Frank Cowell UB Public Economics June Welfare Analysis

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

Frank Cowell: The role of public economics UB Public Economics n n 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: u u u n 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?

Frank Cowell: Economic rôle of government. . . ? UB Public Economics n Regulator and enforcer u u n Spender u u n Public goods Public provision of private goods Revenue raiser u n Enforcement of property rights Prices, quantity, quality standards Taxes, user charges. . . Redistributor u Taxes, and spending. . . A brief agenda. .

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

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

Frank Cowell: Finding room for public economics UB Public Economics n n n 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.

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

Frank Cowell: Market economy: operation n Assumptions: UB Public Economics u u n Implications: u u n Given property distribution informed optimisation Free contracting Known prices Incomes are automatically generated Equilibrium (CE) under fairly general conditions Equilibrium system: a fundamental mapping property distribution n goods allocation individual welfare Is this a means of steering the economy?

Frank Cowell: Market economy: basic results n UB Public Economics n Using the mapping seems a powerful argument. It is strengthened by appeal to welfare theorems: 1. 2. n Implications: u u u n Any CE is Pareto Efficient (PE) Any PE allocation can be “supported” by a CE 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?

Frank Cowell: Problems with the market ? UB Public Economics n n Why might the delivery system not work? Classic issues in market failure: u externalities u public goods u non-existence of equilibrium Informational problems in redistribution u unobservable resources u uncertainty about prices Opens up natural discussion of role for public sector

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

Frank Cowell: Policy options UB Public Economics n n 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?

§ A classic trade-off § Social values § An optimum? UB Public Economics efficiency Frank Cowell: An standard approach? §Need to define terms. . . §What is “efficiency”? §What is “equity”? l equity

Frank Cowell: Efficiency-equity trade-off n Is there necessarily a trade-off? UB Public Economics u n What is efficiency? u u n 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: u n Not if we can redistribute resources without transactions cost. A criterion for Public Economics applications such as tax design. What is equity? u u Raises issues of definition. Also of the case for egalitarianism (Putterman et al. - JEL 98).

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

Frank Cowell: Welfare approaches UB Public Economics n Ordinal approaches to welfare u u u n Welfarism u u u n These are of little use Run into the Arrow (1953) problem Hence are hopelessly indecisive 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…

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

Frank Cowell: Ingredients of an approach UB Public Economics n A model of individual resources n A measure of individual welfare n A basis for interpersonal comparisons n An intellectual base for state intervention n We will deal with the first three of these now.

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

§ Two persons § The feasible set ity al eq u of y ra UB Public Economics Janet’s income Frank Cowell: A simple model for the distributional problem Income distributions with given total 45° 0 Irene’s income § The interesting distributions § The basic cake-sharing income-distribution problem

Frank Cowell: Limitations of this basic model UB Public Economics n Just 2 persons u n Fixed-size cake u u n Economic growth? Waste through distortion? Essential to first-best welfare economics Costlessly transferable incomes u u n n ³ 3 persons for the inequality problem The “leaky bucket” problem Analysed further in discussion of incentives Incomes or utilities?

Example 1 Frank Cowell: Example 2 For welfare purposes we are concerned with utility. . . UB Public Economics 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) =2 U(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. n What is the relationship of utility to income? n What properties does utility have? u u n n Is it measurable? Is it comparable? These properties are independent We need a We usually need both simple model of utility. .

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

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

Frank Cowell: Basic questions about income UB Public Economics n Is it unique? n How comprehensive should it be? n What is the relevant receiving unit? n Is it comparable between persons?

Frank Cowell: Income: Uniqueness? n Should we use univariate or multivariate analysis? u UB Public Economics u u n A relationship between different types of “income”? u u n income and expenditure? income and wealth? income over time? covariance of earnings and asset income? conditional transfers? Several definitions may be relevant? u u u gross income? disposable income? other concepts?

Frank Cowell: Income: comprehensiveness? n Is income “full income”? u UB Public Economics u n Is income a proxy for economic welfare? u u n discount for risk? valuation over time? . . Can income be zero? u n final income + value of leisure +. . . ? rental income? . . . or less than zero? u business losses?

