OPHI Oxford Poverty & Human Development Initiative Department of International Development Queen Elizabeth House, University of Oxford www.ophi.org.uk

Multidimensional Poverty Measures: New Potential Sabina Alkire, Busan, 28 October 2009 Why Multidimensional not income poverty measures? Non-deprived in Deprived in non- non-monetary monetary dimension dimension Not income Group A Group B (I) poor Income Group C (II) Group D Poor Ruggieri-Laderchi 2007

If income/consumption poverty is used for policy & targetting purposes, Group B represents a targeting error I (omission of some poor) Group C represents a targeting error II (inclusion of some non-poor) Oversights from income poverty:

I (omission)

II (overcount)

Conclusion: Income mis-identifies other deprivations. Ruggieri-Laderchi, Saith and Stewart ‟03, „07 Why Multidimensional Poverty? Growth

India: 15 years of strong economic growth.

1998-9: 47% children under 3 are undernourished

2005-6: 46% are undernourished (FOCUS 06) (wt-age) François Bourguignon, Agnès Bénassy-Quéré, Stefan Dercon, Antonio Estache, Jan Willem Gunning, Ravi Kanbur, Stephan Klasen, Simon Maxwell, Jean-Philippe Platteau, Amedeo Spadaro

‘The correlation between GDP per capita growth and non- income MDGs is practically zero…’ Other uses: to replace, supplement, or combine with the official measures ~ Mexico, Bhutan to monitor the level and composition of poverty, and the reduction of poverty, over time ~ India to monitor the impact of programmes ~ Education to target the poorest for Social Protection ~ Oportunidades to compare the composition of poverty and identify vulnerable or excluded groups ~ All Why Now? Why Now?

1. In economic downturn (and aid pressures), the need for efficiency increases. MD analysis can identify synergies, sequences, interconnections, and high impact entrance points. 2. During crises, multidimensional poverty can be reduced even in the absence of growth – and progress can be seen more quickly and directly than waiting for it to affect growth results. 3. Some seek a wider economic framework. Counting and Multidimensional Poverty Measurement

Sabina Alkire (OPHI, University of Oxford) and James E. Foster (George Washington University and OPHI, University of Oxford) How to construct a MD poverty measure? • Variables, Weights • Cutoffs • Identification • Aggregation (Sen 1976) Our Proposal

• Variables, Weights – Assume given. • Identification – Dual cutoffs • Aggregation – Adjusted FGT • Cutoffs – Purpose of exercise, dominance

• Important Note for today’s session: Participation can be used in the selection of domains, their weighting, and setting poverty cutoffs. Indeed, participatory and qualitative data can even be used in computing M0. Review: Unidimensional Poverty

Variable – income Identification – poverty line Aggregation – Foster-Greer-Thorbecke ‟84

Example Incomes = (7,3,4,8) poverty line z = 5

Deprivation vector g0 = (0,1,1,0) 0 Headcount ratio P0 = m(g ) = 2/4 Normalized gap vector g1 = (0, 2/5, 1/5, 0) 1 Poverty gap = P1 = m(g ) = 3/20 Squared gap vector g2 = (0, 4/25, 1/25, 0) 2 FGT Measure = P2 = m(g ) = 5/100 Multidimensional Data

Matrix of well-being scores for n persons in d domains

Domains 13.1 14 4 1   15.2 7 5 0 y  Persons 12.5 10 1 0   20 11 3 1  

 Multidimensional Data

Matrix of well-being scores for n persons in d domains

Domains 13.1 14 4 1   15.2 7 5 0 y  Persons 12.5 10 1 0   20 11 3 1  

z ( 13 12 3 1) Cutoffs  Deprivation Matrix

Replace entries: 1 if deprived, 0 if not deprived

Domains 13.1 14 4 1    15.2 7 5 0   Persons y    12.5 10 1 0   20 11 3 1   

 Deprivation Matrix

Replace entries: 1 if deprived, 0 if not deprived

Domains 0 0 0 0    0 1 0 1  g 0  Persons 1 1 1 1    0 1 0 0 

 Normalized Gap Matrix

Normalized gap = (zj - yji)/zj if deprived, 0 if not deprived

Domains 13.1 14 4 1    15.2 7 5 0   Persons y    12.5 10 1 0   20 11 3 1   

z ( 13 12 3 1) Cutoffs  These entries fall below cutoffs Normalized Gap Matrix

Normalized gap = (zj - yji)/zj if deprived, 0 if not deprived

Domains  0 0 0 0    0 0.42 0 1 1   Persons g    0.04 0.17 0.67 1    0 0 08 0 0   . 

