Download w=0.9*sd*(n

Poverty, Inequality, and the World
Distribution of Income
By Xavier Sala-i-Martin
World GDP
World GDP
$45,000,000,000
$40,000,000,000
$35,000,000,000
$30,000,000,000
$25,000,000,000
$20,000,000,000
$15,000,000,000
$10,000,000,000
$5,000,000,000
20
00
19
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
19
78
19
76
19
74
19
72
19
70
$0
World Population
World Population
6,000,000
5,000,000
4,000,000
3,000,000
2,000,000
1,000,000
20
00
19
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
19
78
19
76
19
74
19
72
19
70
0
GDP Per Capita
World GDP Per Capita
$8,000
$7,000
$6,000
$5,000
$4,000
$3,000
$2,000
$1,000
20
00
19
98
19
96
19
94
19
92
19
90
19
88
19
86
19
84
19
82
19
80
19
78
19
76
19
74
19
72
19
70
$0
-1%
-2%
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
World Growth Rate
World Growth Rate
5%
4%
3%
2%
1%
0%
Initial Approach to WDI:
Histogram Income Per Capita
.3
Fraction
.2
.1
0
331.656
5000
ypc70
10000 15000
20000
Initial Approach to: World
Distribution of Income (1970)
.5
Fraction
.4
.3
.2
.1
0
331.656
5000
ypc70
10000 15000
20000
Initial Approach to: World
Distribution of Income (2000)
.6
.5
Fraction
.4
.3
.2
.1
0
481.873
20000
ypc2000
40000
-Divergence
Figure 2. Variance of Log- Per Capita Income: 125 Countries
1.40
1.30
1.20
1.10
1.00
0.90
0.80
19
70
19
71
19
72
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
0.70
Variance of Log Per Capita Income Across Countries
β-Divergence
growth
.05886
-.027063
5.8041
9.93357
ypc70l
Aggregate Numbers do not show
Personal Situation: Need
Individual Income Distribution
• Problem: we do not have each person’s
income
• We have
– (A) Per Capita GDP (PPP adjusted)
– (B) Income Shares for some years
• We can combine these two data sources to
estimate the WORLD DISTRIBUTION OF
INCOME
Method
• Use micro surveys to anchor the dispersion
• Use GDP Per Capita to anchor de MEAN of
the distribution.
– This is subject to CONTROVERSY.
Controversy: Scaling by National
Accounts or Survey Means?
• The surveys that we use to compute income shares
have “means”
• World Bank uses those means to estimate income
inequality (Milanovic (2001)) and Poverty (Chen
and Ravallion (2001))
• But this mean is much smaller than Per Capita
income (or Consumption) from the National
Accounts
• Moreover, the ratio of Survey Mean to National
Account mean tends to go down over time
Anchoring the Distribution with
National Accounts Data
• I anchor the distribution with National Accounts
data because:
– (a) the mean of our distribution corresponds to the per
capita variables that people are used to using
– (b) the NA are available every year (so we do not have
to forecast the data for years in which there are no
surveys)
– (c) Surveys have problems of underreporting and
systematic non-compliance
• (d) Survey means are very “strange”
– Survey says Hong Kong income is 5% richer
than USA (NA says USA GDP is 25% larger)
– Survey says Korea is 2% richer than Sweden
(NA says Sweden is 49% richer)
– Survey says Nicaragua is 77% richer than
Thailand (NA says Thailand is 83% richer)
– Survey says Ghana is 112% richer than India
(NA says they are about the same)
– Survey says that Kenya is 81% richer than
Senegal (NA says Senegal is 20% richer)
– Survey says Tanzania is 16% richer than
Indonesia (NA says Indonesia is 168% richer)
– And the list goes on and on…
Methodology
• From Survey data:
• Based on how many surveys we have 3 types of
countries
– (A) countries for which we have more than TWO
SURVEYS (70 countries –85 countries after collapse of
Soviet Union- with 5 billion people or 84% of world
population)
– (B) countries for which we have only ONE SURVEYS
(29 countries with 316 million people or 5.4% of
population)
– (C) countries with NO SURVEYS (28 countries with
232 citizens or 3.9% of world’s population)
From Surveys…
• Let s(ikt) is the income share for quintile k,
for country i during year t.
