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Capacitybuilding in distributional
indicators and micro-simulationslinked
to CGE modeling
Dario Debowiczand Sherman Robinson
Schedule week by week
Week 1. Introduction and Poverty and Inequality Measurement
Week 2. Practice on Measurement. Linking CGE and micro-simulations
model
Week 3. Linking IFPRI CGE model with HIES 2010-11 to microsimulate
poverty indicators. Explanation and illustration with productivity-related
simulations
Week 4. Group presentations extending previously done analysis (tax,
exchange rate, energy)
Week 5. First draft of appendix to previous studies
Week 6. Feedback on studies
Week 7. Delivery of appendix to previous studies.
Dario Debowicz
20 March 2013
Based on Patricia
Justino, 15 January 2009
The Measurement of Poverty and
Inequality
Summary
1. The concept of inequality
2. The relationship between poverty and inequality
3. Indices of inequality
4. Inequality decompositions
5. Multidimensional inequality
6. Income mobility across quintiles and generations
7. A recent study of inequality
1. The concept of inequality
• Economic inequality: disparities in income
(consumption expenditure) or wealth between
individuals, households or groups of individuals
or households. Unit can also be region, country,
etc
• Important to distinguish between short-term
and long-term inequality (inequality estimates
move very slowly)
Inequalityinworldincome…
• World incomes are unequally distributed (inequality
between countries). In 2002:
• Pc per year income of richest country (Switzerland) (US$ 37930)
421 times largest than poorest country (RD Congo) (US$ 90)
• PPP pc per year income of richest country (Norway) (US$ 35840)
73 times largest than poorest country (Sierra Leone) (US$ 490)
• Low and middle income countries produce 19.4% of
world’s income (43.6% ppp); they have around 85% of
world’s pop
• Share of income of richest (poorest) countries more or
less unchanged since 1960. However:
• World distribution can be constant in relative terms but there has
been lots of change within the distribution.
• Ups as well as downs!
• Greatest mobility amongst middle-income countries
…Inequalityinworldincome
• Income distribution is also highly unequal within
countries
• E. g. UK (1991): poorest 10% of population (lowest decile) gets
2.6% of all national income; richest 10% of population (top decile)
gets 27.3% of total income
• There seems to be an inverted-U pattern in both between
and within country inequality (Kuznets):
• Low inequality amongst poor countries; high inequality amongst
middle income countries; low inequality amongst high income
countries
• For a given country: low inequality at low levels of economic
development; higher inequality in transition periods, lower
inequality at higher levels of development
Inequalityof what?
• Underlying notion of well-being can include many
dimensions (like poverty):
• Income or consumption expenditure
• Education, health, nutrition and life expectancy
• Wealth
• Access to public services
• Participation in public life
Unitofanalysis
• We need to distinguish between inequality
between countries (weighted and unweighted)
and inequality between individuals/households
• Since WWII, unweighted inequality between
country risen, while weighted between country
inequality has fallen
• Inequality between individuals is larger than
inequality between countries
Equalityofopportunitiesor equalityof
outcomes?
Whatviewonsocialjustice?
• Inequality of “outcomes”: refers to the distribution of
incomes (or other welfare dimension) resulting jointly from
the efforts made by a person and the particular
circumstances under which this effort is made; it is mostly
concerned with income inequality
• Inequality of “opportunities”: refers to the heterogeneity in
personal circumstances that lie beyond the control of the
individual, but that nevertheless affect the results of his
efforts, and possibly the levels of those efforts themselves
(Roemer, 1998: John Rawls, Amartya Sen and others)
• If there is equality of opportunities then resulting income
inequality reflects the results of a fair system because it
reflects differences individual talents, efforts and
accomplishments
But:
• Unequal education systems
• Changing demographic patterns i.e. population ageing
• Unequal access to health care
• Etc………
• This can be counteracted by income mobility (implies looking
at inequality in long-term):
→ it is often argued that the USA can sustain larger income
inequality than other industrialized countries because
possibilities for income mobility (across time for same individual
and across generations) are higher; i.e. equality of opportunities
is higher. More on this later………
• Data typically allows us to analyse distribution of outcomes
(monetary and non-monetary); difficult to capture and
measure distribution of opportunities (see paper by
Bourguignon and Ferreira in reading list for discussion and
example…)
Why concernwith inequality?
