Summer School on Capability d M l idi i l Pand Multidimensional Poverty

27 August-8 September, 2009g p ,Lima, Peru

OPHIOxford Poverty & Human yDevelopment InitiativeUniversity of Oxford www.ophi.org.uk

Measuring Multidimensional PovertyPoverty

S bi Alki (OPHI)Sabina Alkire (OPHI)

31 August, 2009

Outline

• Aggregate MD Poverty measures– Example: HPIp

• Indy or Hh MD Pov Measures Introduction– Introduction

– One MD Poverty measureE pl f ppli ti– Examples of application

– Some alternatives A i– Axioms

Multidimensional Measures areMultidimensional Measures are exploding

• Bandura (2006) found that over 50% of composite (multidimensional) indices related p ( )to many topics had been developed within the past five years. p y

• In the area of poverty/well-being the proportion appears to be even higherproportion appears to be even higher.

Various groups are synthesising different aspects of measurement methodology e g this 2008methodology – e.g. this 2008 Handbook

Most use aggregate datagg gExample: Human Poverty Index

• Calculated since 1997.

• Measures deprivation in three dimensions:Measures deprivation in three dimensions: health, education, economic deprivation.

• HPI-I is for developing countries; HPI-II is for developed countries The thresholdsfor developed countries. The thresholds differ. HPI-II also reflects social exclusion.

• Multidimensional: applies cutoff to each dim.

Purpose of HPI:

Dimensions of HPI: Ed, H, Econ

How Justified? Education exampleHow Justified? Education example

Justification acknowledgesJustification acknowledges considerations of Data Quality

Human Poverty Index – HPI -IyDimension Indicator

Survival deprivation •P1: Probability at birth of not surviving to age 40.

Ed cation depri ation •P Ad lt illiterac rateEducation deprivation •P2: Adult illiteracy rate

Economic deprivation P3: Equally weighted avg of:% f l i i h•% of population without

access to an improved water source•% of children under weight for age

Human Poverty Index – HPI-I

HPI-I={(1/3)[(P1)α+(P2)α+(P3)α]}1/α

• This is the general means expression.• With α=1, HPI is the arithmetic mean, all

dimensions are equally weighted. • For α>1 higher weight is given to ‘higher entries’• For α>1, higher weight is given to higher entries ,

ie: the dimensions in which there is most deprivation. F 1 hi h i h i i ‘l i ’ i• For α<1, higher weight is given to ‘lower entries’, ie: the dimensions in which there is least deprivation.

• Value used by the HDRO: α=3.Va ue used by t e H O: α 3.

Example of HPI-I: AngolaExample of HPI-I: Angola• Prob. of not surviving 40: 48.1%Prob. of not surviving 40: 48.1%

• Adult illiteracy rate: 33.2%

% f i h i d• % of pop. without access to improved water: 50% . Children under weight for age: 31%. Th (50+31)/2 40 5%Then: (50+31)/2=40.5%

HPI-I={(1/3)[(48.1)3+(33.2)3+(40.5)3]}1/3=

=41.5

HDI & HPI’s AdvantagesTh ib d h hif f i• They contributed to the shift of attention from the unidimensional space of income, to h l idi i l i hi hthe multidimensional space in which

development must be evaluated.

• They are easy to calculate and not very demanding in terms of data.

Criticisms• Arbitrary selection of dimensions and indicators. Why not

including other indicators within dimensions (ex. nutrition) g ( )or other dimensions (ex. political participation)?

• Arbitrary aggregation and weights.d l h d b f h• Does not consider inequality in the distribution of each

dimension (Foster, Lopez-Calva, Szekely, 2005 propose to use general means to aggregate data within and across g gg gdimensions).

• Does not reflect the ‘coupling’ of disadvantages

But remains a key class of measures for aggregate data; could be used with different dimensions; could be used ;with general weights or tested for robustness of weights.

An alternative?An alternative?• Consider only data coming from one surveyConsider only data coming from one survey.

• Identify all the deprivations each household suffers.

• Is household* is poor? (*person ideal but data difficult)

• Let us define an aggregate measure for which the unit of analysis is the household rather than the nation.

• Recall: this requires aggregation first across dimensions and then across households (may require intra-hh aggregation or gg gselection also for some variables, e.g. education)

Normative Motivation:

• Focus on People as unit of analysis when possible because poverty is worse when people are deprived in more dimensions at the same time.

