Inequality

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Inequality

• Lecture 8

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• The General Assembly Adopts the following
  Declaration
• United Nations Millennium Declaration
• I. Values and principles
• 2. We recognize that, in addition to our separate
  responsibilities to our individual societies, we
  have a collective responsibility to uphold the
  principles of human dignity, equality and equity
  at the global level. As leaders we have a duty
  therefore to all the worlds people, especially
  the most vulnerable and, in particular, the
  children of the world, to whom the future
  belongs.

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Interview with the World Bank's New Chief
Economist (F. Bourguignon) World BankNovember
12, 2003

• Equity has not been an area of particular
  emphasis for the World Bank. Is this a new
  direction?
• Its true that the Bank has focused on poverty
  and did not insist so much and as explicitly on
  inequality. I believe we must give more space to
  the problem of inequality and income distribution
  in general. Of course, growth is critical to
  poverty reduction, but we need to analyze more
  closely who actually benefits from growth, and
  from the policies, programs and projects
  undertaken to reduce poverty. Will one or another
  group, or class, benefit more than others? Are
  our strategies reducing or increasing inequality?
  Are they pro-poor, benefiting everybody in the
  same proportion or benefiting relatively more
  those who are already better off?

Source http//www.globalpolicy.org/socecon/bwwto/
wbank/2003/1112bourguignon.htm
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Interview with the World Bank's New Chief
Economist (F. Bourguignon) World BankNovember
12, 2003

• Although pro-poor growth has entered our
  vocabulary, such questions have occupied little
  space in the debate up to now. In part this is
  due to a problem of the techniques at our
  disposal to analyze policies or development
  strategies.
• It is one thing to evaluate a program in terms of
  its aggregate result it is another thing to
  measure its effect on different classes of society

Source http//www.globalpolicy.org/socecon/bwwto/
wbank/2003/1112bourguignon.htm
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Allocative versus distributional efficiency

• When we represent the utility possibility set, we
  know that every point on the frontier satisfies
  the criterion of allocative efficiency.
• On the other hand, if we compare two different
  points on the frontier, then clearly we are
  concerned about distributional issues
• Consider a limit point on the frontier one
  individual has all the resources in the economy
  and the other is left with nothing. Such a point
  is efficient in the sense of allocative
  efficiency!

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Inequality

• Allocative efficiency does not take into account
  distributional problems!
• Why should we care about distribution?
• ethical concern
• political concern
• Economic concern
• Hence, suppose we care about distribution. How
  can we compare two alternative distribution in
  order to evaluate which one is more egalitarian?
• Equality of utilities?

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Some Fundamental Questions on Inequality

• But what exactly is inequality?
• How is it measured?
• How can we make meaningful comparisons over time,
  or across space?
• How can we begin to analyze the underlying
  structure of inequality?
• What policies can successfully reduce inequality?

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Different concepts of inequality equality of
primary goods

• Rawls Imagine two persons, one satisfied with a
  diet of milk, bread and beans, while the other is
  distraught without expensive wines and exotic
  dishes. In short one person has expensive tastes,
  the other does not
• Clearly, if we apply the principle of equal
  utilities in this case we could obtain a very
  unequal distribution of resources!
• Solution equality of primary goods
• Similarly, Dworkin proposes the principle of
  equality of primary resources.

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Different concepts of inequality Equalities of
Capabilities

• However, this concept of equality does not take
  into account other aspects of welfare that do not
  derive from material goods, such as for example
  freedom.
• Amartya Sen (1998 Nobel Price in Economics)
  proposes a broader concept of equality, the
  equality of capabilities
• Sen capability of a person represents the
  freedom to achieve valuable human functioning,
  which can vary from such elementary things as
  being well nourished and avoiding morbidity and
  mortality, to such complex achievements as having
  self respect, being well integrated and so on

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Inequality Measurement

• Consider the distribution of a given variable
  (income, consumption, or some other welfare
  indicator or attribute)
• Usually inequality is captured as the
  dispersion of a distribution, whether that be
  income, consumption or some other welfare
  indicator or attribute of a population.
• Even if we agree on the concept of inequality,
  the measurement may be problematic and it is not
  simple to find a good indicator that summarized
  the distribution

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Inequality Measurement

• Can we use the VARIANCE of a distribution?
• Problem this is not independent of the income
  scale (doubling all incomes would imply a
  quadrupling of the estimate of income
  inequality!)
• How do we construct a satisfactory measure of
  inequality?

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Axiomatic Approach

• The Axiomatic approach requires the following
  axioms to be satisfied
• 1. The Pigou-Dalton Transfer Principle (Dalton,
  1920, Pigou, 1912). This axiom requires the
  inequality measure to rise (or at least not fall)
  in response an income transfer from a poorer
  person to a richer person and to decrease
  following an income transfer from a richer to a
  poorer person (see Atkinson, 1970, 1983, Cowell,
  1985, Sen, 1973).
• 2. Income Scale Independence. This requires the
  inequality measure to be invariant to uniform
  proportional changes if each individuals income
  changes by the same proportion (as happens say
  when changing currency unit) then inequality
  should not change. (see Cowell, 1999).

