INDEX

Aaberge, R. 116, 258n6

Abe, A. 133

absolute rate of change 264-5, 266, 269 achievement matrix 25-6, 35, 49

AdjustedHeadcountRatio 161-2, 163-4, 167

AF methodology 150, 155-6, 173 dominance properties 52, 58, 59, 60, 61, 62-3, 64, 65-6, 82

invariance properties 52-3, 54, 55, 56, 57 multidimensional poverty measurement 30, 31, 32, 33-4

statistical approaches 88, 89, 92 subgroup properties 67, 68 achievements 25, 30, 32-3, 35, 38, 43, 108, 119, 145 multidimensional poverty measurement 30, 32-3 see also achievement matrix

adaptive preferences 7

Addison, T 196n20, 283n22 additive decomposability 117, 260 Adjusted Headcount Ratio (M₀) 21, 22, 116, 118, 127n13, 139, 144, 145-8, 156-68, 171-3, 184, 188-92, 199

censored headcount ratio 34n22

chronic multidimensional poverty 287, 289, 290-2, 294

comparability 48

inequality among the poor 256-9, 263-4 regression models 295, 296, 297-8, 302, 308-10 robustness analysis 234, 236-7, 238, 247 standard errors 248, 249, 250, 251, 254-5 statistical inference 242, 243-5, 247 targeting 142, 143 intertemporal changes descriptive analysis 264-73 by dynamic subgroups 273-6, 279, 280-1 weights 210, 211

AdjustedPovertyGap (M₁) 116, 145-8, 160, 174-5, 176-7

Adjusted Squared Poverty Gap/Adjusted FGT Measure (M₂) 116, 145-8, 160, 175, 176, 177

Adler, M.

D. 186n1,210n30 administrative records/data 217-18 admissible mathematical transformations 41-3, 44, 45, 56-7

AF methodology see Alkire and Foster (AF) indices/measures; Alkire and Foster (AF) methodology

agency 8 aggregate achievement approach 33, 110-11, 118-20, 154

dominance approach 81, 85 statistical approaches 89, 99 aggregation 37, 49, 74

AF methodology 115, 144-5, 146-7, 148, 149, 154, 155, 156-6, 173

axiomatic approach 110, 115, 120 chronic multidimensional poverty 284, 286-7, 292 fuzzy set approaches 105-8, 109 multidimensional poverty measurement 32-4,

51, 56

statistical approaches 87-91 unidimensional poverty measurement

27-9

Ahmed, A.

I. M. U. 133 ALEP definition 62n59

Alkire, S. 2, 2n1, 2n2, 4n5, 6n9, 8, 14n23, 18, 19,

19n29, 24, 26n4, 27n7, 28, 29, 29n14, 31, 36, 36n27, 37, 38n28, 51, 51n42, 56, 58, 58n53, 63n60, 66n60, 68n63, 72, 74n3, 74n4, 75, 77, 90, 109, 110, 113, 115, 116, 116n53, 118n55, 121, 122, 124, 125n5, 126, 132, 138, 139, 139n41, 140, 140n42, 142-3, 144, 147, 152, 158, 161n11, 165, 168, 168n15, 169, 172, 173, 176, 177, 177n17, 178, 183, 188n4, 190, 190n9, 195, 195n16, 196n19, 200, 202, 203, 203n24, 206, 207, 208n28, 209, 209n29, 210, 213, 215n35, 225, 226-8, 226n10, 228n12, 230n13, 236, 237, 238n7, 239, 240, 241, 243, 246, 246n16, 247, 257-8, 259, 259n7, 260, 263, 264, 264n10, 266, 267, 268, 270, 271, 272, 279, 283n21,284, 287, 289

Alkire and Foster (AF) indices/measures 115-16, 118, 121, 144, 210n30, 221,256-7

regression models 295-310

see also Adjusted Headcount Ratio; Adjusted Poverty Gap; Adjusted Squared Poverty Gap/FGT Measure