• By aggregating first across dimensions for each person, poverty measures can reflect two different aspects:– Depth or cardinal shortfall from cutoff in each dimension– Breadth or number of dimensions in which person is deprived

Background: to axiomatic measuresAxiomatic approaches to multidimensional poverty pp p y

began to gain momentum in the late 1990sBrandolini, A., D’Alessio, G., 1998. Measuring g

Well-being in the Functioning Space. Mimeo. Rome. Banco d’Italia Research Department.

Chakravarty, S.R., Mukherjee, D., Renade, R.R., 1998. On the Family of Subgroup and F D bl M fFactor Decomposable Measures of Multidimensional Poverty. Research on Economic Inequality, 8, 175-194.Inequality, 8, 175 194.

Key papers• Anand, S., Sen, A.K., 1997. Concepts of Human

Development and Poverty: A Multidimensional p yPerspective. New York, UNDP.

• Tsui, K. 2002., Multidimensional Poverty Indices. , , ySocial Choice and Welfare, vol. 19, pp. 69-93.

• Atkinson, A.B., 2003. Multidimensional Deprivation. Contrasting Social Welfare and Counting Approaches. Journal of Economic I li 1 51 65Inequality. 1, 51-65

• Bourguignon, F., Chakravarty, S. R., 2003. The M t f M ltidi i l P t J lMeasurement of Multidimensional Poverty. Journal of Economic Inequality. 1, 25-49.

Recent collections of articlesRecent collections of articles (axiomatic, information theory, fuzzy)

• Kakwani, N., Silber, J., 2008a. The Many Dimensions of Poverty. Palgrave MacMillanf y g

• Kakwani, N., Silber, J., 2008b. Quantitative Approaches to Multidimensional PovertyApproaches to Multidimensional Poverty Measurement. Palgrave Macmillan.

• World Development June 2008• World Development June 2008

Background: to counting measuresg g• Much larger and longer history; far more

mpiri l ppli ti ns id p li sempirical applications; wide policy use. • From 1968: Scandinavian level of living. • Mack, J., Lansley S., 1985. Poor Britain. • Smeeding et al. 1993. Review of Income & Wealthg f• Jayaraj & Subramanian~on Child Labor India• 2005 UNICEF Child Poverty Report• 2005 UNICEF Child Poverty Report. • 2006: Chakravarty & D’Ambrosio (combo

i i d i l l i i )axiomatic and social exclusion counting)

This class and tomorrow• We will focus on one of several new

multidimensional poverty measures, teach itmultidimensional poverty measures, teach it and do exercises on it so that you are confident using it.confident using it.

• However there are several other interesting axiomatic measures These areinteresting axiomatic measures. These are summarised in Chakravarty & Silber 2008. “Measuring Multidimensional Poverty: TheMeasuring Multidimensional Poverty: The Axiomatic Approach,” in Kakwani & Silber, Eds Quantitative Approaches p 192 209Eds., Quantitative Approaches... p 192-209.

This class and tomorrow• There are also other interesting

nonaxiomatic approaches (Info theory,nonaxiomatic approaches (Info theory, fuzzy set, counting etc).

• For a review of some of these see Deutsch J• For a review of some of these see Deutsch, J., Silber, J., 2005. Measuring Multidimensional Poverty An Empirical Comparison ofPoverty. An Empirical Comparison of Various Approaches. The Review of Income and Wealth 51 145 174Wealth. 51, 145-174

Focus of this class

• Alkire, S., Foster, J.E., 2007. “Counting and Multidimensional Poverty Measurement.” yOxford Poverty & Human Development Initiative OPHI Working Paper 7. g p

• Note: some things taught here are not present• Note: some things taught here are not present in the working paper but will be available in the final versionthe final version.

Multidimensional Poverty- our challenge:

• A government would like to create an official m ltidim i l p rt i di t rmultidimensional poverty indicator

• Desiderata– It must understandable and easy to describe – It must conform to “common sense” notions of poverty

It t b bl t t t th t k h d id– It must be able to target the poor, track changes, and guide policy.

– It must be technically solidy– It must be operationally viable– It must be easily replicable

• What would you advise?

Multidimensional Poverty ComparisonsComparisons

• There are many steps to creating index: – Choice of purpose for the index (monitor, target, etc)p p ( , g , )– Choice of Unit of Analysis (indy, hh, cty)– Choice of Dimensions

Choice of Variables/Indicator(s) for dimensions– Choice of Variables/Indicator(s) for dimensions– Choice of Poverty Lines for each indicator/dimension– Choice of Weights for indicators within dimensions– If more than one indicator per dimension, aggregation– Choice of Weights across dimensions– Identification method– Aggregation method – within /across dimensions.

