ 2,...,υ n } Based on interpretation of veil of ignorance Rawls interpreted it differently, but rather vaguely

8 Egalitarianism Pure Egalitarianism Origin goes back to Plato Reinterpreted by Meade (1976) Superegalitarianism Welfare is perceived in terms of pairwise differences: υ i υ j,..., 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

9 Max-min and superegalitarianism

10 General SWF

11 Social-welfare functions Characterise structure of SWF A standard approach to welfare assessment individual utility as equivalised income: υ = x = y/ν(a) income distributions x := (x 1,x 2,...,x n ) (fixed population of n ) SWF evaluates all possible distributions for each distribution x: get one specific number W = W(x) = W(x 1,x 2,...,x n ) Properties will depend on economic principles similar principles used in other measurement problems inequality, poverty, mobility

12 SWF axioms Axiomatic approach (Amiel and Cowell 1999 Appendix A) Anonymity If x is a permutation of x then W (x ) = W (x) Population principle W (x ) W (x) W (x,...,x ) W (x,...,x) Decomposability W (x ) W (x) W (x,x ) W (x,x ) Monotonicity W(x 1,x 2,...,x i + δ,...,x n ) W(x 1,x 2,...,x i,...,x n ) Transfer principle (Dalton 1920) If x i < x j then, for small δ, W(x 1,...,x i + δ,...,x j δ,...,x n ) W(x 1,...,x n ) Scale invariance W (x ) W (x) W (λx ) W (λx)

13 Classes of SWF Anonymity and pop principle: SWF in terms of distribution function Introduce decomposability: get class of additive SWFs W : W (x) = n i=1 ζ (x i) ζ is social utility or social evaluation function however W excludes some well-known welfare criteria Impose monotonicity: get W 1 W, ζ increasing subclass where marginal social utility always positive Impose transfer principle: get W 2 W 1, 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

14 Evaluation function

15 Welfare-based inequality Equally Distributed Equivalent income ξ : W (x) = W (ξ 1) = W (ξ,ξ,...,ξ ) EDE depends on income distribution: ξ (x) = ξ (x 1,x 2,,x n ) 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 [ xi ] ] 1 1 ε 1 ε µ (x) Trade-off in SWF: W (x) = Ω(µ (x), I (x)) (Ebert and Welsch 2009)

16 SWF and inequality

17 Where do values in SWF come from? Consensus? Again the problem of the Arrow Theorem Personal concern for distribution υ i = u(x i,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)

18 Harsanyi: Impartial observer theorem Based on individual preferences V i over lotteries Lottery of Life each lottery is a vector of probabilities p V i satisfy EU axioms i = 1,...,n Impartial observer j imagines self as person i (objective circumstances, preferences ) j imagines an equal chance of being anyone in {1,...,n} calculates average EU of each p using weights {1/n,..., 1/n} V j (p) = 1 n n i=1 V i (p) Reinterpret the sum-of-utilities approach equivalent to: 1 n υ n υ n υ n reinterpreted as p 1 υ 1 + p 2 υ p n υ n, where p i = 1 n

19 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? (Cowell and Schokkaert 2001, Kroll and Davidovitz 2003, Carlsson et al. 2005) concerned only with expected utility? take account of more information?

20 Values: the issues SWF is central to public policy making practical example in H. M. Treasury (2011), pp 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

21 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 is high 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? (Pirttilä 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

22 Dominance criteria F(x): proportion of population with incomes x qth quantile, defined as x q := inf{x F(x) q} where (0 q 1) qth cumulant, defined as c q := x q x 0 xdf(x) qth share, defined as s q := c q /c 1 = c q /µ 1st-order dominance: x q x q for all q, with > for some q if both are n-vectors: x (i) x (i), for all i, with > for some i each ordered income in x larger than that in x 2nd-order dominance: c q c q for all q, with > for some q if n-vectors: i j=1 x (j) i j=1 x (j), for all i, with > for some i each cumulated income sum in x larger than that in x

23 Welfare and 1st-order dominance W (x ) > W (x) for all W W 1 if and only if x 1st-order dominates x

24 Welfare and 2nd-order dominance W (x ) > W (x) for all W W 2 if and only if x 2nd-order dominates x (Shorrocks 1983)

25 Lorenz dominance Lorenz dominance: x L x if s q s q for all q, with > for some q If µ(x ) = µ(x): W (x ) > W (x) for all W W 2 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 coefficient x i x j = 1 nµ(x) n i=1 x (i) 1 2n 2 µ(x) n i=1 n j=1 [ 2i 1 n 1 ]

