4&5. poverty and inequality

8/2/2019 4&5. Poverty and Inequality

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ECON 181

Poverty and Inequality.

WARNING: The slides are NOT lecture notes. You still need to read the assigned papers.

Econ 181: Inequality and Poverty October 10, 2011 1


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Contents

1 Poverty 3

1.1 Poverty measures . . . . . . . . . . . . . . . . . . . . . 4

1.2 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Inequality 15

2.1 Some preliminary information (WDR, 2006) . . . . . . 16

2.2 Measuring inequality . . . . . . . . . . . . . . . . . . . 20

2.3 Lorenz curve . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Other measures . . . . . . . . . . . . . . . . . . . . . . 35

2.5 Evidence . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.6 Kuznetss curve . . . . . . . . . . . . . . . . . . . . . . 43

2.7 Is economic growth pro-poor? . . . . . . . . . . . . . . 44



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1 Poverty



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1.1 Poverty measures

Concepts

Poverty line: a critical threshold below which individuals aredeclared to be poor.

The threshold could refer to income, consumption or access to

goods and services.

Nutrition-based lines: the amount of money needed toguarantee minimum consumption of calories.



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Key issues1. Overall consumption or item-by-item consumption (e.g., enough

for for food but not for clothing.)

2. Absolute vs. relative: how can we compare different needs in

different countries?

3. Households vs individuals. Consumption is observed at the

household level and we usually dont know how it is distributed.

why do we need a poverty line?

Say poverty line is $1 per day. How different are individuals

with $1.01 and those with 99 cents?

Read the article by A. Deaton (2006).



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Measures

Let denote y income (or expenditure), m the average income, p

the poverty line.

If yi < p, then individual i is poor.

Consider a country with N individuals.

The first measure is to count how many poor are in a country:

how many indiv. earn less than p.

However, we want to account for the total number of people

living in this country.

Hence, the Poverty Head-count (PHC) is

P HC =N

i=11(yi


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PHC is a widely used.

However, there are some problems.

1. Consider two countries with the same PHC and with p = 100.

In one country all the poor earn $99 each and in the second

they all earn $50 each. Can we still say that both countries areequally poor?

2. Consider this poverty alleviation policy. Lets tax the very poor

and give the revenues to the ones just below the poverty line so

they can escape poverty.

The main problem with PCH is that it does not account for the

extent of the poverty.



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To solve this problem we can use the Income Gap (IG).

It measures the average gap in poverty (p yi) relative to thepoverty line

IG = 1N

Ni=1(

pyip

)1(yi < p)

This measure its also used but its less popular.

Problems1. Consider two countries with the same IG and with p = 100. In

one country all the poor earn $40 each and in the second half

the poor earn $20 and the other half makes $60. Can we still

say that both countries are equally poor?.

2. Consider a transfer from the very poor to the less poor such that

they escape poverty. Will IG be the same after the transfer?

3. Consider the same transfer but now the less poor do not escape

poverty, will IG be the same?



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To solve this problems Foster, Greer and Thorbecke proposedwhat is now known as the FGT index

P =1N

Ni=1(

pyip

)1(yi < p)

The parameter could take different values.

When = 0 then P0 = P HC.

When = 1 then P1 = IG.

An interesting case is when = 2. Thus P2 takes into account

the distribution among the poor.

P2 then solves all the problems described above.

However, P2 is not very commonly used.



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1.2 Evidence



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SSA is the region with the highest PHC.

Figure 2: Poverty measures by region 1981-2004(a) Headcount index

0

10

20

30

40

50

60

1980 1985 1990 1995 2000 2005

SSA

SAS

EAPLAC

MNA ECA

% living below $1 a day



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in Africa the levels are going back to 1981.Table 1: Poverty measures for $1 a day

(a) Percentage of population

Region 1981 1984 1987 1990 1993 1996 1999 2002 2004

East-Asia and Pacific (EAP) 57.73 39.02 28.23 29.84 25.23 16.14 15.46 12.33 9.05Of which China 63.76 41.02 28.64 32.98 28.36 17.37 17.77 13.79 9.90

Eastern-Europe+Central Asia (ECA) 0.70 0.51 0.35 0.46 3.60 4.42 3.78 1.27 0.94

Latin America+Caribbean (LAC) 10.77 13.07 12.09 10.19 8.42 8.87 9.66 9.09 8.64

Middle East+North Africa (MNA) 5.08 3.82 3.09 2.33 1.87 1.69 2.08 1.69 1.47

South Asia (SAS) 49.57 45.43 45.11 43.04 36.87 36.06 34.92 33.56 30.84

Of which India 51.75 47.94 46.15 44.31 41.82 39.94 37.66 36.03 34.33

Sub-Saharan Africa (SSA) 42.26 46.20 47.22 46.73 45.47 47.72 45.77 42.63 41.10

Total 40.14 32.72 28.72 28.66 25.56 22.66 22.10 20.13 18.09Total excl.China 31.35 29.69 28.75 27.14 24.58 24.45 23.54 22.19 20.70



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Comparing different measures.