Today’s focus

• Purpose, Variables, Dimensional Cutoffs, Weights and all other steps – Assume givenWeights and all other steps – Assume given

• Identification – Dual cutoffsIdentification – Dual cutoffs

• Aggregation – Adjusted FGT

Key methodological points:

Multidimensional poverty methodology mpri id tifi ti d r ticomprises identification and aggregation, as

well as the choice of space. (Sen 1976)

• Identification is critically important• Axioms are joint restrictions on identification

and aggregation. • Ordinal data are common as are hybrids.• Decomposability by sub-group and (postDecomposability by sub group, and (post

identification) by factor, is key for policy.

Review: Unidimensional PovertyVariable – incomeIdentification – poverty linep yAggregation – Foster-Greer-Thorbecke ’84

E l I (7 3 4 8) li 5Example Incomes = (7,3,4,8) poverty line z = 5

Deprivation vector g0 = (0,1,1,0) p g ( )Headcount ratio P0 = (g0) = 2/4

Normalized gap vector g1 = (0, 2/5, 1/5, 0)P P ( 1) 3/20Poverty gap = P1 = (g1) = 3/20

Squared gap vector g2 = (0, 4/25, 1/25, 0)FGT Measure = P2 = (g2) = 5/100GT eas e 2 (g ) 5/ 00

Multidimensional DataMatrix of well-being scores for n persons in d domains

Domains

13.1 14 4 1

Personsy 15.2 7 5 012.5 10 1 0

20 11 3 1

Multidimensional DataMatrix of well-being scores for n persons in d domains

Domains

13.1 14 4 1

Personsy 15.2 7 5 012.5 10 1 0

20 11 3 1

z ( 13 12 3 1) Cutoffs

Note - Poverty Cutoffs have been skipped and are v criticalskipped and are v critical

• Schooling: “How many years of schooling have you completed?”– 6 or more (bold is non-poor)– 1-5 years (non-bold is poor)

D i ki W “Wh i h i f d i ki f hi h h ld?”• Drinking Water: “What is the main water source for drinking for this household?”– 9. Piped Water – 8. Well/Pump (electric, hand)– 7. Well Water– 6. Spring Water6. Sp g Wate– 5. Rain Water – 4. River/Creek Water – 3. Pond/Fishpond– 2. Water Collection Basin

1 O h– 1. Other • Sanitation: “Where do the majority of householders go to the toilet?”

– 11. Own toilet with septic tank– 10. Own toilet without septic tank– 9. Shared toilet– 8. Public toilet– 7. Creek/river/ditch (without toilet)– 6. Yard/field (without toilet)– 5. Sewer

4 P d/fi h d– 4. Pond/fishpond – 3. Animal stable – 2. Sea/lake– 1. Other

• Income: (the national or a nutrition-based poverty line is often used)

Deprivation MatrixReplace entries: 1 if deprived, 0 if not deprived

Domains

13.1 14 4 1

Personsy 15.2 7 5 012.5 10 1 0

20 11 3 1

Deprivation MatrixReplace entries: 1 if deprived, 0 if not deprived

Domains

0 0 0 0

Personsg0 0 1 0 11 1 1 1

0 1 0 0

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

Domains

13.1 14 4 1

Personsy 15.2 7 5 012.5 10 1 0

20 11 3 1

z ( 13 12 3 1) Cutoffs

These entries fall below cutoffsThese entries fall below cutoffs

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

Domains

0 0 0 0

Personsg1 0 0.42 0 1

0.04 0.17 0.67 1

0 0.08 0 0

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

Domains

0 0 0 0

Personsg1 0 0.42 0 1

0.04 0.17 0.67 1

0 0.08 0 0

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

Domains

0 0 0 0

Personsg2 0 0.176 0 1

0.002 0.029 0.449 1

0 0.006 0 0

Identification

Domains

0 0 0 0

Personsg0 0 1 0 11 1 1 1

0 1 0 0

Matrix of deprivations

Identification – Counting Deprivations

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

0 1 0 0

1

Identification – Counting DeprivationsQ/ Who is poor?

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

0 1 0 0

1

Identification – Union ApproachQ/ Who is poor?A1/ Poor if deprived in any dimension ci ≥ 1p y i

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

0 1 0 0

1

Identification – Union ApproachQ/ Who is poor?A1/ Poor if deprived in any dimension ci ≥ 1

Domains c

0 0 0 0

0

Personsg0

0 1 0 11 1 1 1

24

0 1 0 0

1

ObservationsUnion 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 = dp i

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

0 1 0 0

1

Identification – Intersection Approach Q/ Who is poor?A2/ Poor if deprived in all dimensions ci = dp i

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

Observations0 1 0 0

1

Demanding requirement (especially if d large)Often identifies a very narrow slice of populationAtkinson 2003 first to apply these terms.

