Welfare Analysis of Distribution

1. Welfare Analysis of Distribution Public Economics: University of Barcelona Frank Cowell http://darp.lse.ac.uk/ub June 2005

2. The role of public economics • What is the motivation for our subject? • What is the reason for intervention by public sector in private economic activity? • This is a main purpose of this lecture • We will: • Examine the rationale of the public sector • Analyse alternative philosophical bases for intervention • Develop a simple model of welfare • First: how to characterise the role of the public sector?

3. Economic rôle of government...? • Regulator and enforcer • Enforcement of property rights • Prices, quantity, quality standards • Spender • Public goods • Public provision of private goods • Revenue raiser • Taxes, user charges... • Redistributor • Taxes, and spending... A brief agenda....

4. Agenda • Previous classification is ad hoc. • We seek a reasoned basis for the rôle of public sector. • Use the standard microeconomic model as context. • Find the rôle for the public sector in this context. • Examine “Equity-efficiency trade-off”. • Incorporate social values.

5. Overview... Welfare Analysis of Public Economics A model of intervention Roots in basic microeconomics Income, welfare, utility The basis for redistribution Risk and welfare

6. Finding room for public economics • We want to ground the public sector within conventional economics. • The public sector should not be seen as a kind of alien invader. • It should follow naturally from the model of the economic system. • In effect we “find room” for the public sector within microeconomics . • We begin with a standard paradigm.

7. A simple model of the economy • The basics: • A collection of persons • A collection of resources • A collection of firms • Private ownership: • Entitlement to the resources • Shares in the firms • A market allocation: • Consumption basket for each person • Output/input programme for each firm • A set of prices • Competitive if everyone is maximising A complete description of the economy? Determines incomes in market allocation A complete description of a social state?

8. Market economy: operation • Assumptions: • Given property distribution • informed optimisation • Free contracting • Known prices • Implications: • Incomes are automatically generated • Equilibrium (CE) under fairly general conditions • Equilibrium system: a fundamental mapping  individual welfare property distribution  goods allocation • Is this a means of steering the economy?

9. Market economy: basic results • Using the mapping seems a powerful argument. • It is strengthened by appeal to welfare theorems: • Any CE is Pareto Efficient (PE) • Any PE allocation can be “supported” by a CE • Implications: • Decide on the type of efficient outcome you want. • Use political system to get resource distribution right • Use the competitive system as a delivery vehicle • But could there be trouble in this competitive paradise?

10. Problems with the market ? • Why might the delivery system not work? • Classic issues in market failure: • externalities • public goods • non-existence of equilibrium • Informational problems in redistribution • unobservable resources • uncertainty about prices • Opens up natural discussion of role for public sector

11. Rôle for government? • Facilitate the economic system • Enforce property rights • Correct “market failure” • Externalities • Public goods • Information problems • Change the resource distribution • But may not be possible without excessive cost • Change the relationship between resources and allocations • A policy trade-off…?

12. Policy options • Often depicted as a trade-off. • But what kind of trade-off? • Is a trade-off actually necessary? • And how to make the choice from the trade-off options?

13. An standard approach? • A classic trade-off • Social values • An optimum? efficiency • Need to define terms... • What is “efficiency”? • What is “equity”? equity

14. Efficiency-equity trade-off • Is there necessarily a trade-off? • Not if we can redistribute resources without transactions cost. • 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 efficiency gains and losses: • A criterion for Public Economics applications such as tax design. • What is equity? • Raises issues of definition. • Also of the case for egalitarianism (Putterman et al. - JEL98).

15. Components of the policy problem • Specification of the technology • Production of private and public goods • Enables precise definition of efficiency • A definition of equity • Also related concepts such as inequality • See later lectures • An analysis of the nature of the trade-off • Informational problems • See lecture on design issues • A statement of social preferences • What is the basis for concern with distribution? • We deal with this in the current lecture

16. Welfare approaches • Ordinal approaches to welfare • These are of little use • Run into the Arrow (1953) problem • Hence are hopelessly indecisive • Welfarism • Uses a cardinally measurable and interpersonally comparable approach to welfare. • Usually based on individualism • Provides the basis for a coherent model • Need to examine the basic building blocks…

17. Overview... Welfare Analysis of Public Economics A model of intervention The basic units of analysis Income, welfare, utility The basis for redistribution Risk and welfare

18. Ingredients of an approach • A model of individual resources • A measure of individual welfare • A basis for interpersonal comparisons • An intellectual base for state intervention • We will deal with the first three of these now.

