Poverty and Inequality Measurement By Dr. Dario Debowicz

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

• 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

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

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.

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

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
Total 100.0 100.0 100.0 100.0 100.0
Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household

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

Poverty and Inequality Measurement By Dr. Dario Debowicz

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