Table 3.3 Poverty in 21 African Countries Using National Poverty Lines,

1990s

Indicator Rural Urban Overall

Headcount ratio (percent) 56 43 52Poverty gap (percent) 23 16 22Squared poverty gap (percent) 13 8 12Mean expenditure (dollars a person per year) 409 959 551Mean poverty line (dollars a person per year) 325 558

Source:Ali 1999.



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...and an example from Ivory Coast (1985-1988)



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2 Inequality



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2.1 Some preliminary information (WDR, 2006)



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Percentage not covered

70

60

50

40

30

20

10

0

Poorest

Wealthiest

Egypt

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Colo

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Figure 1 Wealth matters for the immunization of children

Source:Authors own calculations from Demographic Health Survey (DHS) dataNote:* indicates that the poorest quintile have higher access to childhood immunization services than the wealthiest quintile.The continuous orange line represents the overall percentage of children without access to a basic immunization package in each country,while the endpoints indicate the percentages for the top and the bottom quintile of the asset ownership distribution.



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40 60 7050

100

90

80

70

60

110

Wealthiest 25%

Median score Median score

Poorest 25th%

40 60 7050Age in months Age in months

Wealthiest and poorest quartiles Maternal education

100

90

80

70

60

110

12 or more years

05 years

Figure 2 Opportunities are determined earlyCognitive development for children ages three to five in Ecuador differs markedly across family

backgrounds

Source:Paxson and Schady (2005).Note:Median values of the test of vocabulary recognition (TVIP) score (a measure of vocabulary recognition in Spanish,standardized against an international norm) are plotted against the childs age in months. The medians by exact monthof age were smoothed by estimating fan regressions of the median score on age (in months), using a bandwidth of 3.



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0.15

0.12

0.09

0.06

0.03

0.00

90th percentile or 11 years




10th percentile or 0 year

Years of maternal education

199819941990198619821978

Probability of dying in the first year

Adjusted infant mortality rates by maternal education

Source:Paxson and Schady (2004).



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2.2 Measuring inequality



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Initial ideas

Suppose we have two people only.

Clearly, a 50-50 division is equal.

A 90-10 or 10-90 are clear unequal distributions.

Consider now the case we three individuals.

Which distribution is more unequal, 22-22-56 or 20-30-50?

We hence need some criteria to rank distributions.

That is, we need a set of goals for any inequality measure.



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Four criteria

1. Anonymity principle.

Ethical arguments require that it doesnt matter who earns

the income. If Nthabiseng makes R100 a week and Pieter R500, the

inequality should be the same if Nthabiseng now makes

R500 and Pieter only R100.

All we care about if the ranking of income (yi):

y1 y2 . . . yn



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2. Population principle.

Cloning the entire population (with their corresponding income)

should not alter inequality.

The size of the population shouldnt matter in order to measure

inequality.

Comparing the income distribution over n people and other

with same income but twice (2n) the population should lead to

the same inequality measure.



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3. Relative income principle.

It shouldnt matter whether income is expressed in dollars,

rands or metacais.

If we multiply the income of all individuals by = 0 inequality

should remain unchanged.

That is, the inequality on an income distribution of (10,20,40)

should be the same as the one from (1000,2000,4000.)

All that matter are shares of total income.



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4. The Dalton principle.

Dalton (1920)s principle suggest that transfer from poor

individuals to richer ones should increase inequality.

That is, taking money from a person with income yi to another

one with income yj yi increases inequality.

This is also called a regressive transfer.



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We can now formalize these four criteria as follows.

Let the income distribution of income (y1 y2 . . . yn).

and let I(y1, y2, . . . , yn) a measure of inequality.

1. Anonymity: the function I does not vary with a

permutation on the income distribution of individuals

{1,2,...,n}.

2. Population principle:

I(y1, y2, . . . , yn) = I(y1, y2, . . . , yn; y1, y2, . . . , yn)

3. Relative income principle:

I(y1, y2, . . . , yn) = I(y1, y2, . . . , yn)

4. Dalton principle: for > 0,

I(y1, y2, . . . , yn) < I(y1, . . . , yi , . . . , yj + , . . . , yn)



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2.3 Lorenz curve

Before looking at some alternative inequality measure, lets

start with a graphical device.

The Lorenz curve relates the share of total income held by x%of the population.

In figure 6.4, point A shows that the income of share of the

bottom 20% of the population is 10%.

Point B say that the bottom 80% holds 70% of total income. Put differently, the rich 20% enjoys 30% of total income.



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Ray, D. (1998)



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Consider the case when income is equally distributed

(everybody enjoys the same 1n

th of total income).

The Lorenz curve in such case will be equal to the diagonal,

the bottom 20% of pop. enjoys 20% of total income

Hence, the x% of population enjoys x% of total income.