• Ethical and moral reasons: similar individuals
should not be treated differently
• Functional reasons: inequality may affect prospects
for economic growth and poverty reduction
2. The relationship between poverty and inequality
Inequalityvs Poverty
• Inequality refers to the whole distribution, rather than
just the part below the poverty line; it’s a more
relative concept
• Is there a relationship between poverty and
inequality?
• Rising income inequality slows down the poverty
reducing effect of growth
• High initial income inequality reduces subsequent
poverty reduction; it is possible for inequality to
increase sufficiently high to result in rising poverty
(Ravallion)
• Inequality impacts on level of growth that is possible;
therefore potential to reduce poverty will be affected
3. Indices of inequality
Main indicators
• Share of income received by top 20% or bottom
20%
• Ratio of top 20% to bottom 20% income (or
consumption expenditure)
• Relative mean deviation
• Coefficient of variation
• Gini coefficient
• Generalised entropy measures
Measuringeconomicinequality
• Define a vector y = y1, y2….yi….yn, with yi∈ℜ
• n = number of units in the population (such as households,
families, individuals or earners for example)
• Let I(y) be an estimate of inequality using a hypothetical inequality
measure:
• Anonymity: inequality measure independent of any characteristic
of individuals other than their income → there is always a ranking
y1 ≤ y2 ≤ ... ≤yn
• Principle of Population: inequality measures invariant to
replications of the population (population size does not matter; it’s
proportion of population groups that matter)
for any scalar λ>0, I(y) = I(y[λ])
• Income Scale Independence (relative income principle):
inequality measure invariant to uniform proportional
changes: if each individual’s income changes by the same
proportion (as happens say when changing currency unit)
then inequality should not change:
for any scalar λ>0, I(y) = I(λy)
• The Pigou-Dalton Transfer Principle: an income transfer
from a poorer person to a richer person should register as
a rise (or at least not as a fall) in inequality and an income
transfer from a richer to a poorer person should register
as a fall (or at least not as an increase) in inequality
Consider vector y’ = transformation of the vector y
obtained by a transfer δ from yj to yi , where yi>yj , and
yi+δ >yj-δ,
transfer principle is satisfied iff I(y’) ≥ I(y)
Relativemean deviation
• M takes into account the entire distribution and not
only the extremes
• M=0 if there is perfect equality; M=2(1-1/n) if all
the income is held by one individual
• M is not sensitive to transfers from a poorer person
to a richer person as long as both lie on the same
side of the mean income
∑=
−=
n
i
i
y
y
n
M
1
_
1
1
Coefficientof variation
• Independent of mean income; concentrates on the
relative variation of incomes
• A transfer from a richer person to a poorer person will
always reduce the value of C (i.e., C passes the Pigou-
Dalton test)
• However, a transfer from a person with $500 to a
person with $400 or from a person with $100100 to a
person with $100000 causes C to fall by exactly the
same amount because C is very sensitive to transfers in
the upper tail
C V y=
1
2
/
_
The Ginicoefficient
• Measures average difference between all possible pairs of incomes
in the population expressed as a proportion of total income
• 0 ≤ G ≤1; G = 0 indicates perfect equality; G = 1 means that one
individual holds the whole income
• G is sensitive to transfers from rich to poor at every level
• G is closely related to the Lorenz curve of the distribution: area
between the line of absolute equality (the diagonal) and the Lorenz
curve, when the size of each axis (those measuring acc % of
individuals and of income) equal one.
• G attaches higher weight to people in the middle of the
distribution; thus it does not fulfil the transfer sensitivity axiom.
• G is a mean independent measure: if the incomes of everyone were
to double, the Gini coefficient would not be altered.
