NEW FRONTIERS IN POVERTY MEASUREMENT James E. Foster George Washington University and OPHI, Oxford
New Frontiers Demand for new tools Country Demand Policy Driven Historical Emphasis Aggregation Step Sen (1976) Emet Frontier Central Role of Identification of the Poor New concepts of poverty New methods of identification
New Frontiers Outline Traditional Ultrapoverty Hybrid Poverty Lines Chronic Poverty Multidimensional Poverty Methods MPI Country Applications WEAI Misunderstandings
Traditional Poverty Measurement Variable – Single dimensional indicator Identification – Poverty line Aggregation – FGT (1984) Emet Example Incomes y = (7,1,4,8) Poverty line z = 5 Deprivation vector g 0 = (0,1,1,0) Headcount ratio P 0 (y;z) = µ (g 0 ) = 2/4 Normalized gap vector g 1 = (0, 4/5, 1/5, 0) Poverty gap = P 1 (y;z) = µ (g 1 ) = 5/20 Squared gap vector g 2 = (0, 16/25, 1/25, 0) FGT Measure = P 2 (y;z) = µ (g 2 ) = 17/100
Measuring Ultrapoverty There are great differences among the poor General idea behind construction of P 1 and P 2 Not P 0 ! Greater depth matters Who are the ultrapoor? How to measure ultrapoverty? Several possibilities Deeply Deprived Persistently Deprived Multiply Deprived Spatially Concentrated Deprivation Work in progress: Conferences at GW and Oxford
Measuring Ultrapoverty Why not simply use P(x;z u ) for a very low z u ? Can give misleading picture Although it identifies ultrapoor Aggregation at lower line can reduce measured poverty Separate identification and aggregation Use z u to identify and z to aggregate Resulting P u (x;z u ) satisfies all axioms (including focus)
Measuring Ultrapoverty Example Incomes y = (7,1,4,8) Poverty line z = 5 and Ultrapoverty line z u = 3 Deprivation vector g u 0 = (0,1,0,0) Headcount ratio P u0 (y;z) = µ (g u 0 ) = 1/4 Normalized gap vector g u 1 = (0, 4/5, 0, 0) Poverty gap = P u1 (y;z) = µ (g u 1 ) = 4/20 Squared gap vector g u 2 = (0, 16/25, 0, 0) FGT Measure = P u2 (y;z) = µ (g u 2 ) = 16/100 Contribution of ultrapoor to overall poverty? Headcount: 1/4 out of 1/2; Poverty gap: 4/20 out of 5/20 FGT: 16/100 out of 17/100
Hybrid Poverty Lines Absolute poverty line z a such as $1.25/day Unchanging over time and space Hence 0 elasticity of poverty line wrt income Useful for comparing countries at similar levels of development for a window of time However make little sense for evaluating poverty across countries or regions at very different levels of development are fundamentally unsustainable over time ie have problems measuring poverty over time and space Ex Is growth good for the poor? Foster and Szekely (2008) IER
Hybrid Poverty Lines Relative poverty line z r such as 50% of mean income Changes with the standard of living Elasticity of poverty line wrt income is 1 However this seems too responsive Wind up measuring inequality, not poverty Empirical evidence: elasticity is between 0 and 1 Citro and Michael (1995) Measuring Poverty Which poverty lines for measuring poverty over space and time?