Alkire and Foster (AF) methodology 2, 22, 70, 109, 115, 124, 132, 144-85, 196-7

AF class 28, 34n22 child poverty 139 chronic multidimensional poverty 284, 284, 285 deprivation cutoffs 31, 208n27

FGT measures 29 intermediate criterion 33 policy 20-1 targeting 142 intertemporal changes by dynamic subgroups 281 Altimir, O. 134, 136 Amarante, V. 101 Amemiya, T. 299 Anaka, M. 84

Anand, S. 6, 6n9, 74, 161, 190, 195, 196n17,

207n26

Anderson, G. 85n15, 215n35, 247n17

Andrews, F. M. 47, 206n25 Angulo Salazar, R. C. 2n3, 143, 208n28 Anh, V. T. 90

annualized absolute rate of change 266, 269 annualized relative rate of change 266

Apablaza, M. 132, 139, 178, 280, 281, 283n21, 284, 287, 289, 305, 306

applicable population 222-6

Araar, A. 242, 244n15, 281 Aristotle 5

Arminger, G. 98

Arndt, C. 2n2, 178, 188n5

Asselin, L. M. 87n17, 88, 90 association 60, 73, 228-31, 238-9 association-decreasing deprivation rearrangement among the poor 64-5, 66 association-decreasing rearrangement among the poor

61-6, 68, 114

Atkinson, A.

B. 3, 4n4, 6n9, 27n7, 33n21, 34, 38, 60, 62,

62n59, 79, 80, 81, 83, 84, 86, 120, 123, 126, 127,

150, 152n5, 206, 207, 209, 257, 258 axiomatic approach 22, 26n6, 51, 70, 71-2, 85, 196 see also Alkire and Foster (AF) indices/measures;

Alkire and Foster (AF) methodology; axiomatic measures; axioms axiomatic measures 109-22

see also axiomatic approach; axioms axioms 51

counting approaches 138, 143

FGT measures 29

multiple correspondence analysis 88 statistical approaches 99, 100 see also Alkire and Foster (AF) indices/measures;

Alkire and Foster (AF) methodology; axiomatic approach; axiomatic measures; properties Azevedo, V. 2n2, 142, 178

Baca, J. 179

Baker, R. M. 297n6

Baliamoune-Lutz, M. 101

Balisacan, A. M. 2n3

Ballon, P. 89, 89n21, 90, 91, 228n12, 230n13, 305, 306 Baluch, B. 283n22

Bandura, R. 74n3

Banerjee, A. V. 196n17

Barrett, G. 247n17 Barrientos, A. 3 Barro, R. J. 298

Bartholomew, D. J. 86, 86n16, 92, 94, 98 basic needs 3, 4, 10, 17, 70, 72, 148n2 counting approaches 124-6, 127, 133-8, 141, 142, 143

Basilevsky, A. T. 91n22

Basu, K. 6n9, 49n38, 225

Batana, Y. M. 2n2, 83n14, 84, 90, 179, 237

Battiston, D. 2n2, 18, 179 Bauman, K. 133n31 Bavetta, S. 189n8 Beccaria, L. 136 Bedi, T. 135n34 Beja, E. L., Jr 2n2, 179 Belhadj, B. 101, 104n43 Bellier, L. 95 Bennett, C. J. 215n35, 244n14 Benzecri, J. P. 95 Berenger, V. 2n2, 101, 177 Berger, R. L. 250

Betti, G. 2n2, 101, 102, 104, 104n43, 106, 107n47, 177 between-group inequality 261, 262n9, 263 Bhutan 2, 18, 177

Bibby, J. M. 86n16, 93n25, 100 Biewen, M. 253

Biggeri, M. 2n2, 139, 181 bistochastic matrix 40, 59, 60 Blanchet, D. 74n3, 186n1 Blasius, J. 95, 96n32 Boarini, R. 132n29

Boland, P. J. 61n57, 61n58, 238n7 Bollen, K. A. 90, 97, 98

Boltvinik, J. 136-7, 137n36, 137n37, 137n38, 138n39, 142, 143

Bolzani, E. 77

Booth, C. 26n5, 70n1, 125 bootstrap

algorithm 253 method 253-5 replications 255 samples 255 standard errors 253-5 of adjusted headcount ratio 254 of partial indices 254

Booysen, F.