G
n y n
y yi j
j
n
i
n
=
−
−
==
∑∑
1
2 1 11
_
( )
GeneralisedEntropy(GE)
measures
• Any measure I(y) that satisfies all of the axioms described above is a member
of the Generalised Entropy (GE) class of inequality measures:
• n: number of individuals in the sample
• yi: income of individual i, i ∈ (1, 2,...,n)
• y bar= (1/n) ∑yi, the arithmetic mean income
• Value of GE(α) ranges from 0 to ∞, with zero representing an equal
distribution (all incomes identical) and higher values representing higher
levels of inequality
• α represents the weight given to distances between incomes at different
parts of the income distribution, and can take any real value:
• for more negative values of α GE becomes more sensitive to gaps between
incomes in the lower tail of the distribution
• for more positive values GE becomes more sensitive to changes that affect the
upper tail
• the commonest values of α used are 0,1 and 2
( ) ( )∑=
−
−
=
n
i
iyyGE
1
2
2
1
)(
αα
α
y
• When α = 0 (v close to zero) we have the mean log
deviation :
• When α = 1 we have the Theil index:
• With α=2 the GE measure becomes 1/2 the squared
coefficient of variation, CV:
∑=
=
n
i
i
y
y
n
GE
1
log
1
)0(
∑=
=
n
i
ii
y
y
y
y
n
GE
1
log
1
)1(
( )
2
1
1
211






∑ −=
=
n
i
i yy
ny
CV
Cumulative % of Population
Line of Equality
45°
100
0 100
Cumulative %
of Income
Lorenz
Curve
A
B
If two Lorenz curves cross → need partial rankings given by inequality measures
Lorenz curves
Gini Coefficient =
AreaBAreaA
AreaA
+
The coefficient can vary between 0 and 1:
0: no inequality – everyone receives exactly the
same amount of welfare
1: perfect inequality – one person owns all the
wealth (or education, or power, etc)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100
BOLIVIA
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100
ETHIOPIA
3B. Poverty measurement
Foster-Greer-Thorbeque (FGT) Poverty Measures
P0 = Poverty Headcount Ratio (HCR)
P1 = Poverty Gap Ratio
P2 = Squared Poverty Gap Ratio
where:
z is the poverty line
yi is the income of person i
N is the number of people in the population
M is the number of poor people
α
α ∑=





 −
=
M
i
i
z
yz
N
P
1
)(1
Poverty and Inequality in Brazil, 1985-2001
Headcount
index
Poverty
gap
Squared
poverty
gap
Income
Gini
1985 15.8 4.7 1.8 0.60
1995 14.0 3.9 1.5 0.60
1996 14.9 4.6 1.9 0.60
1999 9.9 3.2 1.3 0.61
2001 8.2 2.1 0.7 0.59
Source: World Bank, Global Poverty Monitoring, http://www.worldbank.org/research/povmonitor/index.htm
Note: The headcount index indicates the percentage of individuals below the poverty line of US$1 per day.
4. Inequality decompositions
Often we need to distinguish between:
• Inequality ‘between’ and ‘within’ countries or groups of
individuals/households or regions that form the country
(unweighted and weighted)
Year Inequality
within
countries
Inequality
between
countries
Total
Inequality
1820 0.462 0.061 0.522
1910 0.498 0.299 0.797
1950 0.323 0.482 0.805
1992 0.342 0.513 0.855
Source: Bourguignon and Morrisson (2002), “Inequality Among World Citizens, 1820-1992”, American Economic Review.
Within-Group Income Inequalities in Brazil 1996
Pop. % Mean income GE(0) GE(1)
White 54.5 323.7 0.63 0.66
Black 7.2 135.7 0.46 0.49
Asian 0.5 580.6 0.54 0.49
Mixed 37.7 136.5 0.55 0.59
Indigenous 0.2 153.3 0.77 0.74
North 4.8 180.2 0.59 0.66
North East 29.1 130.2 0.71 0.85
Centre West 6.8 249.3 0.63 0.73
South East 43.9 309.2 0.57 0.61
South 15.4 268.2 0.57 0.62
Urban 79.7 277.5 0.62 0.66
Rural 20.3 95.4 0.55 0.64
Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household
Welfare: An Empirical Analysis, mimeo.
Share of Between-Group Inequalities in Total Inequality in
Brazil 1996
Race State Region Urban/Rural
GE(0) 13.2 12.0 9.3 10.9
GE(1) 11.5 10.5 7.8 7.9
GE(2) 4.7 4.4 3.0 2.8
Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household
Welfare: An Empirical Analysis, mimeo.
5. Multidimensional inequality
As with poverty, inequality is a multidimensional
phenomenon………
Summary Measures of Household Income and
Education Inequality in Brazil 1996
Pc
income
Pae
income
Max
years
schooling
Schooling
head
Schooling
father
Schooling
mother
Mean 240.54 464.46 7.590 4.908 2.444 2.119
St dev 441.45 760.05 4.124 4.350 3.400 3.098
Gini 0.596 0.569 0.310 0.490 0.644 0.675
GE (0) 0.677 0.601 0.730 2.441 4.190 4.705
GE (1) 0.718 0.635 0.177 0.444 0.826 0.916
GE (2) 1.684 1.339 0.148 0.393 0.968 1.069
Note: Information on education of father and mother was collected for individuals aged 15
or above.
Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and
Household Welfare: An Empirical Analysis, mimeo.
Correlation Matrix for Income and Education Household
Inequalities in Brazil 1996
Income
quintile 1
Income
quintile 2
Income
quintile 3
Income
quintile 4
Income
quintile 5
Education quintile 1 58.53 36.40 25.49 13.41 5.54
Education quintile 2 17.70 20.27 15.79 10.22 3.49
Education quintile 3 16.50 26.72 29.51 27.24 12.63
Education quintile 4 6.65 15.08 25.14 36.02 31.11
Education quintile 5 0.63 1.54 4.07 13.10 47.23
Total 100.0 100.0 100.0 100.0 100.0
Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household
Welfare: An Empirical Analysis, mimeo.
6. Income mobility across quintiles and generations
• Income mobility refers to the amount of
movement across income ranks experienced by
persons or families
• The simplest measure of economic mobility is the
percentage of individuals who move into a new
income quintile
• Income mobility is important because it offsets
inequality: increasing inequality may be more
accepted if accompanied by increasing mobility
Income Mobility Transition Matrix for USA, 1968-91
Gottschalk
1968
Income
Quintile
1991 Income Quintile
Lowest Second Middle Fourth Highest Total
Lowest 46.7 24.5 17.3 8.7 2.7 100.0
Second 23.6 26.2 26.4 14.3 9.6 100.0
Middle 13.6 21.8 20.2 26.2 18.2 100.0
Fourth 9.2 16.7 20.4 26.2 27.6 100.0
Highest 6.7 10.8 16.1 24.5 42.0 100.0
Total 100.0 100.0 100.0 100.0 100.0
• Dahan and Gaviria (1999): use sibling correlations in
schooling to measure differences in intergenerational
mobility in Latin America
• Intuition: if there is perfect social mobility, family
background would not matter and siblings should
behave as two random people chosen from the total
population. If, on the other hand, family background
matters, then siblings would behave in a similar
fashion
Sibling Correlations of Schooling Outcomes: Latin America and the
United States
Country Year Mobility index Inequality of schooling
Argentina 1996 0.437 0.26
Bolivia 1997 0.561 0.35
Brazil 1996 0.531 0.49
Chile 1996 0.435 0.25
Colombia 1997 0.587 0.38
Costa Rica 1995 0.340 0.36
Ecuador 1995 0.577 0.35
Mexico 1996 0.594 0.38
Nicaragua 1993 0.576 0.66
Panama 1997 0.480 0.32
Peru 1997 0.385 0.27
El Salvador 1995 0.599 0.55
Uruguay 1995 0.418 0.25
Venezuela 1995 0.438 0.32
Average 0.490 0.37
USA 1996 0.203 0.17
Factorsthat influenceincome
mobility
• Family transmission of wealth (through inheritance)
• Family transmission of ability (better educated parents
tend to have better educated children)
• Imperfect capital markets (inability to borrow and other
constraints)
• Neighbourhood segregation effects (self-imposed and
externally imposed)
• Self-fulfilling beliefs (sociology and phycology)
7. A recent study of inequality
Milanovic,Branko,Lindert,Peterand
Williamson,Jeffrey(2007),MeasuringAncient
Inequality,WorldBankPolicyResearch
WorkingPaperno.4412,TheWorldBank,
November2007.
