Efficiency, Equality, Poverty Doctoral Course, Université de la Méditerranée – 2008-2009 Nicolas Gravel.

Efficiency, Equality, Poverty

Doctoral Course, Université de la Méditerranée – 2008-2009

Nicolas Gravel

« The importance of the formal results lies ultimately in their relevance to normal communication, and to things that people argue about and fight for »

Amartya K. Sen

What are the things that people argue about and fight for ?

People argue about and fight for the defense of their private interest (much too often perhaps)

People argue about and fight for the construction of a « better » world

A better world = a world with less suffering, less exploitation, more…justice

« Justice is the first virtue of social institutions, as truth is of systems of thought. A theory however elegant and economical must be rejected or revised if it is untrue; likewise laws and institutions no matter how efficient and well-arranged must be reformed or abolished if they are unjust. »

John Rawls

But what is justice ?

When can we say that a particular social arrangement is « just » and another « unjust » ?

When can we say that a social institution is more just than another ?

Purpose of the course

To present answers proposed by economists to questions

More specifically, to present methods used by economists to compare societies on the basis of their performance in achieving justice

Many methods discussed here are ethically robust

Comparing societies ?

Comparing two different societies at a given moment (is France more just than the US ?)

Comparing a given society at different points of time (is India better now than fifteen years ago ?)

Comparing a society after a tax reform with the same society without the tax reform

Comparing societies ?

Society = A list of individuals Approaches focus on specific attributes

of these individuals Attributes: Income, health, education,

access to public good, etc. Comparing societies amount to

comparing distributions of these attributes across individuals

Robust methods of normative appraisal ?

Method: we want it to be routinely and « easily » implementable

Based on explicit ethical principles Robustness: ethical principles that justify

the methods are widely acceptable Price to pay for robustness:

Incompleteness. The methods may fail to provide answers to the questions above. Ethical principles may conflict.

Comparing societies: some examples

Comparing 12 OECD countries (+ India) based on their distribution of disposable income and some public goods (based on Gravel, Moyes and Tarroux (2008)

Sample of some 20 000 households in each country (1998-2002)

Disposable income: income available after all taxes and social security contributions have been paid and all transfers payment have been received

Incomes are made comparable across households by equivalence scale adjustment

Incomes are made comparable across countries by adjusting for purchasing power differences

disposable income

1 2 3 4 5 6 7 8 9 10

individual rank

Australia

France

Germany

sweden

What are these data saying on justice ?

Except for the 10% poorest, americans in every income group have larger income than French, swedish and German. Does that mean that US is a « better » society than UK, France, or Sweden ?

Americans in every income group have larger income than British, Australians, Italians, spanish and Indians. Does that mean that US is a better society than UK, Australia, Italy, Spain or India ?

It would seem so if income was the only relevant attribute. But is that so ?

Another attribute: regional infant mortality

Infant mortality (number of children who die before the age of one per thousand births) is a good indicator of the overall working of the medical system of the region where individuals live

How do countries compare in terms of the different infant mortality rate that they offer to their citizens on the basis of their place of residence ?

Number of deads per 1000

1 2 3 4 5

infant mortality groups

Australia

France

Germany

Sweden

Other attribute: average class size in public schools

How do countries compare in terms of the distribution of the class sizes at public school ?

Class size: a good indicator of the school quality

Class sizes (number of children/class)

1 2 3 4 5

Groups of Class size

Australia

France

Germany

Sweden

General principles that can be derived from these comparisons Countries differ by the total amount of each

attribute they allocate to their citizens :« size of the cake »

They also differ by the way they share this cake

Less obviously, they also differ by the way they correlate the attribute between people (are individuals who are « rich » in income also those who are « rich » in health, or education? )

2 cakes of different sizes: US & Sweden

Sweden

Sharing the US cake

2% 4%5%

10%12%

Sharing the Swedish cake

11%12%

Ethical principles examined in this course consider that: For a given distribution, a larger cake is

better than a smaller one Given the size, a « more equal »

distribution of the cake is better than a less equal one (requires a definition of what is meant by « more equal »)

