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ECON 181
Poverty and Inequality.
WARNING: The slides are NOT lecture notes. You still need to read the assigned papers.
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Contents
1 Poverty 3
1.1 Poverty measures . . . . . . . . . . . . . . . . . . . . . 4
1.2 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Inequality 15
2.1 Some preliminary information (WDR, 2006) . . . . . . 16
2.2 Measuring inequality . . . . . . . . . . . . . . . . . . . 20
2.3 Lorenz curve . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Other measures . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6 Kuznetss curve . . . . . . . . . . . . . . . . . . . . . . 43
2.7 Is economic growth pro-poor? . . . . . . . . . . . . . . 44
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1 Poverty
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1.1 Poverty measures
Concepts
Poverty line: a critical threshold below which individuals aredeclared to be poor.
The threshold could refer to income, consumption or access to
goods and services.
Nutrition-based lines: the amount of money needed toguarantee minimum consumption of calories.
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Key issues1. Overall consumption or item-by-item consumption (e.g., enough
for for food but not for clothing.)
2. Absolute vs. relative: how can we compare different needs in
different countries?
3. Households vs individuals. Consumption is observed at the
household level and we usually dont know how it is distributed.
why do we need a poverty line?
Say poverty line is $1 per day. How different are individuals
with $1.01 and those with 99 cents?
Read the article by A. Deaton (2006).
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Measures
Let denote y income (or expenditure), m the average income, p
the poverty line.
If yi < p, then individual i is poor.
Consider a country with N individuals.
The first measure is to count how many poor are in a country:
how many indiv. earn less than p.
However, we want to account for the total number of people
living in this country.
Hence, the Poverty Head-count (PHC) is
P HC =N
i=11(yi
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PHC is a widely used.
However, there are some problems.
1. Consider two countries with the same PHC and with p = 100.
In one country all the poor earn $99 each and in the second
they all earn $50 each. Can we still say that both countries areequally poor?
2. Consider this poverty alleviation policy. Lets tax the very poor
and give the revenues to the ones just below the poverty line so
they can escape poverty.
The main problem with PCH is that it does not account for the
extent of the poverty.
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To solve this problem we can use the Income Gap (IG).
It measures the average gap in poverty (p yi) relative to thepoverty line
IG = 1N
Ni=1(
pyip
)1(yi < p)
This measure its also used but its less popular.
Problems1. Consider two countries with the same IG and with p = 100. In
one country all the poor earn $40 each and in the second half
the poor earn $20 and the other half makes $60. Can we still
say that both countries are equally poor?.
2. Consider a transfer from the very poor to the less poor such that
they escape poverty. Will IG be the same after the transfer?
3. Consider the same transfer but now the less poor do not escape
poverty, will IG be the same?
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To solve this problems Foster, Greer and Thorbecke proposedwhat is now known as the FGT index
P =1N
Ni=1(
pyip
)1(yi < p)
The parameter could take different values.
When = 0 then P0 = P HC.
When = 1 then P1 = IG.
An interesting case is when = 2. Thus P2 takes into account
the distribution among the poor.
P2 then solves all the problems described above.
However, P2 is not very commonly used.
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1.2 Evidence
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SSA is the region with the highest PHC.
Figure 2: Poverty measures by region 1981-2004(a) Headcount index
0
10
20
30
40
50
60
1980 1985 1990 1995 2000 2005
SSA
SAS
EAPLAC
MNA ECA
% living below $1 a day
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in Africa the levels are going back to 1981.Table 1: Poverty measures for $1 a day
(a) Percentage of population
Region 1981 1984 1987 1990 1993 1996 1999 2002 2004
East-Asia and Pacific (EAP) 57.73 39.02 28.23 29.84 25.23 16.14 15.46 12.33 9.05Of which China 63.76 41.02 28.64 32.98 28.36 17.37 17.77 13.79 9.90
Eastern-Europe+Central Asia (ECA) 0.70 0.51 0.35 0.46 3.60 4.42 3.78 1.27 0.94
Latin America+Caribbean (LAC) 10.77 13.07 12.09 10.19 8.42 8.87 9.66 9.09 8.64
Middle East+North Africa (MNA) 5.08 3.82 3.09 2.33 1.87 1.69 2.08 1.69 1.47
South Asia (SAS) 49.57 45.43 45.11 43.04 36.87 36.06 34.92 33.56 30.84
Of which India 51.75 47.94 46.15 44.31 41.82 39.94 37.66 36.03 34.33
Sub-Saharan Africa (SSA) 42.26 46.20 47.22 46.73 45.47 47.72 45.77 42.63 41.10
Total 40.14 32.72 28.72 28.66 25.56 22.66 22.10 20.13 18.09Total excl.China 31.35 29.69 28.75 27.14 24.58 24.45 23.54 22.19 20.70
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Comparing different measures.