 Squared Gap Matrix

2 Squared gap = [(zj - yji)/zj] if deprived, 0 if not deprived

Domains  0 0 0 0    0 0.42 0 1 1   Persons g    0.04 0.17 0.67 1    0 0 08 0 0   . 

 Squared Gap Matrix

2 Squared gap = [(zj - yji)/zj] if deprived, 0 if not deprived

Domains  0 0 0 0    0 0.176 0 1 2  Persons g    0.002 0.029 0.449 1    0 0 006 0 0   . 

 Identification

Domains 0 0 0 0    0 1 0 1  g 0  Persons 1 1 1 1    0 1 0 0 

Matrix of deprivations  Identification – Counting Deprivations

Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Identification – Counting Deprivations

Q/ Who is poor?

Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Identification – Union Approach

Q/ Who is poor?

A1/ Poor if deprived in any dimension ci ≥ 1 Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Identification – Union Approach

Q/ Who is poor?

A1/ Poor if deprived in any dimension ci ≥ 1 Domains c

0 0 0 0  0   0 1 0 1  2 g 0  1 1 1 1  4 Persons   0 1 0 0  1

Observations Union approach often predicts high numbers. Charavarty et al ‟98, Tsui 2002, Bourguignon & Chakravarty 2003 etc use the union approach Identification – Intersection Approach

Q/ Who is poor?

A2/ Poor if deprived in all dimensions ci = d Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Identification – Intersection Approach

Q/ Who is poor?

A2/ Poor if deprived in all dimensions ci = d Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1 Observations Demanding requirement (especially if d large) Often identifies a very narrow slice of population Atkinson 2003 first to apply these terms. Identification – Dual Cutoff Approach

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Identification – Dual Cutoff Approach

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2) Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Identification – Dual Cutoff Approach

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2) Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1 Note Includes both union and intersection  Identification – Dual Cutoff Approach

Q/ Who is poor?

A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2) Domains c 0 0 0 0  0   0 1 0 1  2 g 0  1 1 1 1  4   0 1 0 0  1 Note Includes both union and intersection Especially useful when number of dimensions is large  Union becomes too large, intersection too small Identification – The problem empirically

k = H Poverty in India for 10 Union 1 91.2% dimensions: 2 75.5% 91% of population would be 3 54.4% targeted using union, 4 33.3% 5 16.5% 0% using intersection 6 6.3% Need something in the 7 1.5% middle. 8 0.2% (Alkire and Seth 2009) 9 0.0% Inters. 10 0.0%