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

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

§ Plot share of food in budget against household §income A reference household type. . . § Engel Equivalence Scale sfood UB Public Economics proxy for “need” Frank Cowell: A model of income and need 0 childless couple with children xr º yr From budget studies x, y xi yi income

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

Frank Cowell: The relationship between utility and income: UB Public Economics u Increase concavity u = U(y) ^ u = U(y) y

Frank Cowell: A simple model UB Public Economics n As an example take the iso-elastic form: y 1 – d – 1 U(y) = ———— , d ³ 0 1 –d n n We can think of d as risk aversion But it may take on an additional welfare significance

Frank Cowell: What to do with this information? UB Public Economics n We need a method of appraising either the distribution of utilities… n …or, the system by which they were produced n This involves fundamentally different approaches to welfare judgments.

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

Frank Cowell: Five intellectual bases for public action UB Public Economics n …and five social philosophers n Entitlement theories u n Unanimity u n Bentham Concern with the least advantaged u n Pareto Utilitarianism u n Nozick Rawls Egalitarianism u Plato

§ Standard cake-sharing model eq u of y l N ra UB Public Economics al ity § N stands for “Nozick” Janet’s income Frank Cowell: A distributional outcome implications for utility possibilities 45° 0 Irene’s income

§ Plot utility on the axes § Simple cake-sharing § The effect of utility interdependence of eq u UB Public Economics al it y uj l l N N ra y Frank Cowell: Utility-possibility set Assuming that U is strictly concave. . . …and that U is the same function for both Irene and Janet. 0 45° ui

Frank Cowell: Should we move from N? UB Public Economics n What is the case for shifting from the status-quo point? n Answer differs dramatically according to social philosophy: n Entitlement approach is concerned with process n Other approaches concerned with end-states

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

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

§ The utility-possibility set again § The initial point § Pareto superior points l N y of eq u UB Public Economics al ity uj ra Frank Cowell: Pareto improvement: simple case §No case for intervention? 0 45° ui

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

Frank Cowell: Benthamite approach UB Public Economics n General principle is “Seek the greatest good of the greatest number” n This is typically interpreted as maximising the sum of individual welfare. n In Irene-Janet terms: u 1 + u 2 +. . . + un n More generally the SWF is: WB = ò u d. F(u)

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

§ Take a symmetric utilitypossibility set uj § The initial distribution al ity UB Public Economics § Benthamite welfare contour eq u § Maximise welfare of § Optimum in this case l § Implied tax/transfer ra y Frank Cowell: Benthamite redistribution? N l B ui+uj = constant 0 45° ui The general case?

Frank Cowell: The general case. . . uj l N l C l UB Public Economics § Incorporates differential incentive effects etc. § N. The status quo § Pareto improvements § Points that Paretodominate N § C The voluntary solution? § Anywhere above C might be a candidate B § B. Benthamite solution ui 0 §Paretianism leads to multiple solutions §Benthamite utilitarianism leads to a unique, possibly different, solution.

Frank Cowell: General case: discussion UB Public Economics n A motive for changing distribution? u u u n Nozickians might still insist that no move from N is justified unless it came through private voluntary action Applies even to C Implementation: u u Private voluntary action might not be able to implement C Could rise if there were many individuals n Case for egalitarianism? n Clearly Bentham approach does not usually imply egalitarian outcome. Consider two further alternative approaches: u u u Concern for the least advantaged (Rawls) Egalitarianism

Frank Cowell: Rawls (1971) n UB Public Economics Rawls’ distributional philosophy is based on two fundamental principles: 1. 2. n Economic focus has usually been on 2 u u n 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 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 u Avoid confusion with a probabilistic approach we consider later

Frank Cowell: The Rawls approach…? UB Public Economics n n What is meant by the difference principle? This is typically interpreted as maximising the welfare of the worst-off person. u u u n n Based on simplistic interpretation of veil of ignorance argument Rawls interpreted it differently But rather vaguely In Irene-Janet terms: min {u 1 , u 2 , . . . , un} So the suggested SWF is: WR = {min u: F(u)>0}

