Capacity building in distributional indicators and micro-simulations linked to CGE modeling Dario Debowicz and Sherman Robinson

Schedule week by week Week 1. Introduction and Poverty and Inequality Measurement Week 2. Practice on Measurement. Linking CGE and micro-simulations model Week 3. Linking IFPRI CGE model with HIES 2010-11 to microsimulate poverty indicators. Explanation and illustration with productivity-related simulations Week 4. Group presentations extending previously done analysis (tax, exchange rate, energy) Week 5. First draft of appendix to previous studies Week 6. Feedback on studies Week 7. Delivery of appendix to previous studies.

Dario Debowicz 20 March 2013 Based on Patricia Justino, 15 January 2009

The Measurement of Poverty and Inequality

Summary

1. The concept of inequality 2. The relationship between poverty and inequality 3. Indices of inequality 4. Inequality decompositions 5. Multidimensional inequality 6. Income mobility across quintiles and generations 7. A recent study of inequality

1. The concept of inequality

• Economic inequality: disparities in income (consumption expenditure) or wealth between individuals, households or groups of individuals or households. Unit can also be region, country, etc

• Important to distinguish between short-term

and long-term inequality (inequality estimates move very slowly)

Inequality in world income…

• World incomes are unequally distributed (inequality between countries). In 2002: • Pc per year income of richest country (Switzerland) (US$ 37930)

421 times largest than poorest country (RD Congo) (US$ 90) • PPP pc per year income of richest country (Norway) (US$ 35840)

73 times largest than poorest country (Sierra Leone) (US$ 490) • Low and middle income countries produce 19.4% of

world’s income (43.6% ppp); they have around 85% of world’s pop

• Share of income of richest (poorest) countries more or less unchanged since 1960. However: • World distribution can be constant in relative terms but there has

been lots of change within the distribution. • Ups as well as downs! • Greatest mobility amongst middle-income countries

…Inequality in world income

• Income distribution is also highly unequal within countries • E. g. UK (1991): poorest 10% of population (lowest decile) gets

2.6% of all national income; richest 10% of population (top decile) gets 27.3% of total income

• There seems to be an inverted-U pattern in both between and within country inequality (Kuznets): • Low inequality amongst poor countries; high inequality amongst

middle income countries; low inequality amongst high income countries

• For a given country: low inequality at low levels of economic development; higher inequality in transition periods, lower inequality at higher levels of development

Inequality of what?

• Underlying notion of well-being can include many dimensions (like poverty): • Income or consumption expenditure • Education, health, nutrition and life expectancy • Wealth • Access to public services • Participation in public life

Unit of analysis

• We need to distinguish between inequality between countries (weighted and unweighted) and inequality between individuals/households

• Since WWII, unweighted inequality between country risen, while weighted between country inequality has fallen

• Inequality between individuals is larger than inequality between countries

Equality of opportunities or equality of outcomes? What view on social justice?

• Inequality of “outcomes”: refers to the distribution of incomes (or other welfare dimension) resulting jointly from the efforts made by a person and the particular circumstances under which this effort is made; it is mostly concerned with income inequality

• Inequality of “opportunities”: refers to the heterogeneity in personal circumstances that lie beyond the control of the individual, but that nevertheless affect the results of his efforts, and possibly the levels of those efforts themselves (Roemer, 1998: John Rawls, Amartya Sen and others)

• If there is equality of opportunities then resulting income inequality reflects the results of a fair system because it reflects differences individual talents, efforts and accomplishments

But: • Unequal education systems • Changing demographic patterns i.e. population ageing • Unequal access to health care • Etc………

• This can be counteracted by income mobility (implies looking at inequality in long-term): → it is often argued that the USA can sustain larger income

inequality than other industrialized countries because possibilities for income mobility (across time for same individual and across generations) are higher; i.e. equality of opportunities is higher. More on this later………

• Data typically allows us to analyse distribution of outcomes (monetary and non-monetary); difficult to capture and measure distribution of opportunities (see paper by Bourguignon and Ferreira in reading list for discussion and example…)

Why concern with inequality?

• Ethical and moral reasons: similar individuals should not be treated differently

• Functional reasons: inequality may affect prospects for economic growth and poverty reduction

2. The relationship between poverty and inequality

Inequality vs Poverty

• Inequality refers to the whole distribution, rather than just the part below the poverty line; it’s a more relative concept

• Is there a relationship between poverty and inequality?