Aggregation

Censor data of nonpoor

Domains c 0 0 0 0  0   0 1 0 1  2 g 0  Persons 1 1 1 1  4   0 1 0 0  1

 Aggregation

Censor data of nonpoor

Domains c(k) 0 0 0 0  0   0 1 0 1  2 g 0(k)  Persons 1 1 1 1  4   0 0 0 0  0  

 Aggregation

Censor data of nonpoor

Domains c(k) 0 0 0 0  0   0 1 0 1  2 g 0(k)  Persons 1 1 1 1  4   0 0 0 0  0  

Similarly for g1(k), etc  Aggregation – Headcount Ratio

Domains c(k) 0 0 0 0  0   0 1 0 1  2 g 0(k)  Persons 1 1 1 1  4   0 0 0 0  0  

 Aggregation – Headcount Ratio

Domains c(k) 0 0 0 0  0   0 1 0 1  2 g 0(k)  Persons 1 1 1 1  4   0 0 0 0  0  

Two poor persons out of four: H = 1/2  Critique

Suppose the number of deprivations rises for person 2

Domains c(k) 0 0 0 0  0   0 1 0 1  2 g 0(k)  Persons 1 1 1 1  4   0 0 0 0  0  

Two poor persons out of four: H = 1/2  Critique

Suppose the number of deprivations rises for person 2

Domains c(k) 0 0 0 0 0 1 1 0 1 3 g 0 (k)    Persons 1 1 1 1 4   0 0 0 0 0

Two poor persons out of four: H = 1/2 Critique

Suppose the number of deprivations rises for person 2

Domains c(k) 0 0 0 0 0 1 1 0 1 3 g 0 (k)    Persons 1 1 1 1 4   0 0 0 0 0

Two poor persons out of four: H = 1/2 No change! Critique

Suppose the number of deprivations rises for person 2

Domains c(k) 0 0 0 0 0 1 1 0 1 3 g 0 (k)    Persons 1 1 1 1 4   0 0 0 0 0

Two poor persons out of four: H = 1/2 No change! Violates „dimensional monotonicity‟ Aggregation

Return to the original matrix

Domains c(k) 0 0 0 0 0 1 1 0 1 3 g 0 (k)    Persons 1 1 1 1 4   0 0 0 0 0 Aggregation

Return to the original matrix

Domains c(k) 0 0 0 0  0   0 1 0 1  2 g 0(k)  Persons 1 1 1 1  4   0 0 0 0  0  

 Aggregation

Need to augment information deprivation shares among poor

Domains c(k) c(k)/d 0 0 0 0  0   0 1 0 1 2 2 4 0   / Persons g (k)    1 1 1 1 4 4 / 4   0 0 0 0  0  

 Aggregation

Need to augment information deprivation shares among poor

Domains c(k) c(k)/d 0 0 0 0  0   0 1 0 1 2 2 4 0   / Persons g (k)    1 1 1 1 4 4 / 4   0 0 0 0  0  

A = average deprivation share among poor = 3/4  Aggregation – Adjusted Headcount Ratio

Adjusted Headcount Ratio = M0 = HA

Domains c(k) c(k)/d 0 0 0 0  0   0 1 0 1 2 2 4 0   / Persons g (k)    1 1 1 1 4 4 / 4   0 0 0 0  0  

A = average deprivation share among poor = 3/4  Aggregation – Adjusted Headcount Ratio

0 Adjusted Headcount Ratio = M0 = HA = m(g (k))

Domains c(k) c(k)/d 0 0 0 0  0   0 1 0 1 2 2 4 0   / Persons g (k)    1 1 1 1 4 4 / 4   0 0 0 0  0  

A = average deprivation share among poor = 3/4  Aggregation – Adjusted Headcount Ratio

0 Adjusted Headcount Ratio = M0 = HA = m(g (k)) = 6/16 = .375

Domains c(k) c(k)/d 0 0 0 0  0   0 1 0 1 2 2 4 0   / Persons g (k)    1 1 1 1 4 4 / 4   0 0 0 0  0  

A = average deprivation share among poor = 3/4  Aggregation – Adjusted Headcount Ratio

0 Adjusted Headcount Ratio = M0 = HA = m(g (k)) = 6/16 = .375

Domains c(k) c(k)/d 0 0 0 0  0   0 1 0 1 2 2 4 0   / Persons g (k)    1 1 1 1 4 4 / 4   0 0 0 0  0  

A = average deprivation share among poor = 3/4  Note: if person 2 has an additional deprivation, M0 rises Satisfies dimensional monotonicity Adjusted Headcount Ratio Mk0=(ρk,M0) Valid for ordinal data (identification & aggregation) – robust to monotonic transformations of data.

Similar to traditional gap P1 = HI ; this = HA Easy to calculate, easy to interpret Can be broken down by dimension – policy Characterization via freedom – Pattanaik and Xu 1990. Note: If cardinal variables, can go further Aggregation: Adjusted Poverty Gap

Need to augment information of M0 Use normalized gaps

Domains  0 0 0 0    0 0.42 0 1 1   Persons g (k)    0.04 0.17 0.67 1    0 0 0 0   

Average gap across all deprived dimensions of the poor: /  G Aggregation: Adjusted Poverty Gap

Adjusted Poverty Gap = M1 = M0G = HAG

Domains  0 0 0 0    0 0.42 0 1 1   Persons g (k)    0.04 0.17 0.67 1    0 0 0 0   

Average gap across all deprived dimensions of the poor: /  G Aggregation: Adjusted Poverty Gap