19. Individual resources and distribution • We adopt two simple paradigms concerning resources: • The cake-sharing problem • The general case with production • Often distributional analysis can be conducted in terms of typical individuals i and j. • In some cases one needs a more general distributional notation Fixed total income Incorporates incentive effects Irene and Janet The F-form approach

20. Income distributions with given total A simple model for the distributional problem • Two persons • The feasible set • The interesting distributions • The basic cake-sharing income-distribution problem ray of equality Janet’s income 45° 0 Irene’s income

21. Limitations of this basic model • Just 2 persons • n³ 3 persons for the inequality problem • Fixed-size cake • Economic growth? • Waste through distortion? • Costlessly transferable incomes • The “leaky bucket” problem • Analysed further in discussion of incentives • Incomes or utilities? Essential to first-best welfare economics

22. Example 1 For welfare purposes we are concerned with utility... Example 2 • What is the relationship of utility to income? • What properties does utility have? • Is it measurable? • Is it comparable? • These properties are independent • We usually need both 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. We need a simple model of utility....

23. Ingredients • a: personal attributes • Identity • Needs • Abilities • Special “merit” or “desert” • y: income • Could be exogenous • Or you can model as a function of attributes: y=y(a) • u: individual utility • Several ways of modelling this… • …see below • x: “equivalised” income • Dollar/Pound/Euro units… • Can be treated as a version of “utility”

24. Ingredients (2) • F : distribution function • Standard tool borrowed from statistics • U : utility function • A variety of specifications – see below • Gives indicator of how “well-off” a person of given attributes is • c : equivalisation function • A simple way of accounting for differences in needs • Perhaps too simple? • We will try something different in the next lecture

25. Basic questions about income • Is it unique? • How comprehensive should it be? • What is the relevant receiving unit? • Is it comparable between persons?

26. Income: Uniqueness? • Should we use univariate or multivariate analysis? • income and expenditure? • income and wealth? • income over time? • A relationship between different types of “income”? • covariance of earnings and asset income? • conditional transfers? • Several definitions may be relevant? • gross income? • disposable income? • other concepts?

27. Income: comprehensiveness? • Is income “full income”? • final income + • value of leisure +...? • Is income a proxy for economic welfare? • discount for risk? • valuation over time?.. • Can income be zero? • rental income? • ... or less than zero? • business losses?

28. Income: Comparability? • Price adjustment • Normalise by price indices • Adjustment for needs and household size • Usual approach is to introduce equivalence scales • The equivalence transformation is x = c( y, a ) personal attributes Equivalised income nominal income • Usually a simplifying assumption is made. • Write transformation as an income-independent equivalence scale: Number of equivalent adults x = y / n (a) • Where does the function c come from?

29. Equivalence Scales • We will assume that there is an agreed method of determining equivalence scales. • But there is a variety of possible sources of information for equivalence scales: • From official government sources • From international bodies such as OECD • From econometric models of household budgets. • Consider an example of the last of these:

30. A model of income and need • Plot share of food in budget against household income sfood • A reference household type... • Engel Equivalence Scale childless couple proxy for “need” couple with children xr ºyr From budget studies x, y 0 xi yi income

31. Alternative models of utility • u = U (y) • Inter-personally comparable utility • u = U (y;a) • Individualistic utility • May not be comparable, depending on information about a. • u = U (y, F) • Concern for distribution as a kind of externality • Need not be benevolent concern • Evidence that people are • Concerned about relative incomes • “upward looking” in their comparisons. • Ferrar-i-Carbonell (2005) • x= c(y ;a) = y /n(a) • A comparable money-metric utility?