Table 3.3 Poverty in 21 African Countries Using National Poverty Lines,
1990s
Indicator Rural Urban Overall
Headcount ratio (percent) 56 43 52Poverty gap (percent) 23 16 22Squared poverty gap (percent) 13 8 12Mean expenditure (dollars a person per year) 409 959 551Mean poverty line (dollars a person per year) 325 558
Source:Ali 1999.
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...and an example from Ivory Coast (1985-1988)
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2 Inequality
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2.1 Some preliminary information (WDR, 2006)
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Percentage not covered
70
60
50
40
30
20
10
0
Poorest
Wealthiest
Egypt
Jorda
n(*)
Colo
mbi
a
Rwa
nda
Peru
SouthA
fric
a
Kenya
Malawi
Brazil
Zambia
(*)
Vietnam
Turkey
Guate
mala
Tanzania
Indon
esia
Turkmenista
n(*)
Moro
cco
Gh
ana
Benin
Philipp
ines
Banglade
sh
Comoros
Bo
livia
Para
guay
Kazakhsta
n(*)
Yemen
Burki
naFa
so
Came
roon
Uga
nda
India
Maurit
ania
Haiti
T
ogo
Ethio
pia
Central
Afric
anRepublic
Madaga
scar
Mozamb
ique
Guin
eaM
ali
Camb
odia
Pakista
n
Eritr
ea
N
iger
C
had
Figure 1 Wealth matters for the immunization of children
Source:Authors own calculations from Demographic Health Survey (DHS) dataNote:* indicates that the poorest quintile have higher access to childhood immunization services than the wealthiest quintile.The continuous orange line represents the overall percentage of children without access to a basic immunization package in each country,while the endpoints indicate the percentages for the top and the bottom quintile of the asset ownership distribution.
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40 60 7050
100
90
80
70
60
110
Wealthiest 25%
Median score Median score
Poorest 25th%
40 60 7050Age in months Age in months
Wealthiest and poorest quartiles Maternal education
100
90
80
70
60
110
12 or more years
05 years
Figure 2 Opportunities are determined earlyCognitive development for children ages three to five in Ecuador differs markedly across family
backgrounds
Source:Paxson and Schady (2005).Note:Median values of the test of vocabulary recognition (TVIP) score (a measure of vocabulary recognition in Spanish,standardized against an international norm) are plotted against the childs age in months. The medians by exact monthof age were smoothed by estimating fan regressions of the median score on age (in months), using a bandwidth of 3.
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0.15
0.12
0.09
0.06
0.03
0.00
90th percentile or 11 years
75th percentile or 10 years
50th percentile or 5 years
25th percentile or 2 years
10th percentile or 0 year
Years of maternal education
199819941990198619821978
Probability of dying in the first year
Adjusted infant mortality rates by maternal education
Source:Paxson and Schady (2004).
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2.2 Measuring inequality
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Initial ideas
Suppose we have two people only.
Clearly, a 50-50 division is equal.
A 90-10 or 10-90 are clear unequal distributions.
Consider now the case we three individuals.
Which distribution is more unequal, 22-22-56 or 20-30-50?
We hence need some criteria to rank distributions.
That is, we need a set of goals for any inequality measure.
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Four criteria
1. Anonymity principle.
Ethical arguments require that it doesnt matter who earns
the income. If Nthabiseng makes R100 a week and Pieter R500, the
inequality should be the same if Nthabiseng now makes
R500 and Pieter only R100.
