CONTENTS
Listoffigures ix
Listoftables x
LIST OF BOXES xii
1 Introduction 1
1.1 Normativemotivation 3
1.2 Empiricalmotivations 8
1.3 Policy motivation 20
1.4 Contentandstructure 22
1.5 Howtousethisbook 23
2 Theframework 24
2.1 Review of unidimensional measurement
and FGT measures 24
2.2 Notation and preliminaries for multidimensional poverty
measurement 30
2.3 scales of measurement: Ordinal and cardinal data 40
2.4 Comparabilityacrosspeopleanddimensions 48
2.5 Properties for multidimensional poverty measures 50
3 Overview of methods for multidimensional poverty assessment 70
3.1 Dashboardofindicatorsandcompositeindices 72
3.2 Venn diagrams 75
3.3 The dominance approach 78
3.4 Statistical approaches 86
3.5 Fuzzysetapproaches 100
3.6 Axiomaticmeasures 109
4 Counting approaches: Definitions, origins, and implementations 123
4.1 Definitionandorigins 123
4.2 Measures of deprivation in Europe and their influence 128
4.3 Measures of unsatisfied basic needs in Latin America and
beyond 133
4.4 Counting approaches in targeting 139
4.5 Final comments on counting approaches 143
5 TheAlkire-Fostercountingmethodology 144
5.1 The AF class of poverty measures: Overview and practicality 145
5.2 Identification of the poor: The dual-cutoff approach 148
5.3 Aggregation: The adjusted headcount ratio 156
5.4 Distinctive characteristics of the adjusted headcount ratio 159
5.5 The set of partial and consistent sub-indices of the adjusted
headcount ratio 161
5.6 A case study: The global multidimensional poverty index (MPI) 168
5.7 AFclassmeasuresusedwithcardinalvariables 173
5.8 Some implementations of the AF methodology 177
6 Normativechoicesinmeasurementdesign 186
6.1 The adjusted headcount ratio: A measure of capability poverty? 188
6.2 Normative choices 192
6.3 Elements of measurement design 196
6.4 Concludingreflections 214
7 Data and analysis 216
7.1 Data for multidimensional poverty measurement 216
7.2 Issues in indicator design 219
7.3 Relationships among indicators 228
8 Robustness analysis and statistical inference 233
8.1 Robustness analysis 234
8.2 Statistical inference 240
8.3 Robustness analysis with statistical inference 246
9 Distribution and dynamics 256
9.1 Inequalityamongthepoor 256
9.2 Descriptiveanalysisofchangesovertime 264
9.3 Changes over time by dynamic subgroups 273
9.4 Chronic multidimensional poverty 282
10 Some regression models for AF measures 295
10.1 Micro and macro regressions 296
10.2 Generalized linear models 298
10.3 Micro regression models with AF measures 304
10.4 Macro regression models for M0 and H 308
REFERENCES 311
INDEX 343
1.1 Scatter plots comparing cross-country reductions in income poverty to progress
in other Millennium Development Goal 11
1.2 Progress in different MDGs across countries 13
1.3 The importance of understanding joint distribution of deprivations in Brazil 18
1.4 Availability of developing country surveys: DHS, MICS, LSMS, and CWIQ 20
3.1 Venn diagram of joint distribution of deprivations in two dimensions 76
3.2 Venn diagram of joint distribution of deprivations in three dimensions 77
3.3 Venn diagrams of deprivations for four and five dimensions 78
3.4 First-order stochastic dominance using cumulative distribution functions 80
3.5 Identification using poverty frontiers 82
3.6 Multivariate statistical methods 87
3.7 Aggregation sub-steps within multivariate statistical methods 88
8.1 ComplementaryCDFsandpovertydominance 237
8.2 The Adjusted Headcount Ratio dominance curves 237
9.1 Distribution of intensities among the poor in Madagascar and Rwanda 259
9.2 Theoretical decompositions 281
10.1 Logisticregressioncurve—WestJava 307
1.1 Gross-Iabulationofdeprivationsintwoindicators 14
1.2 Average deprivation in pairwise indicators across seventy-five developing
countries 15
1.3 Comparison of India's performance with Bangladesh and Nepal 17
2.1 Joint distribution of deprivation in two dimensions 35
2.2 Comparison of two joint distributions of deprivations in four dimensions 36
2.3 Stevens' classification of scales of measurement 42
3.1 Joint distribution of deprivations in two dimensions 76
3.2 Summary of the multidimensional poverty measurement methodologies 122
4.1 TheUBNpoorandlheincomepoor 136
5.1 Achievementmatricesofsubgroupsinthehypotheticalsociety 164
5.2 (Gensoredjdeprivationmatricesofthesubgroups 164
5.3 Deprivationmatrixofthehypotheticalsociety 167
5.4 Gensoreddeprivationmatrixofthehypotheticalsociety 168
5.5 Dimensions, indicators, deprivation cutoffs, and weights of the global MPI 169
5.6 Thedeprivationmatrixandtheidentificationofthepoor 170
5.7 SameMPIsbutdifferentcompositionsintwosubnationalregions 173
5.8 Summary of research studies that have implemented the AF methodology 178
6.1 Dimensions of poverty 204
7.1 A contingency table for deprivations in two indicators 230
7.2 Contingency tables for Mozambique and Bangladesh 231
7.3 Correlation matrix and overlap measure for Mozambique 232
8.1 Correlation among country ranks for different weights 240
8.2 Confidence intervals for M0, H, and A 243
8.3 ComparisonofIndianstatesusingstandarderrors 246
9.1 Countries with similar levels of MPI but different levels of inequality among the
poor and different levels of disparity across regional MPIs 264
9.2 Reduction in MPI, H, and A in Nepal, Peru, Rwanda, and Senegal 267
9.3 Changes in the number of poor accounting for population growth 268
9.4 Uncensored and censored headcount ratios of the global MPI, Nepal
2006-11 270
9.5 Decomposition of M0, H, and A across castes in India 272
List of Tables xi
9.6 Decomposing the change in M0 by dynamic subgroups 279
9.7 Cardinal illustration with relevant values of k and τ 292
10.1 GeneralizedlinearregressionmodelswithAFmeasures 302
10.2 Logistic regression model of multidimensional poverty in West Java 306
1.1 Poverty, welfare, and policy 4
1.2 Capabilities, resources, and utility 6
2.1 A numerical example of the FGT measures 29
2.2 Example of generalized means 38
2.3 Children’s nutritional z-scores 46
3.1 Different identification functions based on fuzzy logic operators 106
3.2 Informationtheorymeasures 119
5.1 Different identification strategies: Union, intersection, and intermediate cutoff 153
5.2 Obtaining the censored deprivation score vector from an achievement matrix 155
5.3 An alternative presentation of the adjusted headcount ratio using non-normalized
weights 158
5.4 Analternativenotationfortheidentificationfunction 159
5.5 Same M0 but different composition of incidence and intensity 161
5.6 Analternativepresentationof Mα measures using non-normalized weights 176
5.7 AlternativenotationsfortheAFmethod 182
6.1 Unfreedoms and M0 191
7.1 The mile ahead in data collection 218
8.1 Bootstrap standard errors of the adjusted headcount ratio and its components 254
9.1 Decomposing the change in M0 across dynamic subgroups: An illustration 275
9.2 Computing the incidence and duration of chronic poverty 288
9.3 Single- and cross-period indices of chronic poverty 289
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