OPHI Oxford Poverty & Human Development Initiative Department of International Development Queen Elizabeth House, University of Oxford www.ophi.org.uk IFPRI 2007 Beijing Presentation: Counting and Multidimensional Poverty Sabina Alkire & James Foster OPHI Working Paper #7 (forthcoming)

Towards Ending Extreme Poverty & Hunger GHI, and measures of the subjacent, medial and ultra income poor, rely on aggregate data. They extend a current headcount to investigate the depth of poverty – a welcome conceptual step (if the data support it – which needs critical consideration). This does not allow us to identify the most acutely poor across dimensions: Who are deprived in all the dimensions at the same time? This paper proposes an identification strategy and measure that is sensitive to the breadth of poverty across income, hunger, and potentially other dimensions (and also satisfies desirable axioms).

Issues for Multidimensional Poverty Meas. Poverty of what? You have chosen Dimensions You have chosen Variables Some Variables are Ordinal You have set Poverty Lines for each dimension You have set weights for each dimension You have decided how often to measure poverty. Identification : Who is poor? Comparison : How do we make an index?

Breadth of poverty across Dimensions (and indicators for each D) Health Educat’n Income Nutrition Empower-ment Individual 1 or Household 1 Not Poor Poor Individual 2 or Household 2 Individual 3 or Household 3 Individual 4 or Household 4

Multidimensional Poverty Strategy Two cutoffs 1) Poverty line for each domain Bourguignon and Chakravarty, JEI, 2003 “a multidimensional approach to poverty defines poverty as a shortfall from a threshold on each dimension of an individual’s well being.” 2) Cutoff in terms of range of dimensions (number/sum) Ex: UNICEF, Child Poverty Report, 2003 -Two or more deprivations Ex: Mack and Lansley, Poor Britain, 1985 -Three or more out of 26 Focus on Pa family–is general (any additive index can be used) OPTIONS Weights Cardinal or ordinal variable - ordinal can be used with P0 and has good properties

Data Matrix of well-being scores in D domains for N persons (e.g. food energy, income/consumption, presence of a malnourished child in hh, education, and so on) Persons Domains

Data Matrix of well-being scores in several domains for N persons Persons z Domains Domain specific cutoffs These entries achieve target cutoffs These entries do not

Normalized Gaps Persons z Domains Replace these entries with 0 Replace these with normalized gap (zj - yji)/zj

Deprivation Counts Persons Domains Replace these entries with 0

Identification Q/Who is poor? Persons Domains Counts c = (0, 2, 4, 1) = number of deprivations

Identification: Union Q/Who is poor? A/ Poor if deprived in at least one dimension (ci > 1) Persons Domains Counts c = (0, 2, 4, 1) = number of deprivations

Identification: Union Q/Who is poor? A/ Poor if deprived in at least one dimension (ci > 1) Persons Domains Counts c = (0, 2, 4, 1) = number of deprivations Difficulties Single deprivation may be due to something other than poverty (UNICEF) Union approach often predicts very high numbers - political constraints.

Identification Q/Who is poor? Persons Domains Counts c = (0, 2, 4, 1)

Identification: Intersection Q/Who is poor? A/ Poor if deprived in all dimensions (ci > 4) Persons Domains Counts c = (0, 2, 4, 1)

Identification: Intersection Q/Who is poor? A/ Poor if deprived in all dimensions (ci > 4) Persons Domains Counts c = (0, 2, 4, 1) Difficulty: Demanding requirement (especially if J large) Often identifies a very narrow slice of population

Identification Q/Who is poor? Persons Domains Counts c = (0, 2, 4, 1)

Counting Based Identification Q/Who is poor? A/ Fix cutoff k, identify as poor if ci > k Persons Domains Counts c = (0, 2, 4, 1)

Counting Based Identification Q/Who is poor? A/ Fix cutoff k, identify as poor if ci > k Persons Domains Counts c = (0, 2, 4, 1) Example: 2 out of 4

Counting Based Identification Q/Who is poor? A/ Fix cutoff k, identify as poor if ci > k Persons Domains Counts c = (0, 2, 4, 1) Example: 2 out of 4 Note: Especially useful when number of dimensions is large Union becomes too large, intersection too small

Counting Based Identification Implementation method: Censor nonpoor data Persons Domains Counts c = (0, 2, 4, 1)

Counting Based Identification Implementation method: Censor nonpoor data Persons Domains Counts c(k) = (0, 2, 4, 0) Similarly for y(k), g1(k), etc