Identification – Dual Cutoff Approach Q/ Who is poor?A/ Fix cutoff k, identify as poor if ci > k, y p i

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

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), y p i ( )

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

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), y p i ( )

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

Note Includes both union (k = 1) and intersection (k = d)

0 1 0 0

1

Includes both union (k = 1) and intersection (k = d)

Identification – The problem empirically

k = H Poverty in India for 10 Union 1 91.2%

2 75.5% 3 54 4%

ydimensions:

91% of population would 3 54.4%4 33.3% 5 16.5%

be targeted using union,

0% using intersection

6 6.3% 7 1.5% 8 0 2%

Need something in the middle.

8 0.2%9 0.0%

Inters. 10 0.0%

(Alkire and Seth 2009)

e s. 0 0.0%

Aggregation Censor data of nonpoor

Domains c

0 0 0 0

0

Personsg0 0 1 0 11 1 1 1

24

0 1 0 0

1

Aggregation Censor data of nonpoor

Domains c(k)

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

0 0 0 0

0

Aggregation Censor data of nonpoor

Domains c(k)

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

1

0 0 0 0

0

Similarly for g1(k), etc

Aggregation – Headcount Ratio

Domains c(k)

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

0 0 0 0

0

Aggregation – Headcount Ratio

Domains c(k)

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

/

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

Personsg0(k) 0 1 0 11 1 1 1

24

/

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)

00000

Persons43

11111011

)(0

kg

/

00000

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

Critique Suppose the number of deprivations rises for person 2

Domains c(k)

00000

Persons43

11111011

)(0

kg

/

00000

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

Critique Suppose the number of deprivations rises for person 2

Domains c(k)

00000

Persons43

11111011

)(0

kg

/

00000

Two poor persons out of four: H = 1/2No change!Violates ‘dimensional monotonicity’Violates dimensional monotonicity

Aggregation Return to the original matrix

Domains c(k)

00000

Persons43

11111011

)(0

kg

00000

Aggregation Return to the original matrix

Domains c(k)

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

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

Personsg0(k) 0 1 0 11 1 1 1

24

2 / 44 / 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

Personsg0(k) 0 1 0 11 1 1 1

24

2 / 44 / 4

d /

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

Personsg0(k) 0 1 0 11 1 1 1

24

2 / 44 / 4

d /

0 0 0 0

0

A = average deprivation share among poor = 3/4

Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA = (g0(k))

Domains c(k) c(k)/d

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

2 / 44 / 4

d /

0 0 0 0

0

A = average deprivation share among poor = 3/4

Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA = (g0(k)) = 6/16 = .375

Domains c(k) c(k)/d

0 0 0 0

0

Personsg0(k) 0 1 0 11 1 1 1

24

2 / 44 / 4

d /

0 0 0 0

0

A = average deprivation share among poor = 3/4

Aggregation – Adjusted Headcount Ratio Adjusted Headcount Ratio = M0 = HA = (g0(k)) = 7/16 = 0.44

Domains c(k) c(k)/d

00000

Persons4/4....4/3....

43

11111011

)(0

kg

d /

00000

A = average deprivation share among poor = 3/4Note: if person 2 has an additional deprivation, M0 rises

Satisfies dimensional monotonicitySatisfies dimensional monotonicity

Adjusted Headcount Ratio Mk0=(ρk,M0) Valid for ordinal data (identification &

aggregation) – robust to monotonicaggregation) – robust to monotonic transformations of data.

Similar to traditional gap P1 = HI ; this = HASimilar to traditional gap P1 HI ; this HAEasy to calculate, easy to interpretC n b br k n d n b dim n i n liCan be broken down by dimension – policy Dominance Results (mentioned later)Ch i i i f d 990Characterization via freedom – P&X 1990

Note: If cardinal variables, can go further

Pattanaik and Xu 1990 and M0

- Freedom = the number of elements in a set.d d f- But does not consider the *value* of elements

- If dimensions are of intrinsic value and are usually valued in practice, then every deprivationcan be interpreted as a shortfall of something that is valued

- the (weighted) sum of deprivations can be ( g ) pinterpreted as the unfreedoms of each person

- Adjusted Headcount can be interpreted as aAdjusted Headcount can be interpreted as a measure of unfreedoms across a population.