• For countries where we have many annual
surveys, realize that the income shares are
fairly constant over time
USA Income share of Quintile 1
USA Income share of Quintile 2
0.06
0.14
0.05
0.12
0.10
0.04
0.08
y = -0.0004x + 0.056
R2 = 0.7013
Quintile 1
Linear (Quintile 1)
Quintile 2
USA Income share of Quintile 3
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1970
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
0.00
1970
0.02
0.00
1976
0.04
0.01
1974
0.02
y = -0.0007x + 0.1218
R2 = 0.9503
0.06
1972
0.03
Linear (Quintile 2)
USA Income share of Quintile 4
0.3
0.25
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0.2
y = -0.0007x + 0.1795
R2 = 0.8822
0.1
0.05
1998
1996
1994
Linear (Quintile 3)
1992
1990
1988
1986
1984
Quintile 3
1982
1980
1978
1976
1974
1972
1970
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Quintile 5
Linear (Quintile 5)
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
y = 0.002x + 0.4002
R2 = 0.9307
Quintile 4
Linear (Quintile 4)
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0
USA Income share of Quintile 5
1970
y = -0.0002x + 0.2426
R2 = 0.1933
0.15
China Income share of Quintile 1
Quintile 1
Linear (Quintile 1)
Quintile 2
China Income share of Quintile 3
1998
1996
1994
1992
1990
1988
1986
Linear (Quintile 2)
China Income share of Quintile 4
y = -0.002x + 0.2025
R2 = 0.6571
0.25
1984
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0
1982
0.02
1980
0.04
1978
0.06
1976
0.08
y = -0.0022x + 0.1613
R2 = 0.6646
1974
0.1
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1972
y = -0.0021x + 0.1126
R2 = 0.6565
1970
0.12
China Income share of Quintile 2
0.35
0.3
0.2
0.25
0.15
0.2
0.15
0.1
y = -2E-05x + 0.2506
R2 = 1E-05
0.1
0.05
0.05
0
Quintile 3
Linear (Quintile 3)
Linear (Quintile 5)
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
y = 0.0063x + 0.2753
R2 = 0.661
Quintile 5
Linear (Quintile 4)
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
Quintile 4
China Income share of Quintile 5
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1970
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0
India Income share of Quintile 1
0.10
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0.00
India Income share of Quintile 2
0.14
0.12
y = 4E-05x + 0.0873
R2 = 0.0123
y = -0.0002x + 0.1294
R2 = 0.1602
0.10
0.08
0.06
0.04
0.02
Quintile 1
Linear (Quintile 1)
1998
1996
1994
1992
1990
1988
1986
1984
1982
Quintile 2
India Income share of Quintile 3
Linear (Quintile 2)
India Income share of Quintile 4
y = -0.0003x + 0.1694
R2 = 0.2915
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1980
1978
1976
1974
1972
1970
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0.00
0.25
0.2
y = -0.0006x + 0.2234
R2 = 0.4097
0.15
0.1
0.05
Quintile 3
Linear (Quintile 3)
Linear (Quintile 5)
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
y = 0.001x + 0.3903
R2 = 0.2291
Quintile 5
Linear (Quintile 4)
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
Quintile 4
India Income share of Quintile 5
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1970
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
0
Methodology: GROUP A
• Regress s(ikt) on a time trend for k=1,2,4,5 (and
use k=3 as a default to add up to 1) and use the
projections as a measure of yearly income shares.
• We will not be able to say anything about sudden
changes in inequality trends (except for FSU)
• Experimented with two different slopes for India
and China
• Experimented with using actual vs projected
slopes for years in which we have hard shares
Methodology: GROUP B
• Use the level shares for the only year in which we
have a survey and use the “average slopes” of
countries that belong to the same “region”
• Regions are defined by the World Bank (East Asia
and Pacific, Europe and Central Asia, Latin
American and Caribbean, Middle East and North
Africa, South Asia, Sub-Saharan Africa, HighIncome Non-OECD and High-Income OECD).
