Growth and the World Distribution of Income By Xavier Sala-i-Martin
2000 $8,000 $7,000 $6,000 $5,000 $4,000 $3,000 $2,000 $1,000 $0 GDP Per Capita Since 1970 World GDP Per Capita 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 1970
β-divergence.05886 growth -.027063 5.8041 9.93357 ypc70l
1997 1998 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 -Divergence Figure 2. Variance of Log- Per Capita Income: 125 Countries 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 Variance of Log Per Capita Income Across Countries 1972 1971 1970
Distribution: Individuals
Histogram Income Per Capita (countries).3.2 Fraction.1 0 331.656 5000 10000 1500020000 ypc70
Histogram: Population Weighted WDI (1970).5.4 Fraction.3.2.1 0 331.656 5000 10000 1500020000 ypc70
Histogram: Population Weighted WDI (2000).6.5.4 Fraction.3.2.1 0 481.873 20000 40000 ypc2000
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.
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 lognormal
Kernels (B) Estimate non-parametric kernels Which one is better? I will do both (you will see that the results are quite similar) 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 8 9 9 Series1
China China 90,000 80,000 70,000 thousands of people 60,000 50,000 40,000 30,000 20,000 10,000 0 $100 $1,000 $10,000 $100,000 1970 1970 1970 1980 1970 1980 1980 1990 1990 2000
India India 90,000 80,000 70,000 thousands of people 60,000 50,000 40,000 30,000 20,000 10,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
USA USA 18,000 16,000 14,000 thousands of people 12,000 10,000 8,000 6,000 4,000 2,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
USA (corrected scale) USA 18,000 16,000 14,000 thousands of people 12,000 10,000 8,000 6,000 4,000 2,000 0 $1,000 $10,000 $100,000 $1,000,000 1970 1980 1990 2000
Indonesia Indonesia 20,000 18,000 16,000 14,000 thousands of people 12,000 10,000 8,000 6,000 4,000 2,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
Brazil Brasil 8,000 7,000 6,000 thousands of people 5,000 4,000 3,000 2,000 1,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
Japan Japan 14,000 12,000 10,000 thousands of people 8,000 6,000 4,000 2,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
Mexico Mexico 6,000 5,000 thousands of people 4,000 3,000 2,000 1,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
Nigeria Nigeria 7,000 6,000 5,000 thousands of people 4,000 3,000 2,000 1,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1990 2000
Nigeria (corrected scale) Nigeria 7,000 6,000 5,000 thousands of people 4,000 3,000 2,000 1,000 0 $10 $100 $1,000 $10,000 1970 1980 1990 2000
The Collapse of the Soviet Union USSR-FSU 25,000 20,000 thousands of people 15,000 10,000 5,000 0 $100 $1,000 $10,000 $100,000 1970 1970 1970 1980 1970 1980 1970 1980 1990 1980 1990 1989 2000 1989 1989
USSR and FSU Figure 1g: Distribution of Income in USSR-FSU 25,000 20,000 thousands of people 15,000 10,000 5,000 0 $100 $1,000 $10,000 $100,000 1970 1980 1989 1990 2000
World Distribution 1970 Figure 2a: The WDI and Individual Country Distributions in 1970 200,000 $1/day World 160,000 thousands of people 120,000 80,000 China India 40,000 USSR Japan USA 0 $100 $1,000 $10,000 $100,000 Individual Countries World
World Distribution 2000 Figure 2b: The WDI and Individual Country Distributions in 2000 280,000 240,000 $1/day World 200,000 thousands of people 160,000 120,000 80,000 India China 40,000 Nigeria FSU Japan USA 0 $100 $1,000 $10,000 $100,000 Individual Countries World
See Graph
World Distribution Over Time WDI-Various Years 300,000 250,000 thousands of people 200,000 150,000 100,000 50,000 0 $100 $1,000 $10,000 $100,000 1970 1970 1970 1980 1970 1980 1980 1990 1990 2000
Poverty
Poverty Rates Poverty Rates 40% 35% 30% 25% 20% 15% 10% 5% 0% 1970 1975 1980 1985 1990 1995 2000 570$ 826$ 495$
Cumulative Distribution Function Figure 4: Cumulative Distribution Functions (Various Years) 1 $570/year $5000/year 0.8 0.6 $2000/year 78% 75% 73% 67% 0.4 0.2 20% 16% 10% 7% 62% 54% 50% 41% 0 $100 $1,000 $10,000 $100,000 1970 1980 1980 2000
Poverty Headcounts Poverty Counts 1,400,000 1,200,000 1,000,000 800,000 600,000 400,000 200,000 0 1970 1975 1980 1985 1990 1995 2000 570$ 826$ 495$
Regional Poverty Poverty Rates ($570) 60% 50% 40% 30% 20% 10% 0% 1970 1975 1980 1985 1990 1995 2000 Africa Latin America East A sia South Asia Middel East and NA 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 1975 1980 1985 1990 1995 2000 Africa Latin America East Asia South Asia Middel East and NA Eastern Europe and CA
Inequality UNDP 1999 Methodology: Step 1: Show that Inequality within countries has been increasing (cite USA, China, Latin America, etc.) Step 2: Show Per Capita Income Across countries has been diverging (so cross-country inequality has been increasing and cite Pritchett s (1997) Divergence Big Time you could also cite Barro and Sala-i-Martin (1992) or (1994).) Conclude: THEREFORE, global income inequality has been increasing!!! Right?
Wrong! Step 1: refers to citizens Step 2: refers to countries Steps 1 and 2 cannot be added up to come up with global income inequality! The concept of cross country inequality should be inequality that would exist in the world if all citizens within each country had same level of income, but different per capita incomes across countries. The difference? POPULATION SIZES!
Recall β-convergence.05886 growth -.027063 5.8041 9.93357 ypc70l
Population-Weighted β-convergence.07.06.05.04.03 growth.02.01 0 -.01 -.02 -.03 6 7 8 9 10 ypc70l
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
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 1940 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 Bourguignon-Morrisson Sala-i-Martin Global Sala-i-Martin Across
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 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
Mean Logarithmic Deviation 1.0 0.8 Global, 0.90 Global, 0.82 0.6 Across, 0.64 Across, 0.50 0.4 0.2 Within, 0.25 Within, 0.32 0.0 1970 2000
Theil Index 1.0 0.8 Global, 0.84 Global, 0.78 0.6 Across, 0.58 Across, 0.50 0.4 0.2 Within, 0.26 Within, 0.28 0.0 1970 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
Conclusions Poverty: key determinant is GROWTH Inequality: key determinant is GROWTH