Aggregation: Adjusted Poverty Gap Need to augment information of M0 Use normalized gaps

Domains

0 0 0 0

Personsg1 (k) 0 0.42 0 10.04 0.17 0.67 1

d d d

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

Personsg1 (k) 0 0.42 0 10.04 0.17 0.67 1

d d d

0 0 0 0

Average gap across all deprived dimensions of the poor: G

Aggregation: Adjusted Poverty Gap Adjusted Poverty Gap = M1 = M0G = HAG = (g1(k))

Domains

0 0 0 0

Personsg1 (k) 0 0.42 0 10.04 0.17 0.67 1

d d d

0 0 0 0

Average gap across all deprived dimensions of the poor: G

Aggregation: Adjusted Poverty Gap Adjusted Poverty Gap = M1 = M0G = HAG = (g1(k))

Domains

0 0 0 0

Personsg1 (k) 0 0.42 0 10.04 0.17 0.67 1

Ob i l if i d i d di i b

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 FGTConsider the matrix of squared gaps

Domains

0 0 0 0

Personsg2(k) 0 0.422 0 12

0.042 0.172 0.672 12

0 0 0 0

Aggregation: Adjusted FGTAdjusted FGT is M = (g(k))

Domains

0 0 0 0

Personsg2(k) 0 0.422 0 12

0.042 0.172 0.672 12

0 0 0 0

Aggregation: Adjusted FGTAdjusted FGT is M = (g(k))

Domains

0 0 0 0

Personsg2(k) 0 0.422 0 12

0.042 0.172 0.672 12

0 0 0 0

Satisfies transfer axiom

Aggregation: Adjusted FGT FamilyAdjusted FGT is M = (g()) for > 0

Domains

P

0 0 0 00 0 42 0 1

Persons

g (k) 0 0.42 0 10.04 0.17 0.67 1

0 0 0 0

Theorem 1 For any given weighting vector and cutoffs, the methodolog M =(ρ M ) satisfies: decomposabilit

0 0 0 0

methodology Mka =(ρk,M) satisfies: decomposability, replication invariance, symmetry, poverty and deprivation focus, weak and dimensional monotonicity, nontriviality, normalisation, and weak rearrangement for

>0; monotonicity for >0; and weak transfer for >1.

Setting cutoff k: normative or policy• Depends on: purpose of exercise, data, and weights

– “In the final analysis, how reasonable the identification rule isIn 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.” (T i 2002 74)(Tsui 2002 p. 74).

• E.g. a measure of Human Rights; data good = unionT ti di t t ( t 5%) O b d t• 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<d• Poor data, or people do not value all dimensions: k<d• Some particular combination (e.g. the intersection of

income deprived and deprived in any other dimension)income deprived and deprived in any other dimension)

Robustness tests for k• Theorem 2 Where a and a' are the respective attainment

vectors for y and y' in Y (ai=d-ci), we have: y y ( i i),• (i) y H y' a FD a'• (ii) a FD a' y M0 y' a SD a' and the converse(ii) a FD a y M0 y a SD a , and the converse

does not hold.

(i) akin to Foster Shorrocks: first order dominance over attainment vectors ensures that multidimensional headcount is lower (or no higher) for all possible values of k – and the converse is also true.

(ii) shows that M0 is implied by first order dominance, and implies second order, in turn

Properties for Multidimensional Poverty MethodologiesPoverty Methodologies

• axioms are joint restrictions on M = (ρ M)• axioms are joint restrictions on M = (ρ, M)

• Identification is vital for some axioms (poverty focus).

• Previously defined axioms used union approach

• Our axioms are applicable to 0 < k < dpp

Example:• Unidimensional Focus Axiom: requires a

poverty measure to be independent of the data of p y pthe non-poor (incomes at/above z)

• In a multidimensional setting:a non poor person might be deprived in several– a non-poor person might be deprived in several dimensions

– a poor person might not be deprived in all– a poor person might not be deprived in alldimensions.

• How do we adapt the focus axiom?• How do we adapt the focus axiom?

Example:• Poverty Focus: If x is obtained from y by a simple

increment among the non-poor, then M(x;z)=M(y;z).• Deprivation Focus: If x is obtained from y by a simple

increment among the nondeprived, then M(x;z)=M(y;z).

Union: deprivation focus implies poverty focusIntersection: poverty focus implies deprivation

Bourguignon and Chakravarty (2003) assume the deprivation focus axiom (their ‘strong focus axiom’) along with union identification, so their methodology automatically satisfies the poverty focus axiom.