Methodology: GROUP C
• Use the level shares and the slopes of
countries that belong to the same “region”
• Note that groups B and C have a very small
fraction of total population (close to 9%)
Methodology: USSR and FSU
• We use USSR survey and GDP data until 1989
• Then we have data for individual republics for
1990-2000
• All the republics have more than one survey so
they all belong to group A
• Thus, the evolution of inequality (shares) is
common for all republics before 1989, but
independent for each republic after 1990.
Again:
Parametric or Non-Parametric?
• To estimate individual country distributions, we can:
• (A) Assume a functional form (say lognormal), use the
variance from surveys and the mean from NA (or from
surveys) and estimate the distribution
– Bhalla (2002) “smooths out” the Lorenz curve using an underlying
two-parameter distribution
– Quah (2002) estimates distribution for India and China for 1988
and 1998 assuming the distributions are log-normal
• (B) Estimate non-parametric kernels
• Which one is better? I will do both (you will see that the
results are quite similar)
Alternative 1:
Nonparametric Kernels
• Based on Sala-i-Martin (2006)
• Methodology
–
–
–
–
Use GDP per capita to estimate mean
Use 5 income quintiles around this mean
Get a 5-bar histogram
Estimate a kernel density function using Bandwidth
=w=0.9*sd*(n-1/5), where sd is the standard deviation of (log)
income and n is the number of observations
– I also used Silverman’s optimal bandwidth
– I did allow for a different bandwidth for every country and
year and I also forced all to have the same bandwidth. Results
largely the same.
Start with a Histogram
Figure. 2a. Income Distribution: China
100000
80000
60000
40000
20000
0
5
6
6
7
7
Series1
8
9
9
China
China
90,000
80,000
thousands of people
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
$100
$1,000
$10,000
1970 1970 1980
1970 1980
1970 1990
1980 1990 2000
$100,000
India
India
90,000
80,000
thousands of people
70,000
60,000
50,000
40,000
30,000
20,000
10,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
USA
USA
18,000
16,000
thousands of people
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
USA (corrected scale)
USA
18,000
16,000
thousands of people
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
$1,000
$10,000
1970
$100,000
1980
1990
2000
$1,000,000
Indonesia
Indonesia
20,000
18,000
16,000
thousands of people
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
Brazil
Brasil
8,000
7,000
thousands of people
6,000
5,000
4,000
3,000
2,000
1,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
Japan
Japan
14,000
12,000
thousands of people
10,000
8,000
6,000
4,000
2,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
Mexico
Mexico
6,000
thousands of people
5,000
4,000
3,000
2,000
1,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
Nigeria
Nigeria
7,000
6,000
thousands of people
5,000
4,000
3,000
2,000
1,000
0
$100
$1,000
1970
$10,000
1980
1990
2000
$100,000
Nigeria (corrected scale)
Nigeria
7,000
6,000
thousands of people
5,000
4,000
3,000
2,000
1,000
0
$10
$100
1970
$1,000
1980
1990
2000
$10,000
The Collapse of the Soviet Union
USSR-FSU
25,000
thousands of people
20,000
15,000
10,000
5,000
0
$100
$1,000
$10,000
1970 1970 1970
1980 1980
1990 1990
2000 1989 1989
1970 1980
1970
1980 1989
$100,000
USSR and FSU
Figure 1g: Distribution of Income in USSR-FSU
25,000
thousands of people
20,000
15,000
10,000
5,000
0
$100
$1,000
1970
$10,000
1980
1989
1990
$100,000
2000
World Distribution 1970
Figure 2a: The WDI and Individual Country Distributions in 1970
200,000
$1/day
World
thousands of people
160,000
120,000
China
80,000
India
40,000
USSR
Japan
0
$100
$1,000
$10,000
Individual Countries
World
USA
$100,000
World Distribution 2000
Figure 2b: The WDI and Individual Country Distributions in 2000
280,000
$1/day
World
240,000
thousands of people
200,000
160,000
120,000
India
80,000
China
40,000
0
$100
Nigeria
FSU
$1,000
Japan
$10,000
Individual Countries
World
USA
$100,000
World Distribution Over Time
WDI-Various Years
300,000
thousands of people
250,000
200,000
150,000
100,000
50,000
0
$100
$1,000
$10,000
1970 1990
1970 1970 1980
1970 1980
1980 1990 2000
$100,000
Once we have the distribution
• Can Compute Poverty Rates
– But Poverty Rates are Arbitrary…
• Can Compute various measures of
inequality
Poverty Lines are Arbitrary
• Consumption or Income? UN Millenium Goals
talk about Income Poverty. WB talks about
Consumption poverty…
• Original Line: 1 dollar a day in 1985 prices
• Mysterious Change in Definition by the World
Bank: 1.08 dollars a day in 1993 prices (which
does not correspond to 1 dollar in 85 prices)
• We use Original Line, adjust it for US inflation to
convert to 1996 prices: $495/year
• Allow for 15% adjustment for underreporting of
the rich: $570/year
• To get a sense for Consumption (C/Y=0.69): $826
Poverty Rates
Poverty Rates
40%
35%
30%
25%
20%
15%
10%
5%
0%
1970
1975
1980
1985
570$
826$
1990
495$
1995
2000
Inequality does not move fast
enough…
• To change the evolution of poverty.