• → Instead of actual inequality indices, authors calculate inequality
possibility frontiers and inequality extraction ratios, i.e. they assess
how actual inequality compares with the maximum feasible
inequality that could have been extracted by the elite i.e. that
coming from distributing income just to guarantee subsistence
minimum for its poorer classes
• Main findings:
• Income inequality in still-pre-industrial countries today is not very
different from inequality in distant pre-industrial times
• Extraction ratio – how much potential inequality was converted
into actual inequality – was larger in ancient times than now
• Differences in lifetime survival rates between rich and poor
countries and between rich and poor individuals within countries
were higher two centuries ago; there was greater lifetime
inequality in the past than now
Year Gini coefficient
Roman Empire 14 0.394
Byzantium 1000 0.411
England/Wales 1688 0.450
Old Castille 1752 0.525
Moghul India 1750 0.489
Bihar (India) 1807 0.328
England/wales 1801-3 0.515
Naples 1811 0.284
Brazil 1872 0.433
China 1880 0.245
British India 1947 0.497
Brazil 2002 0.588
South Africa 2000 0.573
China 2001 0.416
USA 2000 0.399
Sweden 2000 0.273
Nigeria 2003 0.418
Congo, DR 2004 0.404
Tanzania 2000 0.344
Malaysia 2001 0.479

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Poverty and Inequality Measurement By Dr. Dario Debowicz

  • 1. Capacitybuilding in distributional indicators and micro-simulationslinked to CGE modeling Dario Debowiczand Sherman Robinson
  • 2. Schedule week by week Week 1. Introduction and Poverty and Inequality Measurement Week 2. Practice on Measurement. Linking CGE and micro-simulations model Week 3. Linking IFPRI CGE model with HIES 2010-11 to microsimulate poverty indicators. Explanation and illustration with productivity-related simulations Week 4. Group presentations extending previously done analysis (tax, exchange rate, energy) Week 5. First draft of appendix to previous studies Week 6. Feedback on studies Week 7. Delivery of appendix to previous studies.
  • 3. Dario Debowicz 20 March 2013 Based on Patricia Justino, 15 January 2009 The Measurement of Poverty and Inequality
  • 4. Summary 1. The concept of inequality 2. The relationship between poverty and inequality 3. Indices of inequality 4. Inequality decompositions 5. Multidimensional inequality 6. Income mobility across quintiles and generations 7. A recent study of inequality
  • 5. 1. The concept of inequality
  • 6. • Economic inequality: disparities in income (consumption expenditure) or wealth between individuals, households or groups of individuals or households. Unit can also be region, country, etc • Important to distinguish between short-term and long-term inequality (inequality estimates move very slowly)
  • 7. Inequalityinworldincome… • World incomes are unequally distributed (inequality between countries). In 2002: • Pc per year income of richest country (Switzerland) (US$ 37930) 421 times largest than poorest country (RD Congo) (US$ 90) • PPP pc per year income of richest country (Norway) (US$ 35840) 73 times largest than poorest country (Sierra Leone) (US$ 490) • Low and middle income countries produce 19.4% of world’s income (43.6% ppp); they have around 85% of world’s pop • Share of income of richest (poorest) countries more or less unchanged since 1960. However: • World distribution can be constant in relative terms but there has been lots of change within the distribution. • Ups as well as downs! • Greatest mobility amongst middle-income countries
  • 8. …Inequalityinworldincome • Income distribution is also highly unequal within countries • E. g. UK (1991): poorest 10% of population (lowest decile) gets 2.6% of all national income; richest 10% of population (top decile) gets 27.3% of total income • There seems to be an inverted-U pattern in both between and within country inequality (Kuznets): • Low inequality amongst poor countries; high inequality amongst middle income countries; low inequality amongst high income countries • For a given country: low inequality at low levels of economic development; higher inequality in transition periods, lower inequality at higher levels of development
  • 9. Inequalityof what? • Underlying notion of well-being can include many dimensions (like poverty): • Income or consumption expenditure • Education, health, nutrition and life expectancy • Wealth • Access to public services • Participation in public life
  • 10. Unitofanalysis • We need to distinguish between inequality between countries (weighted and unweighted) and inequality between individuals/households • Since WWII, unweighted inequality between country risen, while weighted between country inequality has fallen • Inequality between individuals is larger than inequality between countries