Another Example:• deprived increment (still below cutoff, deprived)• dimensional increment (now non-deprived)dimensional increment (now non-deprived) • Weak Monotonicity: If x is obtained from y by a

i pl i r t th M( )<M( )simple increment, then M(x;z)<M(y;z).• Monotonicity: M satisfies weak monotonicity

d h f f b d f band the following: if x is obtained from y by a deprived increment among the poor then M ) M )M(x;z)<M(y;z).

• Dimensional Monotonicity: If x is obtained from y by a dimensional increment among the poor, then M(x;z)<M(y;z).

Properties• Our methodology satisfies a number of typical properties of

multidimensional poverty measures (suitably extended):• Symmetry Scale invariance• Symmetry, Scale invariance

Normalization Replication invariancePoverty Focus Weak MonotonicityDeprivation Focus Weak Re arrangementDeprivation Focus Weak Re-arrangement

• M0 , M1 and M2 satisfy Dimensional Monotonicity, Decomposability

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

• M satisfies Weak Transfer (for > 1)• M2 satisfies Weak Transfer (for > 1).

Extension: General WeightsModifying 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 ) gg g ( p y g ptaking the mean)

Extension – General WeightsModifying for weights: identification and aggregation

(technically weights need not be the same but(technically weights need not be the same, but conceptually probably should be)

• Use the g0 or g1 matrixUse the g0 or g1 matrix• Choose relative weights for each dimension wd• Important: weights must sum to the number of dimensionsImportant: weights must sum to the number of dimensions • Apply the weights (sum = d) to the matrix• ck now reflects the weighted sum of the dimensionsck now reflects the weighted sum of the dimensions.• Set cutoff k across the weighted sum.• Censor data as before to create g (k) or g (k)• Censor data as before to create g0 (k) or g1 (k)• Measures are still the mean of the matrix.

Example: Weights

Domains

0 0 0 0

Personsg0 0 1 0 11 1 1 1

0 1 0 0

Matrix of deprivationsWeighting vector ω = (.5 2 1 .5)

Example: Weights

Domains

0000

Persons

5.125.5.0200g

0020

Matrix of deprivationsWeighting vector ω = (.5 2 1 .5)

Example: Weights - Identification

Domains02 5

50200000

2.54 Persons2

00205.125.5.0200g

2 0020

Matrix of deprivationsWeighting vector ω = (.5 2 1 .5) k = 2

Identification changed!

Example: Weights - Identification

Domains02 5

50200000

2.54 Persons2

00205.125.5.0200g

2 0020

Matrix of deprivationsWeighting vector ω = (.5 2 1 .5) k = 2.5

Original Identification for k=2.5

Example: Weights – Aggregationk 2 5k = 2.5

Domains0

0000

2.54 Persons

5.125.5.020

)(0 kg

0

M ill HA f i 6 5/16

0000

M0 still HA = mean of matrix = 6.5/16H = 2/4A = weighted = 6.5/8 etc.

Illustration: USA• Data Source: National Health Interview Survey, 2004, United States

Department of Health and Human Services. National Center for HealthS i i ICPSR 4349Statistics - ICPSR 4349.

• Tables Generated By: Suman Seth.• Unit of Analysis: Individual• 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(2) self reported health– (3) health insurance– (4) years of schooling.

Illustration: USA

Illustration: USA

Illustration: USA – all values of kM 0 Dominance

0.25

0.300.35

M0 Hispanic

0 100.150.20

valu

e o

f M

HispanicWhiteBlackOthers

0.000.05

0.10

1 2 3 4

v Others

1 2 3 4

value of k

Indonesia: Deprivation by dimension

Deprivation Percentage of P l tip Population

Expenditure 30.1% Health (BMI) 17.5% Schooling 36.4%Drinking Water 43.9%Sanitation 33.8%

Indonesia: Breadth of DeprivationN b f P t fNumber ofDeprivations

Percentage of Population

One 26%One 26%Two 23%Three 17%Four 8%Five 2%

Identification as k varies

Cutoff k Percentage of Populationp

1 74.9% 2 49.2%3 26.4% 4 9 7%4 9.7%5 1.7%

And interpretation?pEqual Weights

Measure k=1(Union) k=2 k=3

(Intersection)

H 0.577 0.225 0.039

M0 0.280 0.163 0.039 M1 0.123 0.071 0.016

M2 0 088 0 051 0 011M2 0.088 0.051 0.011

General Weights

Measure k = 0.75 (Union) k = 1.5 k = 2.25 k = 3

(Intersection)(Union) (Intersection)

