1. Inequality: Basic concepts and trends
Session I
March 13, 2008
Branko Milanovic

2. 1. Global: Inequality between countries and individuals

3. Three concepts of inequality defined
Concept 1 inequality
Concept 2 inequality
Concept 3 (global) inequalty

4. Inequality, 1950-2005: The mother of all inequality disputes
0.7
Global inequality (Concept 3)
0.6
Gini coefficient
Weighted international inequalty
(Concept 2)
Weighted international
inequality without China
0.5
Unweighted international inequality
(Concept 1)
0.4
1950
1952
1954
1956
1958
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004

5. (distribution of persons by $PPP or US$ income per capita)
Global inequality
(distribution of persons by $PPP or US$ income per capita)
1988
1993
1998
2002
International dollars
Gini index
61.9
(1.8)
65.2
64.2
(1.9)
(1.6)
US dollars
77.3
(1.3)
80.1
(1.2)
79.5
(1.4)
80.5
(1.1)

6. How big is a Gini of 64-66?
Top
Bottom
Ratio
In PPP dollars
5 percent
33%
0.2%
165-1
10 percent
50%
0.7%
70-1
In current $
45%
0.15%
300-1
67.5%
0.45%
150-1

7. First order positional dominance:year 2002
100
Germany 80
urban China 60
Sri Lanka
percentile of world income distribution
Brazil 40
rural India 20 5 10 15 20
country ventile
twoway (line Y02_c group if contcod=="BRA") (line Y02_c group if contcod=="IDN-R") (line Y02_c group if contcod=="DEU") (line Y02_c group if contcod=="LKA") (line Y02_c group if contcod=="CHN-U"), legend(off) xtitle(country vent> ile) ytitle(percentile of world income distribution) text(90 3 "Germany") text(62 5 "urban China") text(50 6 "Brazi l") text(52 12 "Sri Lanka") text(40 18 "rural India")

8. 2. Relationship between income and inequality: the rise and fall of the Kuznets hypothesis

9. Kuznets curve (defined in 1955)
As income increases, inequality at first goes up and then declines
“It seems plausible to assume that in the process of growth, the earlier periods are characterized by a balance of counteracting forces that may have widened the inequality in the size distribution of total income for a while because of the rapid growth of the non-A [non-agricultural] sector and wider inequality within it. It is even more plausible to argue that the recent narrowing in income inequality observed in the developed countries was due to a combination of the narrowing inter-sectoral inequalities in product per worker, the decline in the share of property incomes in total incomes of households, and the institutional changes that reflect decisions concerning social security and full employment."

10. Kuznets curve: history
Evidence for Kuznets curve in cross-sectional data analyzed in the 1970s, 1980s (Paukert, Lecaillon, Koeble & Thomas)
More than 90% of pooled time-series and cross-sectional Gini variability is due to differences between countries => factors that determine country inequality are stable
Elusive evidence in time-series (Oshima)
Modifications of the Kuznets curve: “strong” and “weak” formulations

11. General formulation (used by Ahluwalia 1976)
We expect β1>0 and β2<0
Control variables include socialist dummy, government transfers, share of state sector employment, openness, age structure of population (Milanovic 1994; Williamson and Higgins 1999)

12. A simple quadratic relationship between Gini and GDI per capita, 1950-2000

13. No controls; a weak inverted U relationship (more than 1000 Gini obs)
Huge variability in inequality; R2 only 0.08
The upward sloping part of the curve particularly hard to discern
Turning point quite unstable; here about $PPP 2,000 (level of Senegal or Zimbabwe)
Gradual disenchantment with the hypothesis

14. Credit market imperfections
Poor households do not invest in human K even if the returns are high; they invest in subsistence-related types of investment
Indivisibilities: minimum threshold of K needed for investment; convex returns
Societies with these problems both more unequal and wasteful in terms of human and capital resources
Example of win-win strategy (inequality&growth)
Solutions: asset redistribution, no school fees, deeper capital markets, micro finance

15. Credit constraint, education, democracy (Li, Squire & Zhou)
pooled
IV formulation
Schooling 1960
-4.6**
-4.4**
Democracy
1.6**
1.5**
Land Gini 60
0.16**
0.15**
Financial depth (M2/GDP)
-7.7**
-10.1** R2
0.62
No. of obs.
166