32. The relationship between utility and income: u Increase concavity u = U(y) ^ u = U(y) y

33. A simple model • As an example take the iso-elastic form: y1 –d– 1 U(y) = ———— , d ³ 0 1 –d • We can think of d as risk aversion • But it may take on an additional welfare significance

34. What to do with this information? • We need a method of appraising either the distribution of utilities… • …or, the system by which they were produced • This involves fundamentally different approaches to welfare judgments.

35. Overview... Welfare Analysis of Public Economics A model of intervention Philosophies, social welfare and the basis for intervention Income, welfare, utility The basis for redistribution Risk and welfare

36. Five intellectual bases for public action • …and five social philosophers • Entitlement theories • Nozick • Unanimity • Pareto • Utilitarianism • Bentham • Concern with the least advantaged • Rawls • Egalitarianism • Plato

37. A distributional outcome • Standard cake-sharing model • N stands for “Nozick” ray of equality Janet’s income • N implications for utility possibilities 45° 0 Irene’s income

38. Utility-possibility set • Plot utility on the axes • Simple cake-sharing uj • The effect of utility interdependence ray of equality • N • N Assuming that U is strictly concave... …and that U is the same function for both Irene and Janet. 45° ui 0

39. Should we move from N? • What is the case for shifting from the status-quo point? • Answer differs dramatically according to social philosophy: • Entitlement approach is concerned with process • Other approaches concerned with end-states

40. Entitlement approach • Focus on Nozick (Anarchy, State and Utopia, 1974). • Answer depends crucially on how N came about • Distinguish three key issues: • fairness in original acquisition • fair transfers • rectification of past injustice • Presumption is that there will be little or no role for the State • “Night watchman”

41. Pareto Criterion • Pareto unanimity criterion is an end-state principle • Approve the move from N to another point… • …if at least one person gains • …and no-one loses • Individualistic • Based on utilities • But utility may have a complicated relationship with income • May depend on the income of others • See how Pareto applies in the simple example

42. Pareto improvement: simple case • The utility-possibility set again • The initial point uj • Pareto superior points ray of equality • N • No case for intervention? 45° ui 0

43. End-state approaches: beyond Pareto • Pareto criterion can be indecisive • Alternative end state approaches use a social welfare function • Typically get unique solution • What principles should this embody? • Individualism? • The Pareto principle? • Additivity? • Take a simple example that combines them all...

44. Benthamite approach • General principle is “Seek the greatest good of the greatest number” • This is typically interpreted as maximising the sum of individual welfare. • In Irene-Janet terms: u1 + u2 + ...+ un • More generally the SWF is: WB=ò udF(u)

45. Distributional implications of utilitarianism • Much of public economics uses utilitarianism. • Efficiency criteria • Sacrifice theories in taxation • But does utilitarianism provide a basis for egalitarian transfers? • Sen has argued that this is a common fallacy • Sen and Foster (1997) • Again look at this within the simple model

46. ui+uj = constant Benthamite redistribution? • Take a symmetric utility-possibility set uj • The initial distribution • Benthamite welfare contour • Maximise welfare ray of equality • Optimum in this case • Implied tax/transfer • N • B The general case? 45° ui 0

47. The general case... uj • N • C • Incorporates differential incentive effects etc. • B • N. The status quo • Pareto improvements • Points that Pareto-dominate N • C The voluntary solution? • Anywhere above C might be a candidate • B. Benthamite solution • Paretianism leads to multiple solutions • Benthamite utilitarianism leads to a unique, possibly different, solution. ui 0

48. General case: discussion • A motive for changing distribution? • Nozickians might still 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? • Clearly Bentham approach does not usually imply egalitarian outcome. • Consider two further alternative approaches: • Concern for the least advantaged (Rawls) • Egalitarianism

49. Rawls (1971) • Rawls’ distributional philosophy is based on two fundamental 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 a probabilistic approach we consider later

50. The Rawls approach…? • What is meant by the difference principle? • This is typically interpreted as maximising the welfare of the worst-off person. • Based on simplistic interpretation of veil of ignorance argument • Rawls interpreted it differently • But rather vaguely • In Irene-Janet terms: min {u1 , u2 , ..., un} • So the suggested SWF is: WR= {minu: F(u)>0}