• Rising income inequality slows down the poverty reducing effect of growth

• High initial income inequality reduces subsequent poverty reduction; it is possible for inequality to increase sufficiently high to result in rising poverty (Ravallion)

• Inequality impacts on level of growth that is possible; therefore potential to reduce poverty will be affected

3. Indices of inequality

Main indicators

• Share of income received by top 20% or bottom 20%

• Ratio of top 20% to bottom 20% income (or consumption expenditure)

• Relative mean deviation • Coefficient of variation • Gini coefficient • Generalised entropy measures

Measuring economic inequality

• Define a vector y = y1, y2….yi….yn, with yi∈ℜ • n = number of units in the population (such as households,

families, individuals or earners for example) • Let I(y) be an estimate of inequality using a hypothetical inequality

measure: • Anonymity: inequality measure independent of any characteristic

of individuals other than their income → there is always a ranking y1 ≤ y2 ≤ ... ≤yn

• Principle of Population: inequality measures invariant to

replications of the population (population size does not matter; it’s proportion of population groups that matter)

for any scalar λ>0, I(y) = I(y[λ])

• Income Scale Independence (relative income principle): inequality measure invariant to uniform proportional changes: if each individual’s income changes by the same proportion (as happens say when changing currency unit) then inequality should not change:

for any scalar λ>0, I(y) = I(λy)

• The Pigou-Dalton Transfer Principle: an income transfer from a poorer person to a richer person should register as a rise (or at least not as a fall) in inequality and an income transfer from a richer to a poorer person should register as a fall (or at least not as an increase) in inequality

Consider vector y’ = transformation of the vector y obtained by a transfer δ from yj to yi , where yi>yj , and yi+δ >yj-δ,

transfer principle is satisfied iff I(y’) ≥ I(y)

Relative mean deviation

• M takes into account the entire distribution and not only the extremes

• M=0 if there is perfect equality; M=2(1-1/n) if all the income is held by one individual

• M is not sensitive to transfers from a poorer person to a richer person as long as both lie on the same side of the mean income

∑=

−=n

i

i

y

yn

M1

_ 11

Coefficient of variation

• Independent of mean income; concentrates on the relative variation of incomes

• A transfer from a richer person to a poorer person will always reduce the value of C (i.e., C passes the Pigou-Dalton test)

• However, a transfer from a person with $500 to a person with $400 or from a person with $100100 to a person with $100000 causes C to fall by exactly the same amount because C is very sensitive to transfers in the upper tail

C V y=1

2 /_

The Gini coefficient

• Measures average difference between all possible pairs of incomes in the population expressed as a proportion of total income

• 0 ≤ G ≤1; G = 0 indicates perfect equality; G = 1 means that one individual holds the whole income

• G is sensitive to transfers from rich to poor at every level • G is closely related to the Lorenz curve of the distribution: area

between the line of absolute equality (the diagonal) and the Lorenz curve, when the size of each axis (those measuring acc % of individuals and of income) equal one.

• G attaches higher weight to people in the middle of the distribution; thus it does not fulfil the transfer sensitivity axiom.

• G is a mean independent measure: if the incomes of everyone were to double, the Gini coefficient would not be altered.

Gn y n

y yi jj

n

i

n

=−

−==∑∑1

2 1 11_( )

Generalised Entropy (GE) measures

• Any measure I(y) that satisfies all of the axioms described above is a member of the Generalised Entropy (GE) class of inequality measures:

• n: number of individuals in the sample • yi: income of individual i, i ∈ (1, 2,...,n) • y bar= (1/n) ∑yi, the arithmetic mean income • Value of GE(α) ranges from 0 to ∞, with zero representing an equal

distribution (all incomes identical) and higher values representing higher levels of inequality

• α represents the weight given to distances between incomes at different parts of the income distribution, and can take any real value: • for more negative values of α GE becomes more sensitive to gaps between

incomes in the lower tail of the distribution • for more positive values GE becomes more sensitive to changes that affect the

upper tail • the commonest values of α used are 0,1 and 2

( ) ( )∑=

−−

=n

iiyyGE

1

2

2

1)(αα

α

y

• When α = 0 (v close to zero) we have the mean log deviation :

