Inequality and Social Welfare Peter Lanjouw Poverty and Inequality Analysis Course 2011 Module 5: Inequality and Pro-Poor Growth

Inequality and Social Welfare

Peter Lanjouw Poverty and Inequality Analysis Course 2011

Module 5: Inequality and Pro-Poor Growth

Thursday March 3 Session 1 (Peter Lanjouw): 9:00-10:45

– Opening Remarks and Introductions– Measurement of Economic Inequality

Session 2 (Francisco Ferreira): 11:15-12:30– Inequality Decompositions and Inequality of

Opportunity Session 3 (Branko Milanovic): 2:00-3:15

– Inequality in History Session 4 (Branko Milanovic): 3:30-5:00

– From Kuznets Curve to Top Income Share

Course Outline

Friday, March 4 Session 5 (Martin Ravallion): 9:30-10:45

– Economy Wide Policies and Pro-Poor Growth Session 6 (Branko Milanovic): 11:30-12:30

– Global Income Inequality Session 7 (Sergiy Radyakin): 2:00-3:30

– A Standard Set of Tools and Calculations

Course Outline Cont.

The Measurement of Economic Inequality:Outline

Constructing a measure of welfare– Income or consumption?– Components and adjustments

Inequality and theories of social justice Inequality measurement and normative judgements The Atkinson class of inequality measures Selecting ε (Okun’s leaky bucket) Recommendations.

Constructing a measure of welfare: alternatives

Consumption per capita– Value of total consumption (whether or not transacted)

Income per capita– Poor indicator when incomes vary; hard to measure

Consumption per equivalent single adult– Problems with forming scales; composition versus size

economies; intra-household inequality. Food-share ("Engel's Law")

– Sources of noise: other parameters; problem of income elasticity near unity. Identification problems.

Nutritional indicators– "Welfarist" critique (welfare and nutrition are different things);

nutritional requirements/ anthropometric standards.

Recommendations

Use a comprehensive consumption measure, spanning consumption space

Choice between income and consumption is largely driven by the greater likelihood of accuracy of information on consumption.

– Although note the interest, now, in both tails of the distribution

Recognize the limitations of consumption based measures; look for supplementary measures, especially access to public services, subjective welfare as a clue to measuring objective welfare.

Constructing a Consumption Measure

The consumption measure serves as the foundation upon which much of the subsequent analysis rests.

Principles– Should be comprehensive– Retain transparency and credibility– Goal is to be able to rank individuals credibly in

terms of welfare

Common Steps

Construct a food consumption measure Add basic non-food items (from consumption

module) Add other non-food items (other modules) Add housing expenditures Add use-value of consumer durables

Aggregating Food and Basic Non-Food Expenditures

Food expenditures should include not only purchased items but also consumption out of home production.

Key issue is to distinguish between investments and consumption (avoid double counting).

Health expenditures are usually excluded Two Additional omissions:

– Leisure– Public goods

Imputing Housing and Durables Expenditures

Many surveys ask specifically what an owner-occupier household would pay in rent if it were renting. Where credible this number can be used for home owners.

Elsewhere one can try to predict rent paid based on regression models estimated on subset of renting households.

Purchases of irregular, lumpy items such as consumer durables (tv, car, etc.) cannot be directly added to the consumption definition.

– If supplementary information is available, it is sometimes possible to impute a stream of consumption services from durables ownership

Aggregate Gini Coefficient

Food Spending 0.359

Food Spending plusBasic Non-Food Spending 0.420

Food plus Basic Non-FoodSpending Including Energyand Education Spending 0.421

Above With Actual or ImputedWater Expenditures 0.415

Above With Actual or Imputed 0.420Value of Housing Services

Above With Imputed Value 0.430of Owned Consumer Durables

Source:

Encuesta de Condiciones de Vida, 1994 (Instituto Nacional de Estatisticos y Censo, Ecuador).

Impact on Inequality of Using Alternative Consumption Aggregations - Ecuador

Adjustments to Consumption Aggregate

Spatial price variation– Cost of living adjustments

Demographic Composition– Equivalence Scales– Economies of Scale

Which unit of analysis?– Household or individual?

Inequality and theories of social justice

Is measurement of inequality solely a positive exercise?

What do different perspectives on social welfare have to say about inequality?– Utilitarianism– Rawlsian liberalism– Libertarianism


Utilitarianism Underpins most standard neo-classical welfare

economics Associated with Adam Smith, Jeremy Bentham, John

Stuart Mill, Francis Edgeworth, and Wilfred Pareto Utilitarianism: “profoundly unconcerned with

inequalities in the variable on which it focuses, individual utilities” (Sen and Foster, 1997).


Individualistic; individuals maximize utility. Problem of social choice is not that different from

individual choice; alternative states and policies are ordered and evaluated in terms of their contribution to maximize a society-wide welfare function.

Social welfare function includes all individual utility functions, with each carrying equal weight.

Goal is to maximize the sum of total utility in society.


Interpersonal comparisons of utility are ruled out.

Pareto criteria are used to evaluate different social positions.

Utilitarianism can tolerate considerable inequalities in utility

Question: what does this imply for income inequality?


“Assume that all individuals value the income they receive according to the same increasing and concave utility function. The standard maximization of the corresponding utilitarian objective (the sum of individual utilities) leads to an optimal distribution of income which is perfectly egalitarian” (Atkinson and Bourguignon, 2000)


Rawlsian Liberalism Developed by John Rawls (1971) Rather than on utility, the focus here is on “primary social goods”, which include income and wealth, but extend also to political rights, rights of voice, association, political participation, etc.