Counting Based Identification Implementation method: Censor nonpoor data Persons Domains Counts c(k) = (0, 2, 4, 0) Similarly for y(k), g1(k), etc Note: Includes both union and intersection Next: Turn to aggregation

Adjusted Headcount Ratio Return to original matrix Persons Domains Counts c(k) = (0, 2, 4, 0)

Adjusted Headcount Ratio Need to augment information of H Persons Domains Counts c(k) = (0, 2, 4, 0)

Adjusted Headcount Ratio Need to augment information of H Persons Domains Counts c(k) = (0, 2, 4, 0) shares of deprivations (0, 1/2, 1, 0)

Adjusted Headcount Ratio Adjusted headcount ratio = D0 = HA = m(g0(k)) Persons Domains Counts c(k) = (0, 2, 4, 0) shares of deprivations (0, 1/2, 1, 0) Average deprivation share among poor A = 3/4

Adjusted Headcount Ratio Adjusted headcount ratio = D0 = HA = m(g0(k)) = 6/16 = .375 Persons Domains Counts c(k) = (0, 2, 4, 0) shares of deprivations (0, 1/2, 1, 0) Average deprivation share among poor A = 3/4

Adjusted Headcount Ratio Adjusted headcount ratio = D0 = HA = m(g0(k)) = 6/16 = .375 Obviously if person 2 has an additional deprivation, D0 rises Persons Domains Counts c(k) = (0, 2, 4, 0) shares of deprivations (0, 1/2, 1, 0) Average deprivation share among poor A = 3/4

Adjusted Headcount Ratio Adjusted headcount ratio = D0 = HA = m(g0(t)) = 6/16 = .375 Obviously if person 2 has an additional deprivation, D0 rises Dim. Mon. Persons Domains Counts c(k) = (0, 2, 4, 0) shares of deprivations (0, 1/2, 1, 0) Average deprivation share among poor A = 3/4

Adjusted Headcount Ratio The next measure relates to work on Amartya Sen’s Development as freedom approach and can be interpreted as a Measure of Unfreedom. (Pattanaik and Xu 1990)

Adjusted Headcount Ratio Adjusted headcount = D0 = HA = m(g0(k)) Persons Domains Assume cardinal variables Q/ What happens when a poor person who is deprived in dimension j becomes even more deprived? (ultra poor) A/ Nothing. D0 is unchanged. Violates monotonicity.

Adjusted FGT Consider the matrix of alpha powers of normalized shortfalls Persons Domains

Adjusted FGT Consider the matrix of alpha powers of normalized shortfalls Persons Domains

Adjusted FGT Adjusted FGT is Da = m(ga(t)) for a > 0 Persons Domains

Adjusted Foster Greer Thorbecke Adjusted FGT is Da = m(ga(t)) for a > 0 Persons Domains Satisfies numerous properties including decomposability, and dimension monotonicity, monotonicity (for  > 0), transfer (for  > 1).

The Measure has good properties The adjusted headcount, adjusted poverty gap, and adjusted FGT measures each satisfy a number of typical properties of multidimensional poverty measures. In particular, all satisfy: Symmetry, Scale invariance Normalization Replication invariance Focus (MD) Weak Monotonicity Dimensional Monotonicity Adjusted FGT satisfy Decomposability and Strong Monotonicity (for  > 0), and Transfer (for  > 1),.

Extensions You can use this counting method of identifying the poor with any other indices. Derive censored matrix y*(k) Replace all nonpoor entries with poverty cutoffs Apply any multidimensional measure – P(y*(k);z) e.g. Tsui 2002, Bourguignon & Chakravarty 2003, Maasoumi Lugo 07,

Extension – weighting dimensions. You can change the weights on the dimensions – making some more important than others. Weighted identification Weight on income: 50% Weight on food access, malnourished child in house: 25% Cutoff k = 0.50 (weighted sum) Poor if income poor, or suffer two or more deprivations Cutoff k = 0.60 Poor if income poor and suffer one or more other deprivations Nolan, Brian and Christopher T. Whelan, Resources, Deprivation and Poverty, 1996 Weighted aggregation

Summary Measuring poverty at the level of the person or hh can identify the acuteness of poverty. This is a simple, intuitive, and easy-to compute measure of multidimensional poverty. NGOs already use a form of it. It can be disaggregated by region, gender… It can be used for targeting purposes, for monitoring, and for national reports.