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Poverty, Inequality, and the World Distribution of Income
By Xavier Sala-i-Martin
World GDP
World GDP
$0
$5,000,000,000
$10,000,000,000
$15,000,000,000
$20,000,000,000
$25,000,000,000
$30,000,000,000
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$45,000,000,000
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World PopulationWorld Population
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GDP Per CapitaWorld GDP Per Capita
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World Growth RateWorld Growth Rate
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-Divergence
Figure 2. Variance of Log- Per Capita Income: 125 Countries
0.70
0.80
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1.00
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1.30
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Variance of Log Per Capita Income Across Countries
β-divergence
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
• Ravallion criticizes that if we do not trust the mean, why do we trust the variance?
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 (ie, we cannot cross-check the variance… but we can cross-check the mean)
– (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…
Two Methods…
• Parametric: Fix the shape of the distribution (say, log normal), and with mean and variance we can construct the entire distribution.
• Non-Parametric: Do not force the distribution to have a particular shape.
Start with a Histogram (Non-Parametric)
Figure. 2a. Income Distribution: China
0
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Series1
ChinaChina
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China
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China
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China
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1970 1980 1990 2000
IndiaIndia
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ple
1970 1980 1990 2000
USAUSA
0
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USA (corrected scale)USA
0
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$1,000 $10,000 $100,000 $1,000,000
thou
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ple
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IndonesiaIndonesia
0
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ple
1970 1980 1990 2000
Brazil
Brasil
0
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Japan
Japan
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Mexico
Mexico
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Nigeria
Nigeria
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Nigeria (corrected scale)
Nigeria
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The Collapse of the Soviet Union
USSR-FSU
0
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thou
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1970
USSR-FSU
0
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USSR-FSU
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USSR and FSU
Figure 1g: Distribution of Income in USSR-FSU
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World Distribution 1970
Figure 2a: The WDI and Individual Country Distributions in 1970
0
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thou
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Individual Countries World
World
China
India
USSR Japan USA
$1/day
World Distribution 2000Figure 2b: The WDI and Individual Country Distributions in 2000
0
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Individual Countries World
World
China
India
FSU Nigeria USA Japan
$1/day
World Distribution Over TimeWDI-Various Years
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WDI-Various Years
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WDI-Various Years
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WDI-Various Years
0
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thou
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ple
1970 1980 1990 2000
If use a Parametric Approach (countries are Log Normal)
Figure 3b: Parametric and Non-Parametric WDI
0
50,000
100,000
150,000
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250,000
300,000
$100 $1,000 $10,000 $100,000
Non-Parametric Parametric (Country LogNormality)
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): $826
Poverty RatesPoverty Rates
0%
5%
10%
15%
20%
25%
30%
35%
40%
1970 1975 1980 1985 1990 1995 2000
570$ 826$ 495$
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)
0
0.2
0.4
0.6
0.8
1
$100 $1,000 $10,000 $100,000
1970 1980 1980 2000
$570/year
$2000/year
$5000/year
20%
16%
10%
7%
62%54%
50%41%
78%
67%
73%75%
Rates or Headcounts?
• Veil of Ignorance: Would you Prefer your children to live in country A or B?
• (A) 1.000.000 people and 500.000 poor (poverty rate = 50%)
• (B) 2.000.000 people and 666.666 poor (poverty rate =33%)
• If you prefer (A), try country (C)
• (C) 500.000 people and 499.999 poor.
Poverty HeadcountsPoverty Counts
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1970 1975 1980 1985 1990 1995 2000
570$ 826$ 495$
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)
0%
10%
20%
30%
40%
50%
60%
1970 1975 1980 1985 1990 1995 2000
Africa Latin America East Asia South Asia Middel East and NA Eastern Europe and CA
Regional PovertyPoverty Counts ($570)
0
50,000
100,000
150,000
200,000
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300,000
350,000
400,000
1970 1975 1980 1985 1990 1995 2000
Africa Latin America East Asia South Asia Middel East and NA Eastern Europe and CA
Poverty in USSR and FSU
Poverty Rates ($570)
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1970 1975 1980 1985 1990 1995 2000
Eastern Europe and CA
Poverty in USSR and FSU
Poverty Counts ($570)
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
5,000
1970 1975 1980 1985 1990 1995 2000
Eastern Europe and CA
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
• The correct definition of “Across-Country Inequality” should be: “inequality that we would have in the world if all citizens within each country had the same level of income but there were differences in income per capita across countries”. Notice that this would correspond to a “population-weighted concept of dispersion”.