16. Secular decline in inequality Due to the declining share of top 1%
Long-run studies using income and inheritance tax data (Picketty et al.): France
Secular decline in inequality
Due to the declining share of top 1%
Due to the decreasing importance of large capital income
Due to progressive taxation and progressive (and high) inheritance taxes
Produces no effect on average K stock but truncates large K holdings (lower concentration of capital income)

17. Story for the US (Piketty & Sanz)
Top K incomes decreased during the Depression and WW2 and never recovered (top estates still lower in real terms than around 1900)
Total K income did not decrease; its concentration did
Change in factoral income composition among the top 1%; no longer mostly capitalists but salaried workers. Δ more pronounced in the US than in France
Conclusion: No spontaneous decline in inequality. Role of depression, wars and progressive taxation. Policy and politics matter the most.

18. Recent findings
A number of similar studies for developed countries reaches the same conclusion: a U-shaped inequality in the 20th century in English-speaking countries (UK: Atkinson 03; Netherlands: Atkinson & Salvedra 03; Italy: Brandolini)
But also for India: Banerji and Piketty 2005
Long L shaped curve for the rest of developed countries

19. Source: Piketty and Saez (2006)

20. Source: Piketty and Saez (2006)

21. Source: Piketty and Saez (2006)

22. But this finding crucially depends on strong ρ btw
But this finding crucially depends on strong ρ btw. Gini and top income share; while true among recent data, not true historically!
twoway scatter top_percent gini if sample==1, msize(vlarge) mlabel( country)
Source: Milanovic, Williamson and Lindert (2007)

23. 3. How inequality might affect growth

24. Channel 1: The median voter hypothesis
Political mechanism
Greater inequality in factor income=>
Relatively poor μ voter=>
Chooses relatively high tax rate
Economic mechanism
High redistribution and distorsionary effect of taxes =>
Lower growth rate

26. Extent of redistribution = = fct (inequality in market income)
Hypothesis 1. More market-unequal countries redistribute more (using two definitions of market income)
Hypothesis 2. If countries do redistribute more, is the mechanism through which it happens, the medum voter hypothesis?

27. Redistribution is greater if the market income share of the poor is less
Source: Milanovic 2000

28. But we cannot show that the middle deciles gains more if market inequality high
Source: Milanovic 2000

29. Channel 2: Inequality and property rights
Political mechanism
Greater inequality creates cleavages =>
They are particularly strong if coincide with ethnic differences (high horizontal inequality)=>
Insecure property rights
Economic mechanism
Insecure property rights =>
Lower growth rate

30. Inequality and property rights (Keefer & Knack)
Cross section
Ln GDP per capita 1985
7.61**
Ethnic tensions
-0.933**
Income Gini circa 1985
-0.196**
Land Gini 1985
-0.097** R2
0.80
No. of obs. 64
Dependent variable: Property rights: ICRG measure Ranges from 0 to 50.

31. Gini (time-dummies included on the RHS)
Excursus: the reverse link and the reverse sign: greater protection of property rights increases inequality
Dependent
Gini
Gini (time-dummies included on the RHS)
Property rights
0.929**
0.709*
Financial development (M2/GDI)
-0.064**
-0.07**
Education
0.026
-0.016
Land inequality
-0.02
Democracy
0.438**
0.323**
Prop. Rights x Democracy
-0.056**
-0.046**
R2 within (N)
0.26 (203)
0.35 (203)

32. Greater protection of property rights increases inequality
The rich elite is also politically powerful and protects its economic assets
The effect is mitigated by the introduction of democracy
=> The negative effect of property rights protection is particularly strong in low-democracy environments
But the regression does not include an income term
(results based on Savoia and Easaw, 2007)

33. Channel 3. Inequality caused by “morally irrelevant” characteristics
Inequalities which are independent of individual effort, entrepreneurship or luck
Wasteful” (vs. instrumental or “useful”) inequality
Examples: education, health, opportunity to better oneself economically, to have a political voice
Horizontal inequalities between ethnic/religious groups, education levels, socio-economic categories, geographical areas