• We have seen that inequality is not related
to growth, but when it goes up, it does not
go up enough to increase poverty in the
country…
• To eradicate poverty, we need to promote
growth NOT equality…
If you don’t like these definitions
of poverty…
• We can look at CDFs: pick your own
poverty line and the CDF tells you the
poverty rate for that particular year…
Cumulative Distribution Function
Figure 4: Cumulative Distribution Functions (Various Years)
1
$570/year
$5000/year
$2000/year
0.8
78%
75%
73%
0.6
67%
0.4
62%
54%
20%
50%
41%
16%
0.2
0
$100
10%
7%
$1,000
1970
$10,000
1980
1980
2000
$100,000
Rates or Headcounts?
• Veil of Ignorance: Would you Prefer your
children to live in country A or B?
• (A) 1.000.000 people and 500.000 poor
(poverty rate = 50%)
• (B) 2.000.000 people and 666.666 poor
(poverty rate =33%)
• If you prefer (A), try country (C)
• (C) 500.000 people and 499.999 poor.
Poverty Headcounts
Poverty Counts
1,400,000
1,200,000
1,000,000
800,000
600,000
400,000
200,000
0
1970
1975
1980
1985
570$
826$
1990
495$
1995
2000
World Poverty: Summary
• All Rates fall dramatically over the last thirty
years
• Drop is largest for higher poverty rates (so if you
want to argue that the poverty rates are large, you
must agree that there has been a lot of
improvement and if you want to argue that there
has been little improvement, you must agree that
poverty rates are small)
But Evolution of Poverty is not
Uniform Across Regions of the
World
Regional Poverty
Poverty Rates ($570)
60%
50%
40%
30%
20%
10%
0%
1970
1975
Africa
Latin America
1980
East Asia
1985
1990
South Asia
Middel East and NA
1995
2000
Eastern Europe and CA
Regional Poverty
Poverty Counts ($570)
400,000
350,000
300,000
250,000
200,000
150,000
100,000
50,000
0
1970
Africa
1975
Latin America
1980
East Asia
1985
South Asia
1990
Middel East and NA
1995
Eastern Europe and CA
2000
Poverty in USSR and FSU
Poverty Rates ($570)
1.40%
1.20%
1.00%
0.80%
0.60%
0.40%
0.20%
0.00%
1970
1975
1980
1985
Eastern Europe and CA
1990
1995
2000
Poverty in USSR and FSU
Poverty Counts ($570)
5,000
4,500
4,000
3,500
3,000
2,500
2,000
1,500
1,000
500
0
1970
1975
1980
1985
Eastern Europe and CA
1990
1995
2000
Poverty and Growth
• The regions of the world that have experienced
high growth (Asia), have also experienced huge
reductions in poverty
• The regions of the world that have experienced
negative growth (Africa), have also experienced
huge increases in poverty
• The regions of the world that have experienced
little growth (Latin America, Arab World) have
experienced little improvements in poverty
Income Inequality
• Popular View:
– FACT 1: Inequality within the USA, within China,
within Latin America, etc. has been increasing
– FACT 2: Per Capita Income Across countries has been
diverging (so cross-country inequality has been
increasing)
– Conclusion: HENCE, global income inequality has
been increasing
• Right?
