MSc Public Economics 2011/12 darp.lse.ac.uk/ec426

1. MSc Public Economics 2011/12 http://darp.lse.ac.uk/ec426 Welfare Analysis of State Intervention Frank A. Cowell 3 October 2011

2. Introduction Two key questions 1. Why Public Economics? 2. What role for government in the economy? Answers to 1: economic issues that involve cooperative rather than purely 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

3. 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: Market deficiency Nonconvexities Externalities Public consumption Perhaps only the first two are really “failure” violations of first or second “welfare theorems” informational problems But all 1,…,4 provide a normative role for public economics all of these addressed in the coming lectures characterisation issue (how solution differs from private –sector outcome) implementation issue (how to design a mechanism)

4. Manipulation 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?

5. 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

6. 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 (Putterman et al. 1998) Is there necessarily a trade-off? Not if we can redistribute resources 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:

7. 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 (Arrow 1963, Blau 1972) a constitution satisfying Unrestricted domain, Pareto unanimity, Independence of Irrelevant Alternatives must be dictatorial 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

8. Welfarism Welfarism: a more restrictive view of welfare comparisons requires that evaluation of social states ignore all non-utility information an implication of Unrestricted domain, Pareto unanimity, Independence of Irrelevant Alternatives (Sen 1979) 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 2007) 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…

9. 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

10. Models of resources Resources allocated among individuals n individuals n = 2 (Irene and Janet) works for many welfare problems need n³ 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 (Okun 1975)

11. Welfare and utility... What properties does utility have? Is it (cardinally) measurable? Is it comparable? (properties are independent) Model 1: u = U(y; a) 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) 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? Is it unique and well-defined? How comprehensive should it be? What is the relevant receiving unit? Example 1 Example 2 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.

12. Utility and income: cardinality • The simple function U u • Change preferences: φ is a concave function of U. utility • Risk aversion increases. lower risk aversion U(y) • More concave f implies higher risk aversion • Example: the iso-elastic form: y1 –d– 1 U(y) = ———— , d ³ 0 1 –d • index of risk aversion, d, may take on a welfare significance • income and utility only equivalent where d = 0 Û(y) Û=φ(U) higher risk aversion y income

13. Utility and income: comparability Adjust for needs using an equivalence scale: x = c( y, a) a: personal attributes (identity, needs, abilities…) y: conventionally defined real income x: equivalised income (money-metric utility) Special case – income-independent equivalence scale x = y / n (a) where n is number of equivalent adults Where does the function c come from? official government sources bodies such as OECD models of household budgets Example: adjusting for need plot share of food in budget against income a reference household type… Engel Equivalence Scale sfood childless couple proxy for “need” xr ºyr From budget studies couple with children x, y 0 yi xi income

14. 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

15. Utility-possibility set • Two persons • Cake-sharing income-possibility set • Utility-possibility set 1 uj • Utility-possibility set 2 ray of equality • Utility-possibility set 3 Janet’s income • U is strictly concave • Same U for Irene and Janet • Case 1: cake sharing, independent. u = U(y) income distributions with given total • Case 2: cake sharing, interdependent. u = U(y, F) • Case 3: production, interdependent. u = U(y, F) 45° ui 0 Irene’s income

16. 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”

17. 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 u1 + u2 + ...+ un Much of public economics uses utilitarianism efficiency criteria sacrifice theories in taxation a basis for egalitarian transfers?