26 Lorenz ranking and tax/benefit Tax and benefit system maps one distribution into another y post = y pre T(y pre ) characterise progression of T in welfare terms Use concept of Lorenz dominance T is progressive if y post Lorenz-dominates y pre (Jakobsson 1976) What ranking would we expect for these 5 concepts in UK? original income gross income disposable income post-tax income final income +cash benefits - direct taxes - indirect taxes +non-cash benefits

27 Lorenz ranking: UK taxes and benefits Source: Jones (2008)

28 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 2015) 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

29 Coming up... We have the first component of design problem individualistic SWF based on end-state principle Need to complete the design model introduce other components methods of solution [lectures 2 and 3] Consider alternative approaches to evaluation of distributions equality of opportunity mobility [lecture 5]

30 Bibliography I Alesina, A., R. Di Tella, and R. MacCulloch (2004). Inequality and happiness: are Europeans and Americans different? Journal of Public Economics 88, Amiel, Y. and F. A. Cowell (1999). Thinking about Inequality. Cambridge: Cambridge University Press. Amiel, Y., F. A. Cowell, L. Davidovitz, and A. Polovin (2008). Preference reversals and the analysis of income distributions. Social Choice and Welfare 30, Amiel, Y., F. A. Cowell, and W. Gaertner (2009). To be or not to be involved: A questionnaire-experimental view on Harsanyi s utilitarian ethics. Social Choice and Welfare 32, Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory 2, Barsky, R. B., F. T. Juster, M. S. Kimball, and M. D. Shapiro (1997). Preference parameters and behavioral heterogeneity : An experimental approachin the health and retirement survey. Quarterly Journal of Economics 112, Blundell, R., M. Browning, and C. Meghir (1994). Consumer demand and the life-cycle allocation of household expenditures. Review of Economic Studies 61, Carlsson, F., D. Daruvala, and O. Johansson-Stenman (2005). Are people inequality averse or just risk averse? Economica 72, Cowell, F. A. (2011). Measuring Inequality (Third ed.). Oxford: Oxford University Press. Cowell, F. A. (2015). Inequality and poverty measures. In M. D. Adler and M. Fleurbaey (Eds.), Oxford Handbook of Well-Being And Public Policy, Chapter 4. Oxford University Press.

31 Bibliography II Cowell, F. A. and K. A. Gardiner (2000). Welfare weights. OFT Economic Research Paper 202, Office of Fair Training, Salisbury Square, London. Cowell, F. A. and E. Schokkaert (2001). Risk perceptions and distributional judgments. European Economic Review 42, Dalton, H. (1920). Measurement of the inequality of incomes. The Economic Journal 30, Ebert, U. and H. Welsch (2009). How do Europeans evaluate income distributions? an assessment based on happiness surveys. Review of Income Wealth 55, 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 of risk-taking. Journal of Political Economy 61, Harsanyi, J. C. (1955). Cardinal welfare, individualistic ethics and interpersonal comparisons of utility. Journal of Political Economy 63, Jakobsson, U. (1976). On the measurement of the degree of progression. Journal of Public Economics 5, Jones, F. (2008). The effects of taxes and benefits on household income, 2006/07. Economic and Labour Market Review 2, Kaplow, L. and S. Shavell (2001). Any non-welfarist method of policy assessment violates the Pareto principle. Journal of Political Economy 109, Kroll, Y. and L. Davidovitz (2003). Inequality aversion versus risk aversion. Economica 70,

32 Bibliography III Lambert, P. J., D. L. Millimet, and D. J. Slottje (2003). Inequality aversion and the natural rate of subjective inequality. Journal of Public Economics 87, Layard, R., S. Nickell, and G. Mayraz (2008). The marginal utility of income. Journal of Public Economics 92, Meade, J. E. (1976). The Just Economy, Chapter VII: Measurement and patterns of inequality. Allen and Unwin. Pirttilä, J. and R. Uusitalo (2010). A leaky bucket in the real world: Estimating inequality aversion using survey data. Economica 77, Rawls, J. (1971). A Theory of Justice. Cambridge, Massachusetts: Harvard University Press. Rawls, J. (1999). A Theory of Justice (Revised ed.). Cambridge, Massachusetts: Harvard University Press. Shorrocks, A. F. (1983). Ranking income distributions. Economica 50, Yu, N. N. (2012). A one-shot proof of Arrow s impossibility theorem. Economic Theory 50,