Hybrid Poverty Lines Hybrid poverty line z = z r ρ z a 1- ρ for 0 < ρ < 1 where z r is a relative poverty line z a is an absolute poverty line ρ is the elasticity of the poverty line with respect to income Foster (1998) AER The elasticity can be estimated for LAC by Foster and Szekely mimeo Or selected arbitrarily and subjected to robustness Madden (2000) RevIncWealth for Ireland Or seen as a normative decision “ To what extent should the poor share in growth? ”
Hybrid Poverty Lines Poverty has two components Absolute – persons below absolute poverty line Relative or Hybrid – persons below hybrid line above abs. With different policy prescriptions As in previous discussions of ultrapoverty Other approaches Atkinson and Bourguignon (2000) use a max function Ravallion and Chen (2011) REStat alter A&B to avoid range where elasticity is 1 Applications Brazil (recent communication with de Barros)
Chronic Poverty Note Previous exercises altered identification The next two alter the variable and identification Chronic Poverty (across many time periods) Multidimensional Poverty (across many dimensions of wellbeing) Closely linked Must have data linked across time or dimensions Must decide how to value different periods ’ income or different dimensions Identification becomes more difficult Foster (2009) and Alkire-Foster (2011 ) JPubE are related
Chronic Poverty First Approach: Components Jalan-Ravallion (2000) JDevS Identify as chronically poor those whose incomes are on average below a poverty line z Aggregate using FGT applied to distribution of average incomes Assumes Equal weights across periods – hence perfect substitutes First aggregate across periods, then see if chronically poor Foster-Santos mimeo Use method of averaging across periods that allows for imperfect substitutability
Chronic Poverty Second Approach: Spells Foster (2009) Poverty Dynamics Identify as chronically poor those whose incomes are frequently below the poverty line (eg 2 out of 4 periods) Aggregate using FGT applied to matrices in which the nonpoor spells have been censored out Assumes No substitution of incomes across periods Indeed incomes are not aggregated Instead check how many periods deprived Aggregate spells across periods Each spell has the same value
Multidimensional Poverty Everyone agrees poverty is multidimensional Real question is what to do about it. How to measure poverty when there are many variables or dimensions of wellbeing?
Multidimensional Poverty Suppose many variables or dimensions Question How to evaluate poverty? Answer 1 If variables can be meaningfully aggregated into some overall resource or achievement variable, traditional methods can be used
Multidimensional Poverty Examples Welfare aggregation Construct each person’s welfare function Set cutoff and apply traditional poverty index However Many assumptions needed Alkire and Foster (2010) mimeo “ Designing the Inequality-Adjusted Human Development Index ” Ordinal variables problematic
Multidimensional Poverty Examples Price aggregation Construct each person ’ s expenditure level Set cutoff and apply traditional poverty index However Many assumptions needed Ordinal and nonmarket variables problematic Link to welfare tenuous (local and unidirectional) Foster, Majumdar, Mitra (1990) “ Inequality and Welfare in Market Economies ” JPubE
Multidimensional Poverty Note Even if an aggregate exists, it may not be the right approach Idea Aggregate resource approach signals what could be The budget constraint Does not indicate what is The actual bundle purchased Ex Consumption poverty is falling rapidly in India Yet 45% of kids malnourished Question Aggregating may hide policy relevant information can’t retrieve
Multidimensional Poverty Suppose many variables or dimensions Question How to evaluate poverty? Answer 2 If variables cannot be meaningfully aggregated into some overall resource or achievement variable, new methods must be used
Multidimensional Poverty Some go to great lengths to avoid this fact: Blinders approach Limit consideration to a subset that can be aggregated, and use traditional methods. Key dimensions ignored Marginal methods Apply traditional methods separately to each variable Ignores joint distribution Where did identification go? Alkire, Foster, Santos (2011) JEI
Alkire-Foster Methodology: Overview Identification – Dual cutoffs Deprivation cutoffs - each deprivation counts Poverty cutoff - in terms of aggregate deprivation values Aggregation – Adjusted FGT Reduces to FGT in single variable case Background papers Alkire and Foster (2011) “ Counting and Multidimensional Poverty Measurement ” Journal of Public Economics Alkire and Foster (2010) “ Understandings and Misunderstanding of Multidimensional Poverty ” Journal of Economic Inequality Alkire, Foster, and Santos (2011) “ Where Did Identification Go? ” Journal of Economic Inequality
Adjusted Headcount Ratio Concept - Poverty as multiple deprivations Mirrors identification used by NGOs – BRAC Depends on joint distribution Ordinal data Dirt floors vs covered floors Qualitative data into quantitative data Transparent Defined by variables, deprivation cutoffs, deprivation values, poverty cutoff Can be replicated and tested for robustness
Adjusted Headcount Ratio Can be implemented at many levels Cross country – MPI in the 2010 HDR Within country – Mexico*, Colombia, Bhutan, etc. Local village level – Participatory methods India, Bhutan, etc Evaluation – Impacts on poverty As a coordination tool – Ministries in Colombia
Adjusted Headcount Ratio Constructing other measures – Gross national happiness index (Bhutan) – Women’s Empowerment in Agriculture Index (USAID/IFPRI/OPHI) – Service delivery performance measure (Allwine and Foster, 2011: Allwine 2011) – Corruption Foster, Horowitz, Mendez, 2012 WBER
Intro to: Multidimensional Methods Matrix of achievements for n persons in d equally important domains (easily generalized) 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
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 $ ' # &
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