Rawls asks the question of what one would do in the “original position” of negotiating a social contract (set of principles of a just social order) behind a “veil of ignorance” about one’s personal position, as well as a degree of risk aversion.

Rawls argues that the outcome of this negotiation will reflect two principles:


a) Liberty Principle: equality of basic rights.

b) Difference Principle: economic and social inequalities will be tolerated only if they provide most benefits to least advantaged members of society, relative to any alternative institutional arrangements.


“Maximin” procedure The Pareto criterion employed by Utilitarians suggests

that you choose options in terms of maximum gain, subject to no-one losing.

The Rawls criterion cares explicitly about who benefits. Comparing two options, the Rawlsians will choose that which offers greatest benefit to the least advantaged, even if the alternative provides much greater benefit to the less deprived.


Libertarian Theories of Justice Nozick (1974) sees liberty and rights as the

constitutive components of a fully worked out libertarian theory of justice.– Reflects concerns voiced by Hayek, Buchanon,

Tullock, Sugden, Failure of justice occurs when specified rights

are violated, irrespective if other basic goals of society are better satisfied.


This version of Libertarianism is quite insensitive to actual social consequences.

For example, within Nozick’s framework the occurrence of famine may not violate social justice. Massive entitlement failure may occur without any rights being violated.

The focus is on process not outcomes. Note the egalitarianism in Nozick’s libertarianism:

everyone’s liberties count equally.


Conclusion There exists a very wide range of defensible

perspectives of social justice. Different perspectives may embody very different views

on inequality Rawls and Nozick represent endpoints along a

spectrum – from infinite concern about inequality, particularly amongst the poorest, to complete indifference.

Inequality measurement and normative judgements

All summary measures of inequality embody some normative judgements regarding inequality and the relative importance of different parts of the income distribution.

– Most measures make these judgements implicitly rather than explicitly.

Some measures are clearly unattractive:– Range: reflects well the distance between the poorest and

richest, but is totally unaffected by changes in the distribution of income within these two extremes.


A particularly desirable property in an inequality measure is that it satisfy the principle of transfers: a transfer from a poorer person to a richer person, all things equal, must result in an increase of inequality (Pigou-Dalton principle).

– This property is not satisfied by the range.

Many other measures do satisfy this property, but not other basic axioms:

– Variance has the problem of not being scale neutral


After sorting through a large set of possible measures we select only those which pass basic properties of:– Principle of transfers– Scale neutrality– Anonymity

Amongst eligible candidates there are still differences in implicit judgements:


Gini Coefficient:– Attaches more weight to transfers affecting middle

income classes– If A has an income of $2000 and B of $1900 and if

A is the 1000th richest man, while B is the 1,100th richest man, then $1 to B is the equivalent to $1.10 to A. But if an additional 100 people get incomes between $1900 and $2000 then the Gini attaches the same weight to $1 to B as to $1.20 to A.


Coefficient of variation: – Attaches equal weights to all income levels– No less arbitrary than other judgements.

Standard deviation of logarithems:– Is more sensitive to transfers in the lower income

brackets. Bottom line: The degree of inequality cannot in

general be measured without introducing social judgements.

The Atkinson class of inequality measures

Atkinson (1970) introduces the notion of ‘equally distributed equivalent’ income, YEDE.

This represents the level of income per head which, if equally shared, would generate the same level of social welfare as the observed distribution.

This then defines a measure of inequality of the following form:

IA = 1- (YEDE/μ)


A low value of YEDE relative to μ implies that if incomes were equally distributed the same level of social welfare could be achieved with much lower average income.

So IA would be large. Everything hinges on the degree of inequality aversion

in the social welfare function. With no aversion, there is no welfare gain from

redistribution so YEDE is equal to μ and IA = 0.


Atkinson proposes the following form for his inequality measure:

1

1

1)(1 ii

iA f

Y

YI


A key role here is played by the distributional parameter ε. In calculating IA you need to explicitly specify a value for ε.

When ε=0 there is no social concern about inequality and so IA = 0 (even if the distribution is “objectively” unequal).

When ε=∞ there is infinite weight to the poorer members of the population (“Rawls”)

How to choose ε?

Selecting ε (Okun’s leaky bucket)

Okun (1975) asks the hypothetical question:“Consider a transfer of $4000 per head from the top 5

percent giving, in principle, $1000 to each of the bottom 20 percent. But some of the money “leaks” away in the process. How much leakage would you be willing to accept before abandoning the proposed redistribution?”


Atkinson shows that the answer to this question can be used to back out a value of ε.

g represents the ratio of the average income of the “transferee” to the “recipient”.

x represents proportion of transfer received by the recipient.

gx

1


Suppose a hypothetical transfer from someone with twice the income level of the proposed recipient (g=2)

If you will not tolerate less than half of the transfer going to the poor (x=0.5) then ε=1.

If you will accept up to 75% leakage, then x=0.25 and ε=2.

Recommendations

No inequality measure is purely ‘statistical’: each embodies judgements about inequality at different points on the income scale.

To explore the robustness of conclusions: Option 1: measure inequality using a variety of

inequality measures (not just Gini). Option 2: employ the Atkinson measure with multiple

values of ε. Option 3: look directly at Lorenz Curves, apply

Stochastic Dominance results.

Documents

Inequality and Social Welfare Peter Lanjouw Poverty and Inequality Analysis Course 2011 Module 5: Inequality and Pro-Poor Growth