  • 11. Equalityofopportunitiesor equalityof outcomes? Whatviewonsocialjustice? • Inequality of “outcomes”: refers to the distribution of incomes (or other welfare dimension) resulting jointly from the efforts made by a person and the particular circumstances under which this effort is made; it is mostly concerned with income inequality • Inequality of “opportunities”: refers to the heterogeneity in personal circumstances that lie beyond the control of the individual, but that nevertheless affect the results of his efforts, and possibly the levels of those efforts themselves (Roemer, 1998: John Rawls, Amartya Sen and others) • If there is equality of opportunities then resulting income inequality reflects the results of a fair system because it reflects differences individual talents, efforts and accomplishments
  • 12. But: • Unequal education systems • Changing demographic patterns i.e. population ageing • Unequal access to health care • Etc……… • This can be counteracted by income mobility (implies looking at inequality in long-term): → it is often argued that the USA can sustain larger income inequality than other industrialized countries because possibilities for income mobility (across time for same individual and across generations) are higher; i.e. equality of opportunities is higher. More on this later……… • Data typically allows us to analyse distribution of outcomes (monetary and non-monetary); difficult to capture and measure distribution of opportunities (see paper by Bourguignon and Ferreira in reading list for discussion and example…)
  • 13. Why concernwith inequality? • Ethical and moral reasons: similar individuals should not be treated differently • Functional reasons: inequality may affect prospects for economic growth and poverty reduction
  • 14. 2. The relationship between poverty and inequality
  • 15. Inequalityvs Poverty • Inequality refers to the whole distribution, rather than just the part below the poverty line; it’s a more relative concept • Is there a relationship between poverty and inequality? • Rising income inequality slows down the poverty reducing effect of growth • High initial income inequality reduces subsequent poverty reduction; it is possible for inequality to increase sufficiently high to result in rising poverty (Ravallion) • Inequality impacts on level of growth that is possible; therefore potential to reduce poverty will be affected
  • 16. 3. Indices of inequality
  • 17. Main indicators • Share of income received by top 20% or bottom 20% • Ratio of top 20% to bottom 20% income (or consumption expenditure) • Relative mean deviation • Coefficient of variation • Gini coefficient • Generalised entropy measures
  • 18. Measuringeconomicinequality • Define a vector y = y1, y2….yi….yn, with yi∈ℜ • n = number of units in the population (such as households, families, individuals or earners for example) • Let I(y) be an estimate of inequality using a hypothetical inequality measure: • Anonymity: inequality measure independent of any characteristic of individuals other than their income → there is always a ranking y1 ≤ y2 ≤ ... ≤yn • Principle of Population: inequality measures invariant to replications of the population (population size does not matter; it’s proportion of population groups that matter) for any scalar λ>0, I(y) = I(y[λ])
  • 19. • Income Scale Independence (relative income principle): inequality measure invariant to uniform proportional changes: if each individual’s income changes by the same proportion (as happens say when changing currency unit) then inequality should not change: for any scalar λ>0, I(y) = I(λy) • The Pigou-Dalton Transfer Principle: an income transfer from a poorer person to a richer person should register as a rise (or at least not as a fall) in inequality and an income transfer from a richer to a poorer person should register as a fall (or at least not as an increase) in inequality Consider vector y’ = transformation of the vector y obtained by a transfer δ from yj to yi , where yi>yj , and yi+δ >yj-δ, transfer principle is satisfied iff I(y’) ≥ I(y)
  • 20. Relativemean deviation • M takes into account the entire distribution and not only the extremes • M=0 if there is perfect equality; M=2(1-1/n) if all the income is held by one individual • M is not sensitive to transfers from a poorer person to a richer person as long as both lie on the same side of the mean income ∑= −= n i i y y n M 1 _ 1 1
  • 21. Coefficientof variation • Independent of mean income; concentrates on the relative variation of incomes • A transfer from a richer person to a poorer person will always reduce the value of C (i.e., C passes the Pigou- Dalton test) • However, a transfer from a person with $500 to a person with $400 or from a person with $100100 to a person with $100000 causes C to fall by exactly the same amount because C is very sensitive to transfers in the upper tail C V y= 1 2 / _