All we care about if the ranking of income (yi):
y1 y2 . . . yn
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2. Population principle.
Cloning the entire population (with their corresponding income)
should not alter inequality.
The size of the population shouldnt matter in order to measure
inequality.
Comparing the income distribution over n people and other
with same income but twice (2n) the population should lead to
the same inequality measure.
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3. Relative income principle.
It shouldnt matter whether income is expressed in dollars,
rands or metacais.
If we multiply the income of all individuals by = 0 inequality
should remain unchanged.
That is, the inequality on an income distribution of (10,20,40)
should be the same as the one from (1000,2000,4000.)
All that matter are shares of total income.
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4. The Dalton principle.
Dalton (1920)s principle suggest that transfer from poor
individuals to richer ones should increase inequality.
That is, taking money from a person with income yi to another
one with income yj yi increases inequality.
This is also called a regressive transfer.
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We can now formalize these four criteria as follows.
Let the income distribution of income (y1 y2 . . . yn).
and let I(y1, y2, . . . , yn) a measure of inequality.
1. Anonymity: the function I does not vary with a
permutation on the income distribution of individuals
{1,2,...,n}.
2. Population principle:
I(y1, y2, . . . , yn) = I(y1, y2, . . . , yn; y1, y2, . . . , yn)
3. Relative income principle:
I(y1, y2, . . . , yn) = I(y1, y2, . . . , yn)
4. Dalton principle: for > 0,
I(y1, y2, . . . , yn) < I(y1, . . . , yi , . . . , yj + , . . . , yn)
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2.3 Lorenz curve
Before looking at some alternative inequality measure, lets
start with a graphical device.
The Lorenz curve relates the share of total income held by x%of the population.
In figure 6.4, point A shows that the income of share of the
bottom 20% of the population is 10%.
Point B say that the bottom 80% holds 70% of total income. Put differently, the rich 20% enjoys 30% of total income.
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Ray, D. (1998)
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Consider the case when income is equally distributed
(everybody enjoys the same 1n
th of total income).
The Lorenz curve in such case will be equal to the diagonal,
the bottom 20% of pop. enjoys 20% of total income
Hence, the x% of population enjoys x% of total income.
Consider the opposite case, where all the income is held but
only person.
The Lorenz curve is flat until it hits 100% of the population
where it becomes vertical.
Given two Lorenz curves, the one closest to the diagonal has
less inequality (for all points).
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L(2) is more or less unequal than L(1)?
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Does the Lorenz curve satisfy the four criteria for inequality?
In homework 2 you will have a chance to answer this question
in detail.
There is one problem with Lorenz comparisons.
When a pair the curves cross we cannot rank them using the
Lorenz criteria.
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We cannot rank L(2) and L(1). Why?
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Examples: 1
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Examples: 2
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2.4 Other measures
Consider a population with n individuals.
Person i has an income equal to yi
Lets define the mean income as
1n
ni=1 yi
We will consider four alternative measure of inequality
commonly found in the literature
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The range
The range (R) is defined as the gap between the richest (yn)and the poorest (y1) income (expressed in terms of the average
income)
Recall than income is sorted from the lowest to highest income
R = 1(yn y1)
Inequality increases when the gap increases.
Note that this measure does not take into account the incomes
between the richest and the poorest.
If the second poorest person transfer money to the second
richest one, the inequality will remain intact.
Does this satisfy the Dalton principle?
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The Kuznets ratios
Introduced by Simon Kuznets.
The idea is to compare the share of income of the top x% of
the population and the bottom z%.
For example, you can compare the income of the top 10% and
the one of the bottom 20%.
Bigger ratios indicate higher inequality.
Does this satisfy the Dalton principle?
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The coefficient of variation
It is the ratio between the standard deviation () and the
mean ().
C =
, where = 1n
ni=1(yi )
2.
Does this satisfy the Dalton principle?.
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The Gini coefficient
This measure is related to the Lorenz curve.
The Gini coefficient is the ratioM
M+S (see next graph.) The Gini coefficient satisfies all the criteria supported by the
Lorenz curve.
