Analysis of Inequality across Multi-dimensionally Poor and Population

Subgroups for Counting Approaches

Suman Seth and Sabina Alkire

Development Studies Association Annual Conference 2013University of Birmingham

November 16, 2013

Motivation

Poverty measurement tools may affect policy design and policy incentive – Incidence

– Intensity

– Inequality

Three I’s of poverty measurement (Jenkins and Lambert 1997)

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Concerns for Inequality

Inequality among the poor– Consideration of inequality in poverty measurement has

been prominent since Sen (1976)

Disparity across population subgroups– Horizontal Inequality (Stewart 2000)

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Counting Approach

Counting measures– Townsend (1979), Atkinson (2003)

– Adjusted headcount ratio (Alkire and Foster): • several national and international (MPI, WEAI) adaptations

Capturing inequality is natural for cardinal dimensions– Can reflect inequality within each dimension

Not so straightforward for ordinal or binary dimensions– But can be captured across deprivation counts

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Example: Concern for Inequality

Deprivation counts

(0, 2, 4, 6, 8, 10)

(0, 2, 2, 4, 8, 10) (0, 2, 2, 5, 8, 9)

Next period I Next period II

Similar reduction in incidence and intensity, but these two situations are not the same

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Consideration for Inequality

Other Approach: Use a separate inequality measure?

An example: Use of standard deviation in child poverty– Delamonica and Minujin (2007), Roche (2013)

Advantage:– Additional information besides incidence and intensity

– If decomposable, can observe inequality decomposition within and between group

– Can be used with intuitive poverty measure such as Adjusted

Headcount Ratio

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Consideration for Inequality

Q: Which inequality measure to use?– Eepends on which properties we want the measure to satisfy

Three key properties– Absolute inequality: if every poor’s deprivation count rises

or decreases by same number, inequality should not change

– Additive Decomposability: within-group + between group

– Within-group Mean Independence: Total within-group does not change if no change in inequality within any subgroup

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Consideration for Inequality

The Inequality Measure?

The only absolute inequality measure that satisfies these properties is a positive multiple of variance

V(x) = i(xi – (x))2/n

where, V(x): positive multiple of variance of distribution x

(x): mean of distribution x

n: population size of distribution x

> 0

Chakravarty (2001), Bosmans and Cowell (2011),Chakravarty and Tyagarupananda (1998)

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Illustrations using the Global Multidimensional Poverty Index (MPI)

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Example on India: Castes (DHS 2 & 3)

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1999Intensity

(MPI)Share of Poor

Inequality (Poor)

 caste A_caste poor_shr var_depr_caste_p

Scheduled Tribe 57.0% 12.6% 0.110  Scheduled Caste 55.0% 22.1% 0.107  Other Backward Classes

52.1% 33.3% 0.095  

General 50.6% 32.0% 0.089  India 52.9% 100% 0.1002006ST 56.3% 12.9% 0.115  SC 52.6% 22.9% 0.098  OBC 50.8% 42.1% 0.090  General 49.7% 22.0% 0.092  India 51.7% 100% 0.097  

Example on India: Castes (DHS 2 & 3)

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1999Intensity

(MPI)Share of Poor

Inequality (Poor)

 caste A_caste poor_shr var_depr_caste_p

Scheduled Tribe 57.0% 12.6% 0.110  Scheduled Caste 55.0% 22.1% 0.107  Other Backward Classes

52.1% 33.3% 0.095  

General 50.6% 32.0% 0.089  India 52.9% 100% 0.1002006ST 56.3% 12.9% 0.115  SC 52.6% 22.9% 0.098  OBC 50.8% 42.1% 0.090  General 49.7% 22.0% 0.092  India 51.7% 100% 0.097  

Inequality among the poor fell for SC and OBC, but not for ST

Indian States (DHS 2 & 3)

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Arunachal Pradesh

Bihar

RajasthanTripuraAssamOrissa

NagalandHimachal Pradesh

Uttar Pradesh

HaryanaMeghalaya

Madhya PradeshNew DelhiKerala West Bengal

GujaratGoaMaharashtra

Jammu Sikkim

Manipur PunjabTamil Nadu

Karnataka

MizoramAndhra Pradesh

-0.040

-0.030

-0.020

-0.010

0.000

0.010

0.020

-0.120 -0.100 -0.080 -0.060 -0.040 -0.020 0.000 0.020 0.040

Ch

ange

in In

equ

alit

y in

Dep

riva

tion

Sco

res a

mon

g th

e P

oor

Change in MPI

Cross Country Comparison

Two countries: different MPIs but similarly unequal

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Country YearHeadcount

Ratio MPI

Average Deprivation

Count (Poor)Inequality

(Poor)

Colombia 2010 5.4% 0.022 40.9% 0.041

Lesotho 2009 35.3% 0.156 44.1% 0.042

Demographic Health Surveys

Disparity in Intensity vs. Disparity in Poverty

Between group inequality among poor is not sufficient for disparity in poverty between groups– Sub-national Disparity (Alkire, Roche, Seth 2011)

Example:

c = (0,0,0,6,6,6,6,6,7,7), cA = (0,0,6,6,7) and cB = (0,6,6,6,7)

c' = (0,0,0,6,6,6,6,6,6,6), c'A = (0,0,0,6,6) and c'B = (6,6,6,6,6)

Overall inequality, within group inequalities, between group inequalities among the poor – all lower in c' than in c

Disparity in poverty between subgroups?

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Cross Country Comparisons

Similar inequality among the poor but very different sub-national disparity

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Country Year MPIInequality

(Poor)

Total Within-Group

Between Group

Between MPI

Bolivia 2008 0.089 0.044 0.042 0.002 0.006Zimbabwe 2011 0.172 0.045 0.044 0.001 0.021

Demographic Health Surveys

Concluding Remarks

We discuss how inequality can be captured among the poor in counting approach through a positive multiple of variance

A separate measure can provide more information besides a poverty measure than just ranking

Although debated (Kanbur, 2006), change in inequality decomposition can provide important information

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Concluding Remarks

It is also important to capture disparity between subgroup’s poverty

Same result if counted in achievement or deprivation space

Future research– Compute the standard error to understand statistical

significance of comparisons

– Deeper analysis across countries to understand inequality decompositions and causes of change in inequality

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