Wrong!!!
• FACT 1: refers to citizens
• FACT 2: refers to countries
• It could be the case that a few very poor and
very populated countries had converged (so
the incomes of many CITIZENS had
converged) and that many poor countries
with few inhabitants had diverged.
Far Fetched?
• The few but very populated countries are
China and India
• The many but little populated countries are
in the African continent
Recall β-convergence
growth
.05886
-.027063
5.8041
9.93357
ypc70l
Population-Weighted
β-convergence
.07
.06
.05
.04
growth
.03
.02
.01
0
-.01
-.02
-.03
6
7
8
ypc70l
9
10
Income Inequality
• Need to estimate measures of PERSONAL income
inequality. Question is: what measures to use?
• Various Measures
– Ad Hoc Indexes (gini, variance of incomes, variance of
logs). Some have nice properties, some do not.
– Social Welfare Function Indexes (Atkinson)
– Axiomatic Indexes (Some nice properties are prespecified)
Income Inequality
• Axiomatic Indexes
– Pigou-Dalton Transfer principle (a good measure
should rise with mean preserving redistribution from
poor to rich). Varlog violates this principle.
– Scale Independence (variance violates)
– Decomposability: I(total)=I(within)+I(across). Only
Generalized Entropy Indexes (Mean Logarithmic
Deviation, Theil and Squared of CV).
Income Inequality
• What measure to use?
• Problem is that different measures might
give different answers so if you can pick
and choose your measure of inequality, you
can pick and choose your conclusion
• We will use estimate and report ALL
measures so you can decide which one you
like
Gini
Figure 7. Bourguignon-Morrisson and Sala-i-Martin: Global and
Across-Country Gini
0.7
0.65
0.6
0.55
0.5
0.45
0.4
1820
1850
1880
1910
Bourguignon-Morrisson
1940
1970 1973 1976 1979 1982 1985 1988 1991 1994 1997
Sala-i-Martin Global
Sala-i-Martin Across
Gini
Gini
0.665
0.66
0.655
0.65
0.645
0.64
0.635
0.63
1970
1975
1980
1985
1990
1995
2000
Variance of Log Income
Variance of Log Income
1.68
1.66
1.64
1.62
1.6
1.58
1.56
1.54
1.52
1.5
1970
1975
1980
1985
1990
1995
2000
Atkinson (0.5)
Atkinson with coefficient 0.5
0.365
0.36
0.355
0.35
0.345
0.34
0.335
0.33
1970
1975
1980
1985
1990
1995
2000
Atkinson (1)
Atkinson with Coefficient 1
0.595
0.59
0.585
0.58
0.575
0.57
0.565
0.56
0.555
0.55
1970
1975
1980
1985
1990
1995
2000
Mean Log Deviation
Mean Logarithmic Deviation
0.91
0.9
0.89
0.88
0.87
0.86
0.85
0.84
0.83
0.82
0.81
0.8
1970
1975
1980
1985
1990
1995
2000
Theil Index
Theil
0.85
0.84
0.83
0.82
0.81
0.8
0.79
0.78
0.77
1970
1975
1980
1985
1990
1995
2000
Ratio Top 20% to Bottom 20%
Figure 7e: World Income Inequality: Ratio Top 20% / Bottom 20%
12
11
10
9
8
7
1970
1975
1980
1985
1990
1995
2000
Ratio Top 10% to Bottom 10%
Figure 7f: World Income Inequality: Ratio Top 10% / Bottom 10%
32
30
28
26
24
22
20
1970
1975
1980
1985
1990
1995
2000
Decomposition
• Global Inequality = Inequality Across
Countries + Inequality Within Countries
Within Country Inequality
• inequality that would exist if all countries
had the same per capita income, but had the
existing differences across its citizens
Across Country Inequality
• Inequality that would exist if all citizens
within each country had the same
• Note that this IS NOT Divergence ACROSS
COUNTRIES (Each country a data point)
Decomposition
• Not all measures can be “decomposed” in
the sense that the within and the acrosscountry component add up to the global
index of inequality
• Only the “Generalized Entropy” indexes
can be decomposed: MLD and Theil
MLD Decomposition
Mean Logarithmic Deviation
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1970
1975
1980
Global
1985
Across-Country
1990
Within-Country
1995
2000
Theil Index Decomposition
Theil
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1970
1975
1980
Global
1985
Across-Country
1990
Within-Country
1995
2000
Lessons
• Across-Country inequalities decline
• Within-Country inequalities increase, but not
enough to offset the decline in across-country
inequalities so that overall inequality actually falls
• Across-Country inequalities are much larger: if
you want to reduce inequalities across citizens,
promote AGGREGATE growth in poor countries!
