1. Poverty, Inequality, and the World Distribution of Income By Xavier Sala-i-Martin

2. World GDP

3. World Population

4. GDP Per Capita

5. World Growth Rate

6. Initial Approach to WDI: Histogram Income Per Capita

7. Initial Approach to: World Distribution of Income (1970)

8. Initial Approach to: World Distribution of Income (2000)

9.  -Divergence

10. β-Divergence

11. 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

12. Method Use micro surveys to anchor the dispersion Use GDP Per Capita to anchor de MEAN of the distribution. –This is subject to CONTROVERSY.

13. 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

14. 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

15. (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…

16. 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)

17. 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

21. 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

22. 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, High- Income Non-OECD and High-Income OECD).

23. 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%)

24. 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.

25. 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)

26. 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.

27. Start with a Histogram

28. China

29. India

30. USA

31. USA (corrected scale)

32. Indonesia

33. Brazil

34. Japan

35. Mexico

36. Nigeria

37. Nigeria (corrected scale)

38. The Collapse of the Soviet Union

39. USSR and FSU

40. World Distribution 1970

41. World Distribution 2000

42. World Distribution Over Time

43. Once we have the distribution Can Compute Poverty Rates –But Poverty Rates are Arbitrary… Can Compute various measures of inequality

44. 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

45. Poverty Rates

46. 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…

47. 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…

48. Cumulative Distribution Function

49. 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.

50. Poverty Headcounts

51. 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)

52. But Evolution of Poverty is not Uniform Across Regions of the World

53. Regional Poverty

55. Poverty in USSR and FSU

57. 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

58. 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?

59. 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.

60. Far Fetched? The few but very populated countries are China and India The many but little populated countries are in the African continent

61. Recall β-convergence

62. Population-Weighted β-convergence

63. 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)

64. 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).

65. 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

66. Gini

68. Variance of Log Income

69. Atkinson (0.5)

70. Atkinson (1)

71. Mean Log Deviation

72. Theil Index

73. Ratio Top 20% to Bottom 20%

74. Ratio Top 10% to Bottom 10%

75. Decomposition Global Inequality = Inequality Across Countries + Inequality Within Countries

76. Within Country Inequality inequality that would exist if all countries had the same per capita income, but had the existing differences across its citizens

77. 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)

78. 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

79. MLD Decomposition

80. Theil Index Decomposition

81. 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!

82. Inequalities have fallen… Because Asia has been catching up with OECD. If Africa does not start growing soon, inequalities will start increasing again...

83. Projected Inequalities if Africa does not Grow…

84. 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.

85. Poverty Rates

86. Poverty Counts

87. Gini

88. Atkinson (coef ½)

89. Atkinson (Coef 1)

90. MLD

91. Theil Index

92. Ratio 75/25

93. Ratio 90/10

94. 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)

95. 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.