H 0.577 0.346 0.180 0.039

M0 0.285 0.228 0.145 0.039

M1 0.114 0.084 0.058 0.015

M2 0.075 0.051 0.036 0.010

And interpretation?pEqual Weights

Mo = H for Measure k=1

(Union) k=2 k=3(Intersection)

H 0.577 0.225 0.039

intersection

M0 0.280 0.163 0.039 M1 0.123 0.071 0.016

M2 0 088 0 051 0 011M2 0.088 0.051 0.011

General Weights

Measure k = 0.75 (Union) k = 1.5 k = 2.25 k = 3

(Intersection)(Union) (Intersection)

H 0.577 0.346 0.180 0.039

M0 0.285 0.228 0.145 0.039

M1 0.114 0.084 0.058 0.015

M2 0.075 0.051 0.036 0.010

And interpretation?pEqual Weights

M0 = H for If all persons have maximal deprivation,

Measure k=1(Union) k=2 k=3

(Intersection)

H 0.577 0.225 0.039

intersectionp ,

then G=1, so M0 = M1. Good if M0 is different from M

M0 0.280 0.163 0.039 M1 0.123 0.071 0.016

M2 0 088 0 051 0 011

different from M1.

M2 0.088 0.051 0.011

General Weights

Measure k = 0.75 (Union) k = 1.5 k = 2.25 k = 3

(Intersection)(Union) (Intersection)

H 0.577 0.346 0.180 0.039

M0 0.285 0.228 0.145 0.039

M1 0.114 0.084 0.058 0.015

M2 0.075 0.051 0.036 0.010

And interpretation?pEqual Weights

M0 = H for If all persons have maximal deprivation,

Measure k=1(Union) k=2 k=3

(Intersection)

H 0.577 0.225 0.039

intersectionp ,

then G=1, so M0 = M1. Good if M0 is different from M

M0 0.280 0.163 0.039 M1 0.123 0.071 0.016

M2 0 088 0 051 0 011

different from M1.

M2 0.088 0.051 0.011

General Weights

Measure k = 0.75 (Union) k = 1.5 k = 2.25 k = 3

(Intersection)(Union) (Intersection)

H 0.577 0.346 0.180 0.039

M0 0.285 0.228 0.145 0.039 Weights affect

M1 0.114 0.084 0.058 0.015

M2 0.075 0.051 0.036 0.010

affect options for k.

Empirical ApplicationsSub-Saharan Africa (14): Assets, Education, BMI,

Empowermentp

Latin America (6) Income, Child in School, hhh Education, Water, Sanitation, Housing

China Income, Education, BMI, Water, Sanitation, Electricity

India Assets, Education, BMI, Water, Sanitation, Housing, Electricity, C ki F l Li lih d Child ECooking Fuel, Livelihood, Child status, Empowerment.

Pakistan Expenditure, Assets, Education, Water, Sanitation, Electricity, Housing, Land, Empowermenty, g, , p

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.

India: We can vary the dimensions to match existing policy interests. The M0 measure (white) in rural areas (with dimensions that match the

G BPL ) i i iki l diff f iGovernment BPL measure) is in some case strikingly different from income poverty estimates (blue), and from (widely criticised) government

programmes to identify those ‘below the poverty line’ (BPL - purple) (Alkire & Seth 2008)& Seth 2008)

Bhutan: Contributions driving significant rank changes between districts

• When moving from the income H ranking to the M0 ranking (from

i h ) G li b 7 0 300.40

poorest to richest), Gasa climbs 7 places (to higher poverty), while Lhuntse drops 1 (to lower poverty). 0.00

0.100.200.30

M0

• Poverty composition explains this:– In Lhuntse income deprivation accounts

for most part of M0

Gasa LhuntseDistrict

Income Education Room– In Gasa deprivation in education is the

main contributor to M0, followed by electricity, room, and only then, income.

Electricity Water

(K=2, GNHS weights)

We can compare countries over time0

.20

.3

Eq

ua

l We

igth

s

0.4

0.6

Equ

al W

eigt

hs

00

.1

M0

with

k=

2 a

nd

00.