Given sizes and distributions of several « cakes », less correlation between cakes is better

Modern theory of economic justice

A difficult birth: An impossibility theorem (Arrow 1951)

It is impossible to define a consistent and informationally parcimonious ranking of societies that is respectful of individual preferences

Escape out of this theorem have taken two routes: welfarist and non-welfarist

What is justice ? A welfarist answer (1) Welfarism: The only thing that matters for

evaluating a society is the distribution of welfare – happiness - between individuals

Individual preferences are important insofar as they are connected to individual welfare

A just society is a society that maximises an increasing function of individual happiness

Philosophical foundations: Hume, Bentham, Beccaria

What is justice ? A welfarist answer (2)

Fundamental assumption: individual happiness can be measured and compared (necessary to escape from Arrow’s theorem)

We don’t need to know how to measure happiness but we have to accept the idea that we can measure it in a meaningful way.

Individual welfare is assumed to depend upon the individual attributes

The relationship between welfare and attributes is assumed to satisfy basic properties

Specifically, we assume:

Happiness is increasing with respect to each attribute (more income makes people happier, so does more health, smaller class sizes, etc.)

The extra pleasure brought about by an extra unit of an attribute decreases with the level of the attribute (a rich individual gets less extra pleasure from an extra euro than does an otherwise identical poorer individual)

The rate of increase in happiness with respect to a particular attribute is decreasing with respect to every other attribute

Which function of individual happiness should we maximize ?

Classical Utilitarianism (Bentham): the sum Modern view point: a function that exhibits

some aversion with respect to happiness-inequality

Extreme form of aversion toward happiness-inequality (John Rawls): Maxi-Min, we should focus only on the welfare of the less happy person in the society.

Contrasting Maxi-min and Utilitarianism

disposable income

1 2 3 4 5 6 7 8 9 10

individual rank

France

disposable income

1 2 3 4 5 6 7 8 9 10

individual rank

France

disposable income

1 2 3 4 5 6 7 8 9 10

individual rank

France

sum of income is larger in USthan in UK and in UK than inFrance

disposable income

1 2 3 4 5 6 7 8 9 10

individual rank

France

sum of income is larger in USthan in UK and in UK than inFrance but the poorest individualis richer in France than in the USor in the UK

To sum up, for welfarism:

1: A society = a list of combinations of observable attributes (one such combination for every individual)

2: Each combination of attributes is transformed into (unobservable) happiness

3: Societies are compared on the basis of their distributions of happiness

Society A is better than society B if the distribution of happiness in A is considered better than that in B by any function that exhibits aversion to happiness-inequality, under the assumption that the relationship between unobservable individual happiness and obervable individual attributes satisfies the above properties (Welfarist dominance)

non-welfarist principles

Some philosophers and economists object to welfarism

They claim that individual happiness is not the only thing that matters, that individual happiness can not be meaningfully measured, and/or that it is not society’s business to be concerned with individual’s happiness

Other individual attributes are considered intrinsically important: freedom, ressources, preferences,…

Object of the course Propose operational methods for comparing societies that

are tightly connected to ethical principles (welfarist or not) Because of the difficulty of accepting a specific ethical

theory, look for methods that are agreed upon by a wide spectrum of ethical theories (robustness)

To the extent possible, try to connect the rankings of societies to elementary operations having a clear meaning

Theory of this is well-established when attention is restricted to distributions of one attribute (income)

A lot of research is needed to develop robust methods for the multi-attributes case

When can we say that one society is better than another ? (the one attribute case)

n individuals identical in every respect other than the considered attribute (income)

y = (y1,…,yn) an income distribution

y(.) = (y(1),…,y(n)) the ordered permutation of y (considered equivalent to y if the ethics used is « anonymous »)

Q: When are we « sure » that y is « more just » than z ?

Anwer no 1: Mana and Robin Hood

When y(.) has been obtained from z(.) by giving mana to some, or all, the individuals

When y(.) has been obtained from z(.) by a finite sequence of bilateral Pigou-Dalton (Robin Hood) transfers between a donator that is richer than the recipient.