• When α = 1 we have the Theil index:

• With α=2 the GE measure becomes 1/2 the squared coefficient of variation, CV:

∑==

n

i

iyy

nGE

1log1)0(

∑==

n

i

iiyy

yy

nGE

1log1)1(

( ) 21

1

211

∑ −==

n

ii yy

nyCV

Cumulative % of Population

Line of Equality

45°

100

0 100

Cumulative % of Income

Lorenz Curve

A

B

If two Lorenz curves cross → need partial rankings given by inequality measures

Lorenz curves

Gini Coefficient =

AreaBAreaAAreaA+

The coefficient can vary between 0 and 1: 0: no inequality – everyone receives exactly the same amount of welfare 1: perfect inequality – one person owns all the wealth (or education, or power, etc)

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

BOLIVIA

0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100

ETHIOPIA

3B. Poverty measurement

Foster-Greer-Thorbeque (FGT) Poverty Measures

P0 = Poverty Headcount Ratio (HCR) P1 = Poverty Gap Ratio P2 = Squared Poverty Gap Ratio where: z is the poverty line yi is the income of person i N is the number of people in the population M is the number of poor people

α

α ∑=

−

=M

i

i

zyz

NP

1

)(1

Poverty and Inequality in Brazil, 1985-2001

Headcount

index

Poverty gap

Squared poverty

gap

Income Gini

1985 15.8 4.7 1.8 0.60 1995 14.0 3.9 1.5 0.60 1996 14.9 4.6 1.9 0.60 1999 9.9 3.2 1.3 0.61 2001 8.2 2.1 0.7 0.59

Source: World Bank, Global Poverty Monitoring, http://www.worldbank.org/research/povmonitor/index.htm Note: The headcount index indicates the percentage of individuals below the poverty line of US$1 per day.

4. Inequality decompositions

Often we need to distinguish between:

• Inequality ‘between’ and ‘within’ countries or groups of individuals/households or regions that form the country (unweighted and weighted)

Year Inequality within

countries

Inequality between countries

Total Inequality

1820 0.462 0.061 0.522 1910 0.498 0.299 0.797 1950 0.323 0.482 0.805 1992 0.342 0.513 0.855

Source: Bourguignon and Morrisson (2002), “Inequality Among World Citizens, 1820-1992”, American Economic Review.

Within-Group Income Inequalities in Brazil 1996

Pop. % Mean income GE(0) GE(1) White 54.5 323.7 0.63 0.66 Black 7.2 135.7 0.46 0.49 Asian 0.5 580.6 0.54 0.49 Mixed 37.7 136.5 0.55 0.59 Indigenous 0.2 153.3 0.77 0.74 North 4.8 180.2 0.59 0.66 North East 29.1 130.2 0.71 0.85 Centre West 6.8 249.3 0.63 0.73 South East 43.9 309.2 0.57 0.61 South 15.4 268.2 0.57 0.62 Urban 79.7 277.5 0.62 0.66 Rural 20.3 95.4 0.55 0.64

Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.

Share of Between-Group Inequalities in Total Inequality in Brazil 1996

Race State Region Urban/Rural GE(0) 13.2 12.0 9.3 10.9 GE(1) 11.5 10.5 7.8 7.9 GE(2) 4.7 4.4 3.0 2.8

Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.

5. Multidimensional inequality As with poverty, inequality is a multidimensional

phenomenon………

Summary Measures of Household Income and Education Inequality in Brazil 1996

Pc income

Pae income

Max years

schooling

Schooling head

Schooling father

Schooling mother

Mean 240.54 464.46 7.590 4.908 2.444 2.119 St dev 441.45 760.05 4.124 4.350 3.400 3.098

Gini 0.596 0.569 0.310 0.490 0.644 0.675 GE (0) 0.677 0.601 0.730 2.441 4.190 4.705 GE (1) 0.718 0.635 0.177 0.444 0.826 0.916 GE (2) 1.684 1.339 0.148 0.393 0.968 1.069

Note: Information on education of father and mother was collected for individuals aged 15 or above. Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.

