New Dimensions in Poverty Measurement

James E. Foster The George Washington University and OPHI

Broadening Opportunities for DevelopmentAnnual Bank Conference in Development Economics

OECD Conference Centre, Paris, France 31 May 2011

Poverty Measurement

Framework – Sen 1976 identification and aggregation

Goals – Who is poor? targeting– How much poverty? in any population

Poverty Measurement

SupposeSingle variable – calories, income or aggregate expend.

Unidimensional methodsIdentification – poverty lineAggregation – Foster-Greer-Thorbecke 1984, 2010

NoteDecomposabilityRobustness

Poverty Measurement

SupposeMany variables How to measure poverty?

Answer If variables can be meaningfully aggregated into some overall resource or achievement variable can use unidimensional methods

Poverty Measurement

ExamplesWelfare aggregation

Construct each person’s welfare functionSet cutoff and apply unidimensional poverty index

Myriad assumptions needed Alkire and Foster (2010) “Designing the Inequality-

Adjusted Human Development Index”Ordinal variables problematicSuggests dominance

Poverty Measurement

ExamplesPrice aggregation

Construct each person’s expenditure levelSet cutoff and apply unidimensional poverty index

Myriad assumptions needed Ordinal and nonmarket variables problematicLink to welfare tenuous (local and unidirectional)

Foster, Majumdar, Mitra (1990) “Inequality and Welfare in Market Economies” JPubE

Poverty Measurement

SupposeMany variables that cannot be meaningfully aggregated into some overall resource or achievement variable. How to measure poverty?

Answers? Blinders Limit consideration to a subset that can be aggregated, and use unidimensional methods.

Key dimensions ignoredMarginal methods Apply unidimensional methods separately to one or more variables in turn.

Inadequate identification. Ignores joint distribution.

Our Proposal - Overview

Identification – Dual cutoffsDeprivation cutoffs - each deprivation countsPoverty cutoff - in terms of aggregate deprivation values

Aggregation – Adjusted FGTReduces to FGT in single variable case

Background papersAlkire and Foster “Counting and Multidimensional Poverty

Measurement” forthcoming Journal of Public EconomicsAlkire and Foster “Understandings and Misunderstanding of

Multidimensional Poverty” forthcoming Journal of Economic Inequality

Adjusted Headcount Ratio - Overview

Concept - Poverty as multiple deprivationMirrors identification used by NGOs – BRACDepends on joint distribution

Ordinal data Transparent

Adjusted Headcount Ratio - Overview

Can be implemented at any levelCross country – MPI in the 2010 HDRWithin country – Mexico*, Colombia, Bhutan, etc. Local village level – Participatory methods India, Bhutan,

etcEvaluation – Impacts on poverty

Can be used with endogenous cutoffsCoherent use across space and time

Outline

UnidimensionalMultidimensionalUnderstandings and MisunderstandingsExtensions

Review: Unidimensional Methods

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

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

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

Squared gap vector g2 = (0, 4/25, 1/25, 0)FGT Measure = P2 = µ(g2) = 5/100

Decomposable across population groups

Multidimensional Methods

Matrix of achievements for n persons in d domains

Domains

Persons

z ( 13 12 3 1) Cutoffs

These entries fall below cutoffs

y =

13.1 14 4 115.2 7 5 012.5 10 1 020 11 3 1

Deprivation Matrix

Replace entries: 1 if deprived, 0 if not deprived

Domains

Persons

g0 =

0 0 0 00 1 0 11 1 1 10 1 0 0

Identification – Dual Cutoff Approach

Q/ Who is poor?A/ Fix cutoff k, identify as poor if ci > k (Ex: k = 2)

Domains c

Persons

Note Includes both union and intersectionEspecially useful when number of dimensions is large

Union becomes too large, intersection too smallNext step - aggregate into an overall measure of poverty

g0 =

0 0 0 00 1 0 11 1 1 10 1 0 0

0241

Aggregation

Censor data of nonpoor

Domains c(k)

Persons

g0(k) =

0 0 0 00 1 0 11 1 1 10 0 0 0

0240

Aggregation – Headcount Ratio

Domains c(k)

Persons

Two poor persons out of four: H = ½ ‘incidence’Critiques

g0(k) =

0 0 0 00 1 0 11 1 1 10 0 0 0

0240

Aggregation – Adjusted Headcount Ratio

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

Domains c(k) c(k)/d

Persons

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

g0(k) =

0 0 0 00 1 0 11 1 1 10 0 0 0

0240

2 / 44 / 4

Aggregation – Adjusted Headcount Ratio

ObservationsUses ordinal dataSimilar to traditional gap P1 = HI

HI = per capita poverty gap= headcount H times average income gap I among poor

HA = per capita deprivation = headcount H times average intensity A among poor

Decomposable across dimensions after identificationM0 = ∑j Hj/d - Hj are “censored” headcount ratios

If data are cardinal can extend to adjusted poverty gap and adjusted FGT

Aggregation: Adjusted FGT Family

Adjusted FGT is Mα = µ(gα(τ)) for α > 0

Domains

Persons

gα (k) =

0 0 0 00 0.42α 0 1α

0.04α 0.17α 0.67α 1α

0 0 0 0

Understandings and Misunderstandings

Concept of Poverty: Multiple deprivationsDepends on joint distribution

M0 = ¼ M0 = 0

Matrix 1 Matrix 2

=

4000

1111000000000000

0 g

=

1111

1000010000100001

0 g

Understandings and Misunderstandings

Data Requirements: Single survey sourcingDepends on joint distribution, need information on joint dist.Q: What if “best available data” are in different datasets?A: Not best available dataEx: Elasticity exercise with best available price data from one

source and best available quantity data from anotherEx: Unlinked expenditure surveys

Understandings and Misunderstandings

Data Requirements: Single survey sourcing

“surveys should be designed to assess the links between various quality of life domains for each person, and this information should be used when designing policies in various fields.”

(Stiglitz Sen Fitoussi 2009)

Understandings and Misunderstandings

Adjusted Headcount Ratio vs. MPI vs. HDI

Adjusted headcount ratio M0 – general methodologyMPI – a specific implementation for cross-country comparisonsHDI – not a poverty measure

Understandings and Misunderstandings

Underpinnings: Poverty and Welfare

Firmly rooted in axiomatic poverty analysisEvaluate methods via axioms satisfied and violatedMPI – a specific implementation

Adjusted headcount ratiocrude (like unidimensional headcount ratio) not directly linked to welfare (ditto) conveys tangible informationtransparent parameters

Understandings and Misunderstandings

Calibration: Who chooses the parameters?

Gonzalo Hernandez will comment on thisContext dependent

Extensions

Cutoffs over space and timeAbove used absolute cutoffs – fixed and givenYet can envision cutoffs (or variables) changing as aggregate

achievements are altered Some variables less elastic more absolute, more an endSome more elastic more relative, more a means

Options include Ravallion and Chen (2009), Atkinson and Bourguignon (2001) or Foster (1998)

Note: Loss of full decomposability of methodologyDecomposable after identification

Need further study of identification especially in the multidimensional environment