18. Nozick, Pareto, Bentham • The status quo • Pareto improvements • C' • Feasible points that Pareto-dominate N • C • N uj • B • A possible voluntary solution ray of equality • 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° ui 0

19. Nozick, Pareto, Bentham: discussion A motive for changing distribution? Nozickians might insist that no move from N is justified unless it came through private voluntary action applies even to C Implementation Private voluntary action might not be able to implement C Could rise if there were many individuals Case for egalitarianism? Bentham approach not usually imply egalitarian outcome Consider two further alternative approaches: Concern for the least advantaged (Rawls) Egalitarianism

20. The Rawls approach Rawls’ (1971) distributional philosophy based on two principles: each person has equal right to the most extensive scheme of equal basic liberties compatible with a similar scheme of liberties for all 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 do not know which position in society I have when 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 {u1, u2 , ..., un} Based on simplistic interpretation of veil of ignorance argument Rawls interpreted it differently, but rather vaguely

21. Egalitarianism? Origin goes back to Plato… …but reinterpreted by Meade (1974) “Superegalitarianism” Welfare is perceived in terms of pairwise differences: [ui - uj]... 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

22. Max-min & egalitarianism • The status quo • Max-min outcome • Superegalitarianism • N uj ray of equality • R • Contours of max-min are L-shaped • Max-min optimum at R (not on diagonal) • Maxi-min does not imply equality • E • Superegalitarian contours are V-shaped • May get equality with superegalitarianism • But E is Pareto-dominated 45° ui 0

23. A general class of SWF We could just use a weaker individualistic form Bergson-Samuelson formulation (Bergson 1938, Samuelson 1947) W(u1 , u2 , ..., un) 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: u1 – e– 1 u(u) = ————— , e ³ 0 1 – e Bentham corresponds to the case e = 0 Max-min (“Rawls”) corresponds to the case e =  Intermediate cases (0 < e < ) are interesting too

24. General SWF • B. Benthamite (e = 0) • W. Intermediate (e = 1) • R. 'Rawlsian' ( e =) • E. ‘Superegalitarianism' (no evalue) • B • W • R • E

25. 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

26. Where do values in SWF come from? Consensus? Again the problem of the “Arrow Theorem...” Personal concern for distribution u = U(y, F) people may have two sets of values, private and public may treat distribution as a “public good” (Hochman and Rodgers 1969) The PLUM principle “People Like Us Matter” – (Champernowne and Cowell 1998) interest groups determine SWF – 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)

27. 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 ai and b such that, for all pL 1 n V(p) = ― SaiVi(p) + b n i=1 Powerful result 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

28. Harsanyi 2: Impartial observer theorem Observer sympathetic to the interests of each member of society makes value judgments assumes interpersonal comparisons of utility (Vickrey 1945) 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) = ― SVi (p) n i=1 I.e. person j’s expected utility

29. Implications of Harsanyi The aggregation theorem gives an argument for additivity Reinterpret the sum-of-utilities approach 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 “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?

30. 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 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? 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

31. 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 Event 1 Event 2 a (1,0) (1,0) b (1,0) (0,1) Consider choice between policies a and b (Diamond 1967) Expected payoffs are: 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

32. 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)

33. 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

34. Responsibility and redistribution • Take account of individual responsibility? • 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 • 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 • 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: SkFk(a) = Skf(ak) • anonymous: if ai = aj then Fi(a) = Fj(a)

35. Responsibility Principles • 1. Equal Income for Equal R-attributes • focus on distribution itself • if aiR= ajR then Fi(a) = Fj(a) • 2. Equal Transfers for Equal C-attributes • focus on changes in distribution • if aiC= ajC then Fi(a) – f(ai) = Fj(a) – f(aj) • Problem (Bossert and Fleurbaey 1996): • EIER and ETEC are incompatible except in the special case • f(ai) = g(aiR) + h(aiC) • In this special case, a natural redistribution mechanism • Fi0(a) = g(aiR) + (1/n)Skh(aiC) • In general case we need a compromise…

36. Compromises • 1. Egalitarian-equivalent mechanisms • 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 • 2. Conditionally-egalitarian mechanisms • FiCE(a) = f(ai) – f(a*R, aiC) + G • G := (1/n) Skf(a*R, akC) • insist on strict compensation (ETEC) but weaken EIER • Both compromises use reference characteristics (R or C) • 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

37. 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? 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? We will come back to consider the implications of these questions

38. 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

39. References 2 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: 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 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

40. 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.