  • 22. The Ginicoefficient • Measures average difference between all possible pairs of incomes in the population expressed as a proportion of total income • 0 ≤ G ≤1; G = 0 indicates perfect equality; G = 1 means that one individual holds the whole income • G is sensitive to transfers from rich to poor at every level • G is closely related to the Lorenz curve of the distribution: area between the line of absolute equality (the diagonal) and the Lorenz curve, when the size of each axis (those measuring acc % of individuals and of income) equal one. • G attaches higher weight to people in the middle of the distribution; thus it does not fulfil the transfer sensitivity axiom. • G is a mean independent measure: if the incomes of everyone were to double, the Gini coefficient would not be altered. G n y n y yi j j n i n = − − == ∑∑ 1 2 1 11 _ ( )
  • 23. GeneralisedEntropy(GE) measures • Any measure I(y) that satisfies all of the axioms described above is a member of the Generalised Entropy (GE) class of inequality measures: • n: number of individuals in the sample • yi: income of individual i, i ∈ (1, 2,...,n) • y bar= (1/n) ∑yi, the arithmetic mean income • Value of GE(α) ranges from 0 to ∞, with zero representing an equal distribution (all incomes identical) and higher values representing higher levels of inequality • α represents the weight given to distances between incomes at different parts of the income distribution, and can take any real value: • for more negative values of α GE becomes more sensitive to gaps between incomes in the lower tail of the distribution • for more positive values GE becomes more sensitive to changes that affect the upper tail • the commonest values of α used are 0,1 and 2 ( ) ( )∑= − − = n i iyyGE 1 2 2 1 )( αα α y
  • 24. • When α = 0 (v close to zero) we have the mean log deviation : • When α = 1 we have the Theil index: • With α=2 the GE measure becomes 1/2 the squared coefficient of variation, CV: ∑= = n i i y y n GE 1 log 1 )0( ∑= = n i ii y y y y n GE 1 log 1 )1( ( ) 2 1 1 211       ∑ −= = n i i yy ny CV
  • 25. Cumulative % of Population Line of Equality 45° 100 0 100 Cumulative % of Income Lorenz Curve A B If two Lorenz curves cross → need partial rankings given by inequality measures Lorenz curves
  • 26. Gini Coefficient = AreaBAreaA AreaA + The coefficient can vary between 0 and 1: 0: no inequality – everyone receives exactly the same amount of welfare 1: perfect inequality – one person owns all the wealth (or education, or power, etc)
  • 30. Foster-Greer-Thorbeque (FGT) Poverty Measures P0 = Poverty Headcount Ratio (HCR) P1 = Poverty Gap Ratio P2 = Squared Poverty Gap Ratio where: z is the poverty line yi is the income of person i N is the number of people in the population M is the number of poor people α α ∑=       − = M i i z yz N P 1 )(1
  • 31. Poverty and Inequality in Brazil, 1985-2001 Headcount index Poverty gap Squared poverty gap Income Gini 1985 15.8 4.7 1.8 0.60 1995 14.0 3.9 1.5 0.60 1996 14.9 4.6 1.9 0.60 1999 9.9 3.2 1.3 0.61 2001 8.2 2.1 0.7 0.59 Source: World Bank, Global Poverty Monitoring, http://www.worldbank.org/research/povmonitor/index.htm Note: The headcount index indicates the percentage of individuals below the poverty line of US$1 per day.
  • 33. Often we need to distinguish between: • Inequality ‘between’ and ‘within’ countries or groups of individuals/households or regions that form the country (unweighted and weighted)
  • 34. Year Inequality within countries Inequality between countries Total Inequality 1820 0.462 0.061 0.522 1910 0.498 0.299 0.797 1950 0.323 0.482 0.805 1992 0.342 0.513 0.855 Source: Bourguignon and Morrisson (2002), “Inequality Among World Citizens, 1820-1992”, American Economic Review.
  • 35. Within-Group Income Inequalities in Brazil 1996 Pop. % Mean income GE(0) GE(1) White 54.5 323.7 0.63 0.66 Black 7.2 135.7 0.46 0.49 Asian 0.5 580.6 0.54 0.49 Mixed 37.7 136.5 0.55 0.59 Indigenous 0.2 153.3 0.77 0.74 North 4.8 180.2 0.59 0.66 North East 29.1 130.2 0.71 0.85 Centre West 6.8 249.3 0.63 0.73 South East 43.9 309.2 0.57 0.61 South 15.4 268.2 0.57 0.62 Urban 79.7 277.5 0.62 0.66 Rural 20.3 95.4 0.55 0.64 Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.
  • 36. Share of Between-Group Inequalities in Total Inequality in Brazil 1996 Race State Region Urban/Rural GE(0) 13.2 12.0 9.3 10.9 GE(1) 11.5 10.5 7.8 7.9 GE(2) 4.7 4.4 3.0 2.8 Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.
  • 37. 5. Multidimensional inequality As with poverty, inequality is a multidimensional phenomenon………
  • 38. Summary Measures of Household Income and Education Inequality in Brazil 1996 Pc income Pae income Max years schooling Schooling head Schooling father Schooling mother Mean 240.54 464.46 7.590 4.908 2.444 2.119 St dev 441.45 760.05 4.124 4.350 3.400 3.098 Gini 0.596 0.569 0.310 0.490 0.644 0.675 GE (0) 0.677 0.601 0.730 2.441 4.190 4.705 GE (1) 0.718 0.635 0.177 0.444 0.826 0.916 GE (2) 1.684 1.339 0.148 0.393 0.968 1.069 Note: Information on education of father and mother was collected for individuals aged 15 or above. Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.