Inequalities have fallen…
Because Asia has been catching up with
OECD.
If Africa does not start growing soon,
inequalities will start increasing again...
Projected Inequalities if Africa
does not Grow…
Global Projections if Same Growth as 1980-2000
1.20
1.00
0.80
0.60
0.40
0.20
0.00
1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 2018 2022 2026 2030 2034 2038 2042 2046 2050
Theil
MLD
Alternative 2: Parametric
• Based on Sala-i-Martin and Pinkovskiy (2007)
• Methodology:
– Assume Log Normal income distribution
– Assume mean income is GDP per capita
– Given mean and lognormality, each income share is associated
with a variance
– So we have 5 estimates of variance per country/year
– Use kernels to estimate a distribution of variances
– Use this distribution to get a random sample of 1,000 sigmas per
country/year. For each of them, we have a lognormal distribution
of income.
– Integrate and get WDI
– For each WDI, estimate poverty and distribution statistics. I
report the mean estimate of each statistic and the 95% confidence
interval.
.05
.1
.15
.2
.25
.3
Poverty Rates
1970
1980
1990
year
povrate_mean
povrate_ciu
2000
povrate_cil
povrate_kernel
2010
200000 400000 600000 800000
Poverty Counts
1970
1980
1990
year
worldpov_mean
worldpov_ciu
2000
worldpov_cil
worldpov_kernel
2010
.6
.62
.64
.66
.68
Gini
1970
1980
1990
year
S_gini_mean
S_gini_ciu
2000
S_gini_cil
S_gini_kernel
2010
.3
.32
.34
.36
.38
.4
Atkinson (coef ½)
1970
1980
1990
year
S_ahalf_mean
S_ahalf_ciu
2000
S_ahalf_cil
S_ahalf_kernel
2010
.5
.55
.6
.65
Atkinson (Coef 1)
1970
1980
1990
year
S_a1_mean
S_a1_ciu
2000
S_a1_cil
S_a1_kernel
2010
.7
.8
.9
1
1.1
MLD
1970
1980
1990
year
S_i0_mean
S_i0_ciu
2000
S_i0_cil
S_i0_kernel
2010
.7
.75
.8
.85
.9
Theil Index
1970
1980
1990
year
S_i1_mean_3
S_i1_ciu_3
2000
S_i1_cil_3
S_i1_kernel
2010
4
6
8
10
12
Ratio 75/25
1970
1980
1990
year
S_7525_mean_3
S_7525_ciu_3
2000
S_7525_cil_3
2010
20
25
30
35
40
45
Ratio 90/10
1970
1980
1990
year
S_9010_mean_3
S_9010_ciu_3
2000
S_9010_cil_3
2010
Conclusion:
The World is Improving…
• Poverty Rates are falling because some large
nations are GROWING
• Poverty Headcounts are falling even though
population is growing
• Inequalities are falling because some poor and
large economies are GROWING
• But, unless AFRICA does not start growing:
– Inequalities will rise again
– Poverty will rise again (because Asia will stop reducing
poverty when they are close to zero)
FINAL CONCLUSION:
GROWTH MATTERS!
• Key Questions for Economists Today:
– Why doesn’t Africa grow?
– How do we make Africa grow?
– Fewer questions in economics (or in any other
science) are more relevant for human welfare.