34. Explaining one’s position in the world income distribution (dependent variable: percentile in world income distribution)
Eq.
Mean per capita income (in ln)
Gini index (in %)
Own income class
Constant
Number of observations
R2 adjusted
F value 1
22.92
(0)
-126.2
2300
0.60
4254 2
22.32
(0)
-0.33
-108.2
2300
0.61
1799 3
22.32
(0)
-0.33
2.80
-137.6
2300
0.91
1202

35. Assumed ρ’s for different parts of the world
Base case
Optrimistic (high mobility)
Pessimistic (low mobility)
Average Gini (year 2002)
Nordic
0.2
0.15
0.3
27.5
Rest WENAO
0.4
0.5
33.7
E. Europe
30.6
Asia
0.6
37.6
LAC
0.66
0.9
53.8
Africa
42.6
Also a super-optimistic: ρ=0.2 for all; and super-pessimistic: ρ=0.9 for all.
ρ’s based on literature review.

36. Explaining one’s position in the world income distribution (dependent variable: percentile in world income distribution)
Eq.
Mean per capita income (in ln)
Gini index (in %)
Own income class (ventile)
Parents’ estimated income class (ventile)
Constant
Number of observations
R2 adjusted
F value
4 (Base)
22.33
(0)
-0.34
2.39
-132.5
230,000
0.80
31,529
5 (Optimistic)
22.32
(0)
-0.34
2.30
-131.5
230,000
0.78
28,467
6 (Pessimistic)
22.42
(0)
-0.35
2.46
-134.0
230,000
0.82
34,155
7 (Hypoth.) --
-0.14
(0)
4.77
23.08
2300
0.96
3353

37. Now, circuscumstances (country + parents’ income class) explain between 76 percent (if world is fairly income-mobile within countries) and 83 percent (if there is less social mobility) of variability in global income position
Coefficient on country mean income remains about the same; coefficient on parental income position (as expected) higher if there is less income mobility

38. As a proxy, WDR06 looks at the contribution of horizontal inequalities to total inequality, or total “feasible between- inequality”
Up to 40-45% of “feasible inequality” explained by education differences
Inequality traps and the interaction between political and economic power

39. Inequality measurement axioms
1. If all incomes are multiplied by a constant (Y1=Y*C), inequality does not change.
2. Increase of all incomes by a constant (Y1=Y+C), reduces inequality (follows from 1). New distribution is Lorenz-superior.
3. If number of recipients is multiplied (at each income level) by a constant, inequality does not change
4. Progressive transfer (which does not change the rankings of individuals) reduces inequality (Dalton’s axiom). (Dalton improvement = income of the poor ↑ by at least as much as income of the rich goes down. “Leakages” may prevent Dalton improvement.)
5. Symmetry or anonymity: if two people swap positions, inequality does not change.
6. Inequality measure lies in [0,1] domain.

40. Measures of inequality Desirable properties and how different measures satisfy them.
Gini
Theil (0)
(not entropy)
Mean log deviation
Relative mean deviation
Formula
Compares person’s income to:
Other persons’ income
his share in population
Mean
Features
Mean-normalized measure. Shows percentage difference between incomes of two randomly selected individuals
Compares relative incomes of all individuals (either population weighted or income weighted)
Mean-normalized measure
Intuitive explanation
Gini of 30 means that the expected difference in income between 2 randomly selected persons is 60 percent of overall mean income
Shows percentage difference between income of a randomly selected individual and overall mean income.
Shows percentage of total income that should be transferred so that all incomes are the same.
Income-scale independence (if all incomes increase by the same %, measure does not change)
Yes

41. Relative mean deviation
Gini
Theil
Mean log deviation
Relative mean deviation
Absolute increase of all incomes reduces inequality
Yes
Size independence (population size does not affect the measure)
Progressive transfer reduces inequality (The Pigou-Dalton transfer principle)
Not if both individuals have incomes greater (or lower) than the mean.
Symmetrical (if two people change their places, measure is not affected)
Measure varies between 0 and 1
Not bounded from above.
Decomposability (between recipients and between income sources)
Yes, between income sources
No, between recipients
Yes (both) No
Sensitivity to transfers
Greatest at the mode (varies as density function of the distribution)
Greatest at low income levels
Insensitive if transfers take place between two individuals with income greater (or lower) than the mean.