When y(.) has been obtained from z(.) by both manas and Robin Hood transfers

Mana ?

1 2 3 4 5 6 7 8 9 10

Mana ?

1 2 3 4 5 6 7 8 9 10

Robin Hood and Mana ?

1 2 3 4 5 6 7 8 9 10

Australia

Canada

Australia

Canada

Australia

Canada

Australia

Canada

Australia

Canada

1 2 3 4 5 6 7 8 9 10

Australia

Canada

1 2 3 4 5 6 7 8 9 10

Australia

Canada

1 2 3 4 5 6 7 8 9 10

Australia

Canada

Answer no 2: Poverty dominance

Important issue: poverty How do we define poverty ? Basic principle: You define a (poverty)

line that partitions the population into 2 groups: poor and rich

2 measures of poverty

1) Headcount: Count the number (or the fraction) of people below the line

2) poverty gap: Calculate the minimal amount of money needed to eliminate poverty as defined by the line

Contrasting headcount and poverty gap

Australia Austria Canada France Germany Italy Portugal Spain sweden Switz. UK USA India

4733 6815 4285 6170 5855 3554 2546 2747 5808 8679 4898 5403 789

9237 10730 8977 9555 10012 6575 4602 5407 9056 14615 8598 11025 1019

11795 12850 11935 11793 12024 8059 6110 7045 10540 17334 10883 14687 1168

14580 14725 14338 13441 13229 9438 7549 8646 11982 19806 13337 18142 1309

17377 16588 16839 15092 14857 10933 8666 10113 13371 22044 15854 21581 1462

20456 18665 19494 16966 16614 12629 10028 11656 14723 24554 18579 25206 1649

24203 20921 22382 19169 18376 14769 11415 13639 16147 27696 21574 29387 1859

28467 24042 25955 22382 21221 17342 13930 16535 18140 32095 25188 34819 2167

34592 28069 30958 26834 25201 20743 18113 20968 21091 38254 30190 43373 2694

54537 38539 44457 40175 39217 31174 32047 35457 30818 61849 49022 79030 4735

Line = 9 600

There are 2 poor in France and 1 poor in germanybut poverty gap in Germany is 3745 while it is only3465 in France

Poverty dominance Problem with poverty measurement: how

do we draw the line ? Criterion: society A is better than society

B if, no matter how the line is drawn, poverty is lower in A than in B for the poverty gap (poverty gap dominance)

Answer no 3: Lorenz dominance Lorenz dominance criterion: Society A

is better than society B if the total income held by individuals below a certain rank is higher in A than in B no matter what the rank is.

Easy to see with Lorenz curves. Let us draw Lorenz curves with our data.

100000

150000

200000

250000

1 2 3 4 5 6 7 8 9 10

individual rank

Australia

France

Germany

Sweden

Cool! the 3 answers are all equivalent to the welfarist dominance answer

It is equivalent to say : society A is more just than society B for any

welfarist ethics One can go from B to A by a finite sequence

of Robin Hood transfers and/or mana Poverty gap in A is lower than in B for all

poverty lines Lorenz curve in A is everywhere above that

This result is a beautiful one

Comes from mathematics: Hardy, Littlewood & Polya (1936), Berge (1959),

Adapted to economics by Kolm (1966;1969), Dasgupta, Sen and Starett (1973) and Sen (1973)

It provides a solid justification for the use of Lorenz curves

Lorenz dominance chart

Switzerland US

UKAustralia

Canada

Austria

France Germany

Sweden

Portugal

Important challenge: to extend to many attributes

Same welfarist ethics Suitable generalization of poverty notions

(poverty in several dimensions) No Lorenz curves New issue: Correlation between

attributes

Aversion to correlation ?

Literacy rate (%)

Income (rupees/month)400 700

a red society

Literacy rate (%)

a red society

and a white society

Literacy rate (%)

a red society

and a white society

white society is more just

Bidimensional dominance chart

Switzerland

USUKAustralia Canada Austria

FranceGermany Sweden

Portugal

Efficiency, Equality, Poverty Doctoral Course, Université de la Méditerranée – 2008-2009 Nicolas Gravel.

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