Growth and the World Distribution of Income. By Xavier Sala-i-Martin

Transcription

1 Growth and the World Distribution of Income By Xavier Sala-i-Martin

2 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

3 β-divergence growth ypc70l

4 Divergence Figure 2. Variance of Log- Per Capita Income: 125 Countries Variance of Log Per Capita Income Across Countries

5 Distribution: Individuals

6 Histogram Income Per Capita (countries).3.2 Fraction ypc70

7 Histogram: Population Weighted WDI (1970).5.4 Fraction ypc70

8 Histogram: Population Weighted WDI (2000) Fraction ypc2000

9 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

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

11 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

12 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.

13 Start with a Histogram Figure. 2a. Income Distribution: China Series1

14 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,

15 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,

16 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,

17 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,

18 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,

19 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,

20 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,

21 Mexico Mexico 6,000 5,000 thousands of people 4,000 3,000 2,000 1,000 0 $100 $1,000 $10,000 $100,

22 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,

23 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,

24 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,

25 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,

26 World Distribution 1970 Figure 2a: The WDI and Individual Country Distributions in ,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

27 World Distribution 2000 Figure 2b: The WDI and Individual Country Distributions in , ,000 $1/day World 200,000 thousands of people 160, ,000 80,000 India China 40,000 Nigeria FSU Japan USA 0 $100 $1,000 $10,000 $100,000 Individual Countries World

28 See Graph

29 World Distribution Over Time WDI-Various Years 300, ,000 thousands of people 200, , ,000 50,000 0 $100 $1,000 $10,000 $100,

30 Poverty

31 Poverty Rates Poverty Rates 40% 35% 30% 25% 20% 15% 10% 5% 0% $ 826$ 495$

32 Cumulative Distribution Function Figure 4: Cumulative Distribution Functions (Various Years) 1 $570/year $5000/year $2000/year 78% 75% 73% 67% % 16% 10% 7% 62% 54% 50% 41% 0 $100 $1,000 $10,000 $100,

33 Poverty Headcounts Poverty Counts 1,400,000 1,200,000 1,000, , , , , $ 826$ 495$

34 Regional Poverty Poverty Rates ($570) 60% 50% 40% 30% 20% 10% 0% Africa Latin America East A sia South Asia Middel East and NA Eastern Europe and CA

35 Regional Poverty Poverty Counts ($570) 400, , , , , , ,000 50, Africa Latin America East Asia South Asia Middel East and NA Eastern Europe and CA

36 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?

37 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!

38 Recall β-convergence growth ypc70l

39 Population-Weighted β-convergence growth ypc70l

40 Gini Gini

41 Gini Figure 7. Bourguignon-Morrisson and Sala-i-Martin: Global and Across-Country Gini Bourguignon-Morrisson Sala-i-Martin Global Sala-i-Martin Across

42 Variance of Log Income Variance of Log Income

43 Atkinson (0.5) Atkinson with coefficient

44 Atkinson (1) Atkinson with Coefficient

45 Mean Log Deviation Mean Logarithmic Deviation

46 Theil Index Theil

47 Ratio Top 20% to Bottom 20% Figure 7e: World Income Inequality: Ratio Top 20% / Bottom 20%

48 Ratio Top 10% to Bottom 10% Figure 7f: World Income Inequality: Ratio Top 10%/ Bottom 10%

49 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

50 Mean Logarithmic Deviation Global, 0.90 Global, Across, 0.64 Across, Within, 0.25 Within,

51 Theil Index Global, 0.84 Global, Across, 0.58 Across, Within, 0.26 Within,

52 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!

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

54 Projected Inequalities if Africa does not Grow Global Projections if Same Growth as Theil MLD

55 Conclusions Poverty: key determinant is GROWTH Inequality: key determinant is GROWTH