Frank Cowell: Egalitarianism? UB Public Economics n n Origin goes back to Plato… …but reinterpreted by Meade (1974). u “Superegalitarianism” Welfare is perceived in terms of pairwise differences: [ui uj]. . . Welfare might not be expressible as a neat additive expression involving individual utilities. u Finds an echo in more recent welfare developments u Covered in a later lecture

uj l N § A 'Rawlsian' solution § Superegalitarianism R eq u al ity l of UB Public Economics Contours of max min function ra y Frank Cowell: General case (2) l §Maxi-min does not imply equality E §Superegalitaranism implies equality ui 0

Frank Cowell: Bergson-Samuelson approach UB Public Economics n But why an additive form of the SWF? n We could just use a weaker individualistic form. n This is the basis of the Bergson-Samuelson formulation u A generalisation u Subsumes several welfare concepts n In Irene-Janet terms: W(u 1 , u 2 , . . . , un) n More generally the SWF is: WBS = W(F)

Frank Cowell: General individualistic welfare UB Public Economics n The specific welfare functions are special cases of Bergson-Samuelson. n Most satisfy the principle of additivity u Except for the last one (utility differences) n In Irene-Janet terms this means we can write: u(u 1) + u(u 2) +. . . + u(un) n More generally the SWF is: WBSa = ò u(u) d. F(u) n This is clear for Bentham where u(u )= u. But…

Frank Cowell: General individualistic welfare (2) UB Public Economics n …we can say more n Again take the iso-elastic form, this time of the (social) u-function: n u 1–e – 1 u(u) = ————, e ³ 0 1–e Bentham corresponds to the case e = 0. n Max-min (“Rawls”) corresponds to the case e=. n Intermediate cases (0<e< (0< ) are interesting too

Frank Cowell: General case (closeup) § B. Benthamite (e = 0) § W. Intermediate (e = 1) UB Public Economics § R. 'Rawlsian' ( e = ) l B § ‘E. Superegalitarianism' (no e value) l W l R l E

Frank Cowell: A brief summary UB Public Economics n Entitlement theories u n Unanimity u n A basis for egalitarianism? Concern with the least advantaged u n Blairism? Utilitarianism u n Thatcherism? How to be interpreted? (Super)-egalitarianism u u Out of fashion in UK. In Spain. . . ?

Frank Cowell: Overview. . . Welfare Analysis of Public Economics UB Public Economics A model of intervention A reinvention of utilitarianism? Income, welfare, utility The basis for redistribution Risk and welfare

Frank Cowell: But where do the values in the SWF come from. . . ? UB Public Economics n Consensus u n High-minded idealism u n Social and private values. . . ? The PLUM principle u n Runs into the “Arrow Theorem. . . ” “People Like Us Matter” – a cynical approach The Harsanyi approach u Based on individual rationality under uncertainty take another look. . .

Frank Cowell: High-minded idealism? n UB Public Economics n Do people care about inequality or other distributional issues? Multiple values argument u u n Externality argument u u n Suppose that people are “schizophrenic” They have two sets of values, private and public. People treat the income distribution as a “public good” Hochman and Rodgers (AER 1969) Motivates the formulation u = U (y, F) u Individuals care about the income distribution F

Frank Cowell: The PLUM principle UB Public Economics n Interest groups may determine what the SWF is u n n n Champernowne and Cowell (1998) No reason to suppose that it has a direct connection with individual utilities However we may still be able to say something about how values are/should be determined For example they should at least be consistent

Frank Cowell: An approach based on risk analysis UB Public Economics n Social welfare is based individual utility u u n n Each citizen ranks social states on the basis of expected utility These utilities concern life prospects u u u n Utility is of a representative person Harsanyi (Journal of Political Economy 1953, 1955) made behind a “veil of ignorance” similar to Rawls Ignorance concerns income, wealth, social position etc But what of personal values? We need to reconsider and reinterpret the sum-of-utilities approach.