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
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
Convergence Across Countries
Convergence Across Citizens who live in Different Countries
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 pre-specified)
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
Figure 7. Bourguignon-Morrisson and Sala-i-Martin: Global and Across-Country Gini
0.4
0.45
0.5
0.55
0.6
0.65
0.7
1820 1850 1880 1910 1940 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997
Bourguignon-Morrisson Sala-i-Martin Global Sala-i-Martin Across
Gini
Gini
Gini
0.63
0.635
0.64
0.645
0.65
0.655
0.66
0.665
1970 1975 1980 1985 1990 1995 2000
Variance of Log Income
Variance of Log Income
1.5
1.52
1.54
1.56
1.58
1.6
1.62
1.64
1.66
1.68
1970 1975 1980 1985 1990 1995 2000
Atkinson (0.5)
Atkinson with coefficient 0.5
0.33
0.335
0.34
0.345
0.35
0.355
0.36
0.365
1970 1975 1980 1985 1990 1995 2000
Atkinson (1)Atkinson with Coefficient 1
0.55
0.555
0.56
0.565
0.57
0.575
0.58
0.585
0.59
0.595
1970 1975 1980 1985 1990 1995 2000
Mean Log Deviation
Mean Logarithmic Deviation
0.8
0.81
0.82
0.83
0.84
0.85
0.86
0.87
0.88
0.89
0.9
0.91
1970 1975 1980 1985 1990 1995 2000
Theil IndexTheil
0.77
0.78
0.79
0.8
0.81
0.82
0.83
0.84
0.85
1970 1975 1980 1985 1990 1995 2000
Ratio Top 20% to Bottom 20%Figure 7e: World Income Inequality: Ratio Top 20% / Bottom 20%
7
8
9
10
11
12
1970 1975 1980 1985 1990 1995 2000
Ratio Top 10% to Bottom 10%
Figure 7f: World Income Inequality: Ratio Top 10%/ Bottom 10%
20
22
24
26
28
30
32
1970 1975 1980 1985 1990 1995 2000
Decomposition
• Not all measures can be “decomposed” in the sense that the within and the across-country 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
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1970 1975 1980 1985 1990 1995 2000
Global Across-Country Within-Country
Theil Index DecompositionTheil
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1970 1975 1980 1985 1990 1995 2000
Global Across-Country Within-Country
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
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014 2018 2022 2026 2030 2034 2038 2042 2046 2050
Theil MLD
Not All is Income
• UNDP suggests that other things matter also.– Life Expectancy– Child Mortality– Caloric Intake– Literacy Rates and School Enrollment– Access to Water and Sanitation
• UNDP creates and index with various of these measures.
• But how did these measures evolve over time?
Life Expectancy
56
58
60
62
64
66
68
1970 2000
Life Expectancy
Child Mortality
0%
2%
4%
6%
8%
10%
12%
1970 2000
Child Mortality
Caloric Intake
0
500
1,000
1,500
2,000
2,500
3,000
1970 2000
Calory Intake per capita (Third World)
Starving Population
0%
5%
10%
15%
20%
25%
30%
35%
40%
1970 2000
Fraction of Starving Population %
Literacy Rates
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
1970 2000
Literacy Rates
Primary Schooling
0%
20%
40%
60%
80%
100%
1970 2000
Primary Enrollment Ratio
Secondary Schooling
0%
20%
40%
60%
80%
100%
1970 2000
Secondary Enrollment Ratio
Access to Water
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
1970 2000
Access to Water
Sanitation
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
1970 2000
Access to Water
Third World Wages
$0
$500
$1,000
$1,500
$2,000
$2,500
$3,000
1970 2000
Wages (Third World
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
• Other measures of welfare are also improving (they probably correlate with income well).
• 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.
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