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Axiomatic Approach

• 3. Principle of Population (Dalton, 1920). The
  population principle requires inequality measures
  to be invariant to replications of the
  population merging two identical distributions
  should not alter inequality.
• 4. Anonymity. This axiom sometimes also
  referred to as Symmetry - requires that the
  inequality measure be independent of any
  characteristic of individuals other than their
  income (or the welfare indicator whose
  distribution is being measured).
• 5. Decomposability. This requires the overall
  inequality to be related consistently to
  constituent parts of the distribution, such as
  population sub-groups. For example if inequality
  is seen to rise amongst each sub-group of the
  population then we would expect inequality
  overall to also increase.

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Measures of Income Inequality

• Even though, equality of income does not
  guarantee equality of capabilities, from an
  empirical point of view is an acceptable way to
  proceed.
• A widespread measure of inequality is the GINI
  coefficient (satisfies axioms 1-4 but not
  decomposition)

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Lorenz Curve

• Income share

1
450
1
Population share
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Lorenz Curve

• the Lorenz curve plots the cumulative share of
  income against the cumulative population share.
  The diagonal (450 line) represents perfect income
  equality. The further away it is from the
  diagonal, the more unequal the society.
• The Gini coefficient is the area between the
  Lorenz curve and the 450 line divided by 2

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Gini Coefficient

• To compute the Gini coefficient, we first measure
  the area between the Lorenz Curve and the 45
  degree equality line. This area is divided by the
  entire area below the 45 degree line (which is
  always exactly to one half).
• In other words, the Gini coefficient is the area
  shaded in pink divided by the total of the areas
  shaded in pink and light blue-green.
• For a perfectly equal distribution, there would
  be no area between the 45 degree line and the
  Lorenz curve -- a Gini coefficient of zero. For
  complete inequality, in which only one person has
  any income (if that were possible) the Lorenz
  curve would coincide with the straight lines at
  the lower and right boundaries of the curve, so
  the Gini coefficient would be one.

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Theil Index

• where n is the number of individuals in the
  sample, yi is the income of individual i (i
  1,2,...,n), and y the arithmetic mean income.

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Trends in World Income Distribution
BourgignonMorrison, AER, 2002

• This paper examines the evolution of world
  inequality of personal income from 1829 to 1992
• This paper shows that world income inequality was
  already high in the early 19th century (a Gini
  coefficient of 0.50), when the industrial
  revolution was under way in Britain and beginning
  in France.
• From 1820 to the eve of World War I, inequality
  rose almost continuously. The Gini coefficient
  went from 0.50 to 0.61, and the Theil index from
  0.52 to 0.79.
• Changes during the last 50 years look minor
  compared with that dramatic evolution, and the
  situation appears to be stabilizing.

Source F. Bourgignon and C. Morrison, American
Economic Review (2002)
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Trends in World Income Distribution
BourgignonMorrison, AER, 2004

• This overall evolution of world inequality hides
  complex changes in the distribution across
  countries.
• Strong convergence was taking place among
  European countries and their offshoots in America
  and the Pacific
• whereas income disparities between this group of
  countries and the rest of the world were growing
• Similarly, the apparent stabilization of world
  income distribution since 1950 reflects a
  relative slowing of economic growth among
  European countries, a catching up by Japan and
  East Asia, and the take-off of China beginning in
  the 1980s.

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Decomposition of Inequality

• To have a correct picture we need to decompose
  the inequality into two parts
• Inequality within a country (or region)
• Inequality between countries (or regions)

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Trends in World Income Distribution
BourgignonMorrison, AER, 2004

• The decomposition analysis shows that world
  income inequality worsened dramatically over the
  past two centuries.
• The Gini coefficient increased 30 percent and the
  Theil index 60 percent between 1820 and 1992.
• This evolution was due mainly to a dramatic
  increase in inequality across countries or
  regions of the world.
• The between component of the Theil index went
  from 0.06 in 1820 to more than 0.50 in 1992.

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Trends in World Income Distribution
BourgignonMorrison, AER, 2004

• Changes in inequality within countries were
  important in some periods (in particular in the
  first half of the 20th century)
• however, the increase in inequality across
  countries was the leading factor in the evolution
  of the world distribution of income.

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Trends in World Income Distribution
BourgignonMorrison, AER, 2004

• Other indicators of inequality life expectancy
  (proxy of health disparities)
• The evolution of life expectancy parallels the
  evolution of income for about a century, after
  which it reversed!
• If life expectancy is taken as a proxy for the
  health of a population, then evidence suggests
  that health disparities are probably not much
  larger today than they were in the early 19th
  century.
• This could be mitigating the failure of world
  income inequality to decline

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Lifetime income, life expectancy and inequality

• In particular, if one considers inequality in
  lifetime income rather than current income then
  World inequality seems to have fallen since 1950
  as a result of the pronounced drop in
  international disparities in life expectancy.
• However, now disparities in life expectancy are
  back to the levels before the big divergence of
  the 19th century (no more convergence) hence
  this source of convergence has lost its influence

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Questions for next week seminar

• Read the article from the Economist Inequality
  in Latin America A stubburn curse and then
  answer the following questions
• 1. Describe the pattern of inequality in Latin
  America
• 2. The article from the Economists uses the Gini
  coefficient to measure inequality. Explain how
  the Gini coefficient is constructed
• 3. Do you think that the Gini coefficient is a
  good measure of inequality? Motivate your answer.
• 4. Based on the content of this lecture, do you
  conclude that the World Income Distribution has
  become more equal or more unequal during the last
  century?