Frank Cowell: Reinterpret sum-of-utilities UB Public Economics n The Irene-Janet version: u 1 + u 2 +. . . + un n This is equivalent to: (1/n)u 1 + (1/n)u 2 +. . . + (1/n)un n Reinterpreted as: p 1 u 1 + p 2 u 2 +. . . + pnun , where pi : = 1/n n Which is simply E ui

Frank Cowell: Reinterpret sum-of-utilities (2) UB Public Economics n The formal utility function: ò u d. F(u) n This is equivalent to: ò U(y) f(y)dy n Reinterpreted as: òU(y(a)) p(a) da n Which is simply E U(y(a)) n How do we reach this conclusion…?

Frank Cowell: Welfare and Risk? n Expect links between welfare and risk analysis u UB Public Economics u Argument by analogy Atkinson (JET 1970) on inequality n The Harsanyi paradigm (J. Pol. E. 1953, 1955) n Harsanyi’s contribution is fundamental Consists of two strands. n u See Amiel et al (2005)

Frank Cowell: Harsanyi 1 UB Public Economics n n n Aggregation theorem Consider preferences over set of lotteries L 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

Frank Cowell: Harsanyi 1 (contd) UB Public Economics n n n Powerful result Does not assume interpersonal utility comparisons. If such comparisons ruled out, the ai are based on the evaluator’s value judgments (Harsanyi 1978, p. 227) u u u n n n personal? arbitrary? the evaluator? “Judges and other public officials” (1978, p. 226) Need not be a member of the society Must satisfy some consistency requirements

Frank Cowell: Harsanyi 2 UB Public Economics n n n Impartial observer theorem. Basic idea already in Vickrey (1945). Assumes interpersonal comparisons of utility. An impartial observer sympathetic to the interests of each member of society makes value judgments. The observer is to imagine himself being person i. u i’s objective circumstances u i’s preferences

Frank Cowell: Harsanyi 2 (contd) UB Public Economics n n How to get a representative person? Thought experiment u u Evaluator imagines he has an equal chance of being any person in society Equal consideration to each person’s interests. n Impartial observer calculates average expected utility of each lottery in L: n I. e. person j’s expected utility

Frank Cowell: Implications of Harsanyi approach UB Public Economics n The aggregation theorem gives an argument for additivity n The “representative person” induces a probabilistic approach n Then social welfare is found to be inherited from individual expected utility n But on what basis do we get the probabilities here? n And is “expectations” an appropriate basis for social choice?

Frank Cowell: Harsanyi: Some difficulties UB Public Economics n Are preferences known behind the “Veil of ignorance”? u u n n Not in the Rawls approach But Harsanyi assumes that representative person knows others utilities Is it useful to suppose equal ignorance? Subjective probabilities may be inconsistent Should we be concerned only with expected utility? It is not clear that individuals view risk-choices and distributional choices in the same way u u Cowell and Schokkaert (EER 2001). Carlsson et al (Economica 2005)

UB Public Economics the veil of ignorance the cynical approach a general view probability Frank Cowell: Identity | | | 1 2 3 | | i n identity

Frank Cowell: A difficulty with expected utility? n Suppose the outcomes depend on uncertain events u UB Public Economics n probabilities of Events 1, 2 are (p, 1 p) Payoffs for persons (i, j) under two policies are Policy a b n n u n Event 2 (1, 0) (0, 1) Consider choice between policies a and b Expected payoffs are: u n Event 1 (1, 0) 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 u See Diamond (Journal of Political Economy 1967).

Frank Cowell: Views on redistribution UB Public Economics n n Source: Ravallion and Lokshin (JPub. E 2000) Clearly views on distribution depend on (i) your current position and (ii) your expectations

Frank Cowell: Concluding remarks n UB Public Economics n n n We can construct a model with an individualistic base for welfare comparisons. The alternative social philosophies may give support to redistributive arguments, But it raises some awkward questions. . . Should the social basis for redistribution rest on private tastes for equality or aversion to misery? u n Should it rest on individual attitudes to risk? u n What if people like seeing the poor. . ? What if people are not risk-averse? We will come back to consider the implications of these questions