  • 39. Correlation Matrix for Income and Education Household Inequalities in Brazil 1996 Income quintile 1 Income quintile 2 Income quintile 3 Income quintile 4 Income quintile 5 Education quintile 1 58.53 36.40 25.49 13.41 5.54 Education quintile 2 17.70 20.27 15.79 10.22 3.49 Education quintile 3 16.50 26.72 29.51 27.24 12.63 Education quintile 4 6.65 15.08 25.14 36.02 31.11 Education quintile 5 0.63 1.54 4.07 13.10 47.23 Total 100.0 100.0 100.0 100.0 100.0 Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.
  • 40. 6. Income mobility across quintiles and generations
  • 41. • Income mobility refers to the amount of movement across income ranks experienced by persons or families • The simplest measure of economic mobility is the percentage of individuals who move into a new income quintile • Income mobility is important because it offsets inequality: increasing inequality may be more accepted if accompanied by increasing mobility
  • 42. Income Mobility Transition Matrix for USA, 1968-91 Gottschalk 1968 Income Quintile 1991 Income Quintile Lowest Second Middle Fourth Highest Total Lowest 46.7 24.5 17.3 8.7 2.7 100.0 Second 23.6 26.2 26.4 14.3 9.6 100.0 Middle 13.6 21.8 20.2 26.2 18.2 100.0 Fourth 9.2 16.7 20.4 26.2 27.6 100.0 Highest 6.7 10.8 16.1 24.5 42.0 100.0 Total 100.0 100.0 100.0 100.0 100.0
  • 43. • Dahan and Gaviria (1999): use sibling correlations in schooling to measure differences in intergenerational mobility in Latin America • Intuition: if there is perfect social mobility, family background would not matter and siblings should behave as two random people chosen from the total population. If, on the other hand, family background matters, then siblings would behave in a similar fashion
  • 44. Sibling Correlations of Schooling Outcomes: Latin America and the United States Country Year Mobility index Inequality of schooling Argentina 1996 0.437 0.26 Bolivia 1997 0.561 0.35 Brazil 1996 0.531 0.49 Chile 1996 0.435 0.25 Colombia 1997 0.587 0.38 Costa Rica 1995 0.340 0.36 Ecuador 1995 0.577 0.35 Mexico 1996 0.594 0.38 Nicaragua 1993 0.576 0.66 Panama 1997 0.480 0.32 Peru 1997 0.385 0.27 El Salvador 1995 0.599 0.55 Uruguay 1995 0.418 0.25 Venezuela 1995 0.438 0.32 Average 0.490 0.37 USA 1996 0.203 0.17
  • 45. Factorsthat influenceincome mobility • Family transmission of wealth (through inheritance) • Family transmission of ability (better educated parents tend to have better educated children) • Imperfect capital markets (inability to borrow and other constraints) • Neighbourhood segregation effects (self-imposed and externally imposed) • Self-fulfilling beliefs (sociology and phycology)
  • 46. 7. A recent study of inequality
  • 47. Milanovic,Branko,Lindert,Peterand Williamson,Jeffrey(2007),MeasuringAncient Inequality,WorldBankPolicyResearch WorkingPaperno.4412,TheWorldBank, November2007. • → Instead of actual inequality indices, authors calculate inequality possibility frontiers and inequality extraction ratios, i.e. they assess how actual inequality compares with the maximum feasible inequality that could have been extracted by the elite i.e. that coming from distributing income just to guarantee subsistence minimum for its poorer classes • Main findings: • Income inequality in still-pre-industrial countries today is not very different from inequality in distant pre-industrial times • Extraction ratio – how much potential inequality was converted into actual inequality – was larger in ancient times than now • Differences in lifetime survival rates between rich and poor countries and between rich and poor individuals within countries were higher two centuries ago; there was greater lifetime inequality in the past than now
  • 48. Year Gini coefficient Roman Empire 14 0.394 Byzantium 1000 0.411 England/Wales 1688 0.450 Old Castille 1752 0.525 Moghul India 1750 0.489 Bihar (India) 1807 0.328 England/wales 1801-3 0.515 Naples 1811 0.284 Brazil 1872 0.433 China 1880 0.245 British India 1947 0.497 Brazil 2002 0.588 South Africa 2000 0.573 China 2001 0.416 USA 2000 0.399 Sweden 2000 0.273 Nigeria 2003 0.418 Congo, DR 2004 0.404 Tanzania 2000 0.344 Malaysia 2001 0.479