1 Adjusted Poverty Gap = M1 = M0G = HAG = m(g (k))

Domains  0 0 0 0    0 0.42 0 1 1   Persons g (k)    0.04 0.17 0.67 1    0 0 0 0   

Average gap across all deprived dimensions of the poor: /  G Aggregation: Adjusted Poverty Gap

1 Adjusted Poverty Gap = M1 = M0G = HAG = m(g (k))

Domains  0 0 0 0    0 0.42 0 1 1   Persons g (k)    0.04 0.17 0.67 1    0 0 0 0   

Obviously, if in a deprived dimension, a poor person becomes

even more deprived, then M1 will rise. Satisfies monotonicity Aggregation: Adjusted FGT

Consider the matrix of squared gaps

Domains  0 0 0 0    0 0.422 0 12 g2(k)    Persons 0.042 0.172 0.672 12     0 0 0 0 

 Aggregation: Adjusted FGT

 Adjusted FGT is M = m(g (k))

Domains  0 0 0 0    0 0.422 0 12 g2(k)    Persons 0.042 0.172 0.672 12     0 0 0 0 

 Aggregation: Adjusted FGT

 Adjusted FGT is M = m(g (k))

Domains  0 0 0 0    0 0.422 0 12 g2(k)    Persons 0.042 0.172 0.672 12     0 0 0 0 

Satisfies transfer axiom  Aggregation: Adjusted FGT Family

a Adjusted FGT is Ma = m(g (t)) for a > 0

Domains  0 0 0 0     0 0.42a 0 1a  ga (k)  Persons  a a a a  0.04 0.17 0.67 1    0 0 0 0   

Theorem 1 For any given weighting vector and cutoffs, the methodology

Mka =(ρk,Ma) satisfies: decomposability, replication invariance,  symmetry, poverty and deprivation focus, weak and dimensional monotonicity, nontriviality, normalisation, and weak rearrangement for a>0; monotonicity for a>0; and weak transfer for a>1. Setting cutoff k: normative or policy • Depends on: purpose of exercise, data, and weights – “In the final analysis, how reasonable the identification rule is depends, inter alia, on the attributes included and how imperative these attributes are to leading a meaningful life.” (Tsui 2002 p. 74). • E.g. a measure of Human Rights; data good = union • Targeting: according to category (poorest 5%). Or budget (we can cover 18% - who are they?) • Poor data, or people do not value all dimensions: k

• M0 , M1 and M2 satisfy Dimensional Monotonicity, Decomposability

• M1 and M2 satisfy Monotonicity (for a > 0) – that is, they are sensitive to changes in the depth of deprivation in all domains with cardinal data.

• M2 satisfies Weak Transfer (for a > 1). Extension: General Weights Modifying for weights at two points:

1) Identification (k is now a cutoff of the weighted sum of dimensions) 2) Aggregation (simply weight matrix prior to taking the mean)

Both weights are easily applied. Illustration: USA • Data Source: National Health Interview Survey, 2004, United States Department of Health and Human Services. National Center for Health Statistics - ICPSR 4349. • Tables Generated By: Suman Seth • Unit of Analysis: Individual. • Number of Observations: 46009. • Variables: – (1) income measured in poverty line increments and grouped into 15 categories – (2) self-reported health – (3) health insurance – (4) years of schooling. Illustration: USA Illustration: USA Illustration: USA – all values of k Empirical Applications

Sub-Saharan Africa (14 countries): Assets, Education, BMI, Empowerment Latin America (6 countries) Income, Child in School, hhh Education, Water, Sanitation, Housing China Income, Education, BMI, Water, Sanitation, Electricity India Assets, Education, BMI, Water, Sanitation, Housing, Electricity, Cooking Fuel, Livelihood, Child status, Empowerment. Pakistan Expenditure, Assets, Education, Water, Sanitation, Electricity, Housing, Land, Empowerment Bhutan I Income, Education, Rooms, Electricity, Water (land, roads used in rural areas only) Bhutan II Gross National Happiness Indicators, used with poverty cutoffs rather than sufficiency cutoffs. MD Poverty Ranking (NFHS 2005/06) Vs. Income Poverty Ranking (NSS 2004)

Jharkhand Madhya Pradesh Uttar Pradesh Orissa Rajasthan NSS Income Poverty Chhattisgarh Bihar MD Head Count West Bengal Assam Arunachal Pradesh Andhra Pradesh Maharashtra Deteriorated from Rank 1 to Karnataka Gujarat Rank 18 Haryana Tamil Nadu Meghalaya Uttaranchal Jammu and Kashmir