Correlation Matrix for Income and Education Household Inequalities in Brazil 1996

Income quintile 1

Income quintile 2

Income quintile 3

Income quintile 4

Income quintile 5

Education quintile 1 58.53 36.40 25.49 13.41 5.54 Education quintile 2 17.70 20.27 15.79 10.22 3.49 Education quintile 3 16.50 26.72 29.51 27.24 12.63 Education quintile 4 6.65 15.08 25.14 36.02 31.11 Education quintile 5 0.63 1.54 4.07 13.10 47.23 Total 100.0 100.0 100.0 100.0 100.0 Source: Source: Justino, Patricia and Niimi, Yoko (2005), Multidimensional Inequality and Household Welfare: An Empirical Analysis, mimeo.

6. Income mobility across quintiles and generations

• Income mobility refers to the amount of movement across income ranks experienced by persons or families

• The simplest measure of economic mobility is the percentage of individuals who move into a new income quintile

• Income mobility is important because it offsets inequality: increasing inequality may be more accepted if accompanied by increasing mobility

Income Mobility Transition Matrix for USA, 1968-91 Gottschalk

1968 Income Quintile

1991 Income Quintile

Lowest Second Middle Fourth Highest Total Lowest 46.7 24.5 17.3 8.7 2.7 100.0 Second 23.6 26.2 26.4 14.3 9.6 100.0 Middle 13.6 21.8 20.2 26.2 18.2 100.0 Fourth 9.2 16.7 20.4 26.2 27.6 100.0 Highest 6.7 10.8 16.1 24.5 42.0 100.0 Total 100.0 100.0 100.0 100.0 100.0

• Dahan and Gaviria (1999): use sibling correlations in schooling to measure differences in intergenerational mobility in Latin America

• Intuition: if there is perfect social mobility, family background would not matter and siblings should behave as two random people chosen from the total population. If, on the other hand, family background matters, then siblings would behave in a similar fashion

Sibling Correlations of Schooling Outcomes: Latin America and the United States

Country Year Mobility index Inequality of schooling

Argentina 1996 0.437 0.26

Bolivia 1997 0.561 0.35

Brazil 1996 0.531 0.49

Chile 1996 0.435 0.25

Colombia 1997 0.587 0.38

Costa Rica 1995 0.340 0.36

Ecuador 1995 0.577 0.35

Mexico 1996 0.594 0.38

Nicaragua 1993 0.576 0.66

Panama 1997 0.480 0.32

Peru 1997 0.385 0.27

El Salvador 1995 0.599 0.55

Uruguay 1995 0.418 0.25

Venezuela 1995 0.438 0.32

Average 0.490 0.37

USA 1996 0.203 0.17

Factors that influence income mobility

• Family transmission of wealth (through inheritance) • Family transmission of ability (better educated parents

tend to have better educated children) • Imperfect capital markets (inability to borrow and other

constraints) • Neighbourhood segregation effects (self-imposed and

externally imposed) • Self-fulfilling beliefs (sociology and phycology)

7. A recent study of inequality

Milanovic, Branko, Lindert, Peter and Williamson, Jeffrey (2007), Measuring Ancient Inequality, World Bank Policy Research Working Paper no. 4412, The World Bank, November 2007.

• → Instead of actual inequality indices, authors calculate inequality possibility frontiers and inequality extraction ratios, i.e. they assess how actual inequality compares with the maximum feasible inequality that could have been extracted by the elite i.e. that coming from distributing income just to guarantee subsistence minimum for its poorer classes

• Main findings: • Income inequality in still-pre-industrial countries today is not very

different from inequality in distant pre-industrial times • Extraction ratio – how much potential inequality was converted

into actual inequality – was larger in ancient times than now • Differences in lifetime survival rates between rich and poor

countries and between rich and poor individuals within countries were higher two centuries ago; there was greater lifetime inequality in the past than now

Year Gini coefficient

Roman Empire 14 0.394

Byzantium 1000 0.411

England/Wales 1688 0.450

Old Castille 1752 0.525

Moghul India 1750 0.489

Bihar (India) 1807 0.328

England/wales 1801-3 0.515

Naples 1811 0.284

Brazil 1872 0.433

China 1880 0.245

British India 1947 0.497

Brazil 2002 0.588

South Africa 2000 0.573

China 2001 0.416

USA 2000 0.399

Sweden 2000 0.273

Nigeria 2003 0.418

Congo, DR 2004 0.404

Tanzania 2000 0.344

Malaysia 2001 0.479