That is, when inequality
is higher, M will be bigger and the Gini coefficient will be higher.
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M
S
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2.5 Evidence
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Inequality in SSA is the highest, except for LA.( )K. Deininger, L. SquirerJournal of Deelopment Economics 57 1998 259287 263
Table 1
Decadal medians of Gini coefficients for the income distribution, by Region 19601990
1960s 1970s 1980s 1990s
Eastern Europe 22.76 21.77 24.93 28.60South Asia 31.67 32.32 32.22 31.59
OECD and high income 32.86 33.04 32.20 33.20
East Asia and Pacific 34.57 34.40 34.42 34.80
Middle East and North Africa 41.88 43.63 40.80 39.72
Sub-Saharan Africa 49.90 48.50 39.63 42.30
Latin America 53.00 49.86 51.00 50.00
Regions are ordered by increasing inequality in the 1990s. .Source: Deininger and Squire 1996 .
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2.6 Kuznetss curve
How does inequality respond to economic development?
Kuznets hypothesis an inverted-U relation.
Inequality is highest for countries with middle-income and
lower for the rich and poor.
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2.7 Is economic growth pro-poor?
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150100500
Change in log mean consumption or income between surveys (x100)
50100150
500
Change in log poverty headcount index (x100)
400
300
200
100
0
100
200
300
400
y = 2.3841x + 2.3517t-stat = 9.30
R
2
= 0.5225N = 73
BUL
LVA
PER MDAARG
HUN
MLIPOLLAOCIV PAR
YEM VEN SVNMNG
COLTTOZWE BGD
GEOROMSLV
NER
MDG
VNMBDILSO
HRV ZAF NGANICRUS ZMBUGA
GHABWA
UZB EGYETH INDBOL BFALKA BRA PHLKENDZA
HONPANTUR MEXMAULTU CMR ECU
GMBSENCHNALB GUYURY GTM
AZE CRIMAR PAKIDNEST
TUNIRNTHA
LYSJAM
KAZ
0
Figure 4.3 Growth is the key to poverty reduction . . .
Source: WDR 2006.
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150100500
Change in log mean consumption or income between surveys (x100)
50100150
50
Change in log Gini index (x100)
40
30
20
10
0
10
20
30
40
50
60
y = 0.0288x + 3.3717t-stat = 0.515R2 = 0.004N = 73
KAZJAM
LYSTHAIRN
TUN
EST
IDN
PAK
MAR
CRI
AZE GTMURY
GUY
ALB
CHN
SEN
GMB
ECU
CMRLTU
MAU
MEX
TUR
PANHON
DZA
KEN
PHL
BRA
LKA
BFA
BOL
IND
ETH
EGY
UZB
BWA
GHA
UGA
ZMB
RUS
NIC
NGA
ZAF
HRVLSO
BDI
VNMMDG
NER
SLV
ROM
GEO
BGD
ZWE
TTO
COL
MNG
SVN
VEN
YEM
PAR
CIV
LAO
POL
MLI
HUNARG
MDA
PER
LVA
BUL
Figure 4.4 . . . and, on average, growth is distribution-neutral
Source: WDR 2006.
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Sources
Lorenz curves come from Debraj Ray (1998) textbook. Inequality in South Africa: van der Berg et al (2005) Trends
in poverty and inequality since the political transition.
Inequality in SSA (tables 6 and 7) from by Tsikata, Y. (2001)
Globalisation, Poverty and Inequality in Sub-Saharan Africa:
A Political Economy Appraisal.
Inequality in SSA (table 3.1) Okojie, C. and A. Shimeles (2006)
Inequality in sub-Saharan Africa: a synthesis of recent
research on the levels, trends, effects and determinants of
inequality in its different dimensions.
Recent trends in PHC: Chen, S. and M. Ravallion (2007)
Absolute Poverty Measures for the Developing World,
1981-2004 World Bank.
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FGT in Africa: Can Africa Claim the 21st Century? The
World Bank Washington, D.C.
FGT in Ivory Coast: Deaton (1997) The Analysis of Household
Surveys.
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