Consider the opposite case, where all the income is held but

only person.

The Lorenz curve is flat until it hits 100% of the population

where it becomes vertical.

Given two Lorenz curves, the one closest to the diagonal has

less inequality (for all points).



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L(2) is more or less unequal than L(1)?



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Does the Lorenz curve satisfy the four criteria for inequality?

In homework 2 you will have a chance to answer this question

in detail.

There is one problem with Lorenz comparisons.

When a pair the curves cross we cannot rank them using the

Lorenz criteria.



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We cannot rank L(2) and L(1). Why?



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Examples: 1



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Examples: 2



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2.4 Other measures

Consider a population with n individuals.

Person i has an income equal to yi

Lets define the mean income as

1n

ni=1 yi

We will consider four alternative measure of inequality

commonly found in the literature



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The range

The range (R) is defined as the gap between the richest (yn)and the poorest (y1) income (expressed in terms of the average

income)

Recall than income is sorted from the lowest to highest income

R = 1(yn y1)

Inequality increases when the gap increases.

Note that this measure does not take into account the incomes

between the richest and the poorest.

If the second poorest person transfer money to the second

richest one, the inequality will remain intact.

Does this satisfy the Dalton principle?



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The Kuznets ratios

Introduced by Simon Kuznets.

The idea is to compare the share of income of the top x% of

the population and the bottom z%.

For example, you can compare the income of the top 10% and

the one of the bottom 20%.

Bigger ratios indicate higher inequality.

Does this satisfy the Dalton principle?



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The coefficient of variation

It is the ratio between the standard deviation () and the

mean ().

C =

, where = 1n

ni=1(yi )

2.

Does this satisfy the Dalton principle?.



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The Gini coefficient

This measure is related to the Lorenz curve.

The Gini coefficient is the ratioM

M+S (see next graph.) The Gini coefficient satisfies all the criteria supported by the

Lorenz curve.

That is, when inequality

is higher, M will be bigger and the Gini coefficient will be higher.



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M

S



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2.5 Evidence



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Inequality in SSA is the highest, except for LA.( )K. Deininger, L. SquirerJournal of Deelopment Economics 57 1998 259287 263

Table 1

Decadal medians of Gini coefficients for the income distribution, by Region 19601990

1960s 1970s 1980s 1990s

Eastern Europe 22.76 21.77 24.93 28.60South Asia 31.67 32.32 32.22 31.59

OECD and high income 32.86 33.04 32.20 33.20

East Asia and Pacific 34.57 34.40 34.42 34.80

Middle East and North Africa 41.88 43.63 40.80 39.72

Sub-Saharan Africa 49.90 48.50 39.63 42.30

Latin America 53.00 49.86 51.00 50.00

Regions are ordered by increasing inequality in the 1990s. .Source: Deininger and Squire 1996 .



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2.6 Kuznetss curve

How does inequality respond to economic development?

Kuznets hypothesis an inverted-U relation.

Inequality is highest for countries with middle-income and

lower for the rich and poor.



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2.7 Is economic growth pro-poor?



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150100500

Change in log mean consumption or income between surveys (x100)

50100150

500

Change in log poverty headcount index (x100)

400

300

200

100

0

100

200

300

400

y = 2.3841x + 2.3517t-stat = 9.30

R

2

= 0.5225N = 73

BUL

LVA

PER MDAARG

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0

Figure 4.3 Growth is the key to poverty reduction . . .

Source: WDR 2006.



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150100500

Change in log mean consumption or income between surveys (x100)

50100150

50

Change in log Gini index (x100)

40

30

20

10

0

10

20

30

40

50

60

y = 0.0288x + 3.3717t-stat = 0.515R2 = 0.004N = 73

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Figure 4.4 . . . and, on average, growth is distribution-neutral

Source: WDR 2006.



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Sources

Lorenz curves come from Debraj Ray (1998) textbook. Inequality in South Africa: van der Berg et al (2005) Trends

in poverty and inequality since the political transition.

Inequality in SSA (tables 6 and 7) from by Tsikata, Y. (2001)

Globalisation, Poverty and Inequality in Sub-Saharan Africa:

A Political Economy Appraisal.

Inequality in SSA (table 3.1) Okojie, C. and A. Shimeles (2006)

Inequality in sub-Saharan Africa: a synthesis of recent

research on the levels, trends, effects and determinants of

inequality in its different dimensions.

Recent trends in PHC: Chen, S. and M. Ravallion (2007)

Absolute Poverty Measures for the Developing World,

1981-2004 World Bank.



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FGT in Africa: Can Africa Claim the 21st Century? The

World Bank Washington, D.C.

FGT in Ivory Coast: Deaton (1997) The Analysis of Household

Surveys.

Econ 181: Inequality and Poverty October 10 2011 48

4&5. poverty and inequality

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