2

H w

ith k

=2

and

E

1992 1995 2000 2003 2006Year

Urban Argentina Urban BrazilUrban Chile Urban El SalvadorUrban Mexico Urban Uruguay

1992 1995 2000 2003 2006Year

Urban Argentina Urban BrazilUrban Chile Urban El SalvadorUrban Mexico Urban Uruguay

0.5

0.6

d E

qua

l Wei

gths

0.3

0.4

A w

ith k

=2 a

n

1992 1995 2000 2003 2006YYear

Urban Argentina Urban BrazilUrban Chile Urban El SalvadorUrban Mexico Urban Uruguay

We can test the robustness of k. In Sub-Saharan Africa weWe can test the robustness of k. In Sub-Saharan Africa, we compare 5 countries using DHS data and find that Burkina is *always* poorer than Guinea, regardless of whether we count as poor persons who are deprived in only

one kind of assets (0.25) or every dimension (assets, health, education, andone kind of assets (0.25) or every dimension (assets, health, education, and empowerment, in this example).

0.8

Figure 3: M0 as cutoff k isvaried in the five countries

0 20.40.6

M0

BeninBurkinaC

00.2

0.5 1

1.5 2

2.5 3

3.5

CameroonGhanaGuinea

k

We can target the poor more precisely:

Mexico For a population of 600,000 urban households, Opportunidadesstudied the intersection between

Three key deprivations (health, education, income)Three key deprivations (health, education, income) Our multidimensional methodThe current Oportunidades current method.

They found that our multidimensional method more closely matched the 3 key deprivations (health, education, income).

The quadratic distance of the multidimensional method was just 39% of Oportunidades’ current method. (Azevado and Robles 2009)

I di d dIndia Similarly, the current BPL targeting method used nationally, mis-identifies 33% of the extreme poor according to the multidimensional method. (Alkire and Seth 2009)

We can track poverty over time (China: income vs M0)

25

15

20

10

15

%

5

01989 1992 1995 1998 2001 2004

Year

H PG SPG M0

Empirical ApplicationsWe can also choose a unit of analysis other than the

individual (Bhutan) or Household (other), and use the ( ) ( ),same methodology with indicators of institutions, and z cutoffs representing quality, standards, or benchmarks.

G N i l H i (Bh )Gross National Happiness (Bhutan)Quality of Education (Mexico, Argentina)Governance (Ibrahim Index)Targeting (India BPL, Mexico Oportunidades)Child Poverty (Afghanistan, Bangladesh)Social Responsibility/Fair Trade (Altereco)Human Rights (Benetech)

B&C, Tsui: Further MD AxiomsTh O Di i l T f P i i l (OTP) i h if hThe One Dimensional Transfer Principle (OTP), requires that if there

are two poor persons, one less poor than the other with respect to the attribute j, and the less-poor of the two gains a given amount of the attribute and the poorer of the two loses the same amount, the poverty i d h ld dindex should not decrease.

The Multidimensional Transfer Principle (MTP) extends OTP to a matrix and argues that if a matrix X is obtained by redistributing the attributes of the poor in matrix Y according to the bistochastic transformationp g fthen X cannot have more poverty than Y. That is because a bistochastic transformation would improve the attribute allocations of all poor individuals (note that MTP imposes proportions on the exchange of attributes). A final criterion in the case of MTP is the )

Non-Decreasing Poverty Under Correlation Switch (NDCIS) postulates. If two persons are poor with respect to food and clothing, one with more food and one with more clothing, and then they swap clothing bundles and the person with more food now has more clothing as wellbundles and the person with more food now has more clothing as well, poverty cannot have decreased. The converse is the Non-Increasing Poverty Under Correlation Switch postulate (NICIS).

Weak poverty focus makes the poverty index independent of the attribute levels of non poor individuals only allows for substitutionlevels of non-poor individuals only – allows for substitution.

B&C 2002:B&C 2002:higher theta lower subst; theta = 1, perfect substitutes

Tsui 2002:

Maasoumi & Lugo 2007:

• Employ Information Theory – info fctns and entropy measures (rather than fuzzy set / axiomatic approach)

• The basic measure of divergence between two distributions gis the difference between their entropies, or the so called relative entropy. Let Si denote the summary or aggregate function for individual i, based on his/her m attributes (xi1,

i2 i )xi2, …, xim).• Then consider a weighted average of the relative entropy

divergences between (S1,S2, …, Sn) and each xj = (x1j, x2j, j)…, xnj)

• wj is the weight attached to the Generalized Entropy divergence from each attribute

Maasoumi & Lugo 2007:

• This is the αth moment FGT poverty index based on the distribution of S = (S1, S2,…,Sn)( , , , )

MD Poverty & Capability Approach

• Focus on Individuals as unit of analysis when possible• Each dimension might be of intrinsic importance, whether g p

or not it is also instrumentally effective• Normative Value Judgments:

– Choice of dimensions– Choice of poverty lines– Choice of weights across dimensions