Indian StatesIndian Tripura Nagaland Punjab Goa Manipur Himachal Pradesh Mizoram Sikkim Kerala Improved from Rank 7 to Rank 1 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Poverty Rates Bhutan: We decompose the measure to see what is driving poverty. In Bhutan the rank of the districts changed. The relatively wealthy state Gasa fell 11 places when ranked by multidimensional poverty rather than income; the state Lhuntse, which was ranked 17/20 by income, rose 9 places. Decomposing M0 by dimension, we see that in Gasa, poverty is driven by a lack of electricity, drinking water and overcrowding; income is hardly visible as a cause of poverty. In Lhuntse, income is a much larger contributor to poverty.

Composition of Multidimensional Poverty in Two Districts - Mo with k=2

100% 90% 80% 70% 60% 50% 40% 30% 20%

Each Indicator 10% % Contribution of 0% Gasa Lhuntse District

Income Literacy People per Room Drinking Water Electricity Santitation M0 with k=2 and Equal Weights Education Sanitation, Uruguay: & Argentina contribution its increased Income HH. of HH. Education Shelter, Sanitation, contrib: Main Mexico: Chile &

100 20 40 60 80 0 Brazil: 1992 Argentina 1995 2000 2003 Main contrib:Main EducationHH,Sanitation, Income. 2006 El Salvador: 1992 1995 Brazil 2000 Sanitation HH Education Income 2003 2006 1992 More similarcontrib.More across dimensions 1995 Chile 2000 2003 2006 El Salvador El 1992 1995 2000 2003 2006 Shelter Water Running ChildrenSchool in 1992 Mexico 1995 2000 2003 2006 1992 Uruguay 1995 2000 2003 2006 Comparison Between Various African

0.70 Countries using DHS Data

0.60

0.50

0.40

0.30

M0 Poverty Rate Poverty M0 0.20

0.10

0.00 0.1 0.4 0.6 0.9 1.1 1.4 1.6 1.9 2.1 2.4 2.6 2.9 3.1 3.4 3.6 3.9 Poverty Cut-offs Benin Burkina Ghana Kenya Niger Nigeria

Source: Batana Y. M. (2008) ‘Multidimensional Measurement of Poverty in Sub-Saharan Africa’, Working Paper No.13, Oxford Poverty & Human Development Initiative, Oxford University. Example of messages

Headcount = 37% are deprived in at least five of 10 dimensions.

M0 = 0.22 Breadth: most poor people are on average deprived in 6/10. The fullest bowls nationally were Education and Housing The emptiest bowls nationally were Employment and Health

In the state with highest poverty, Ardenia,  Headcount: 82% are poor  Breadth: most poor people are on average deprived in 8/10 Measure can decompose the change in deprivations across time – key M&E. (Example: China panel data. Employment deprivation rising; income and resource deprivations shrinking)

100% 90% 80% Resources 70% Security 60% Employment 50% 40% Health 30% Education 20% Income Contribution to Mo to Contribution 10% 0% 1993 1997 2000 2004 Year Ongoing Studies

Applications have been completed for:

Sub-Saharan Africa (14 countries)

Latin America (6 countries)

China (2), India, (2) Pakistan, (2) Bhutan (2) Ongoing Studies

Other Applications to: Quality of Education (Mexico, Argentina) Child Poverty (Bangladesh, Afghanistan) Governance (Index of African Governance) Fair trade (Human Rights – Benetech) Social Protection (India, Mexico) Gender (international index)

Workshop was 1-2 June, 2010 HDR Preliminary Feedback: benefits a) you can target the poor more accurately. By looking at the breadth and depth of deprivation in each dimension, we can zoom in, like a magnifying glass, on the extreme poor. b) you can see policy cues. This multidimensional measure, displays how the components of poverty vary. The same data tives you more relevant information. c) you can look at people not just households. Children‟s distinct needs can be seen directly, for example. d) you can make a measure that matches your needs. The dimensions, poverty cutoffs, etc can be standardized to ensure comparability. But in many cases it can be useful to tailor these to specific contexts and measurement needs, including via participatory methods.