Bossert, W. 47n36, 51n42, 53n47, 58n53, 68, 117, 121, 258n6, 283n21, 283n22

Bound, J. 297n6 Bourdieu, P. 95 Bourdillon, M. 139 Bourguignon, F. 10, 13, 17, 33n21, 34, 51n42, 53n47, 54n48, 55n50, 58n53, 60, 62, 62n58, 62n59, 63n60, 75, 79, 81, 83, 84, 114, 114n52, 121, 148n2, 149, 208, 211, 257, 257n5, 257n6, 258 Bourguignon and Chakravarty indices 114, 121 Bowley, A. L. 3, 26n5, 70n1, 125 Boyden, J. 139 Bradshaw, J. 10, 10n16 Braybrooke, D. 124n4 breadth of poverty see intensity of poverty Bresson, F. 84

Brighouse, H. 6n11, 186n1 Brown, J. D. 47 Browne, M. W. 98 Browning, M. 223n7 Buen Vivir 3

Burchardt, T. 6, 7n14, 203n24 Burnett-Hurst, A. R. 3, 26n5, 70n1, 125

Callan, T. 130, 130n23, 130n25, 130n26 Callander, E. J. 2n2

Calvo, C. 51n42, 283n21, 283n22 Cannings, T. I. 2n2, 181 Canto, O. 283n21 capabilities 3, 5, 6-7, 199, 202-3

AdjustedHeadcountRatio 161, 188, 189 see also capability approach; capability poverty capability approach 5-8, 70, 101, 127, 187

AF methodology 148, 160

see also capabilities; capability poverty capability poverty 6, 8, 188-92

see also capabilities; capability approach Cardenas, J. C. 2n2, 177 cardinalvariables/data 40-8, 122, 199

AF methodology 148n2, 173-7 axiomatic approach 111, 112-16, 118, 120, 121 chronic multidimensional poverty 285, 287 comparability 48-9, 50 counting approaches 137, 138, 139, 142, 143 dominance approach 85 Fuzzysetapproaches 103-4, 109 inequality among the poor 257 principal component analysis 87 unidimensional poverty measurement 25, 26n3 weights 211

Carpenter, J. 2n2, 177

Casella, G. 250

Castro, J. F. 2n2, 179 categorical scales 41, 42, 43, 44, 98, 199 CBS 140, 141 censored achievement approach 33, 110, 149 counting approaches 138n39, 139, 142 censored achievement matrix 31-2, 55, 64, 111, 114-15 censored deprivation count vector 286 censored deprivation matrix 152, 154, 155, 157, 158, 160

Adjusted Headcount Ratio 162, 164, 168 censored deprivation score vector 155-6, 157, 262-3 censored dimensional duration 290-1 censored distribution 27 censored headcount ratio 34n22, 148, 184

AdjustedHeadcountRatio 165-6, 167-8, 172 chronic multidimensional poverty 289-90, 291, 294 Multidimensional Poverty Index 172-3 statistical inFerence 242 intertemporal changes

descriptive analysis 265, 266, 269-71

by dynamic subgroups 273 censuses 133-5, 139, 141, 143, 217 Ceriani, L.

283n22

Cerioli, A. 101, 103, 104, 105, 106, 107, 108 CGD 124n2

Chakravarty, S. R. 33n21, 47n36, 51n42, 53n47, 54, 54n48, 55n50, 57n52, 58n53, 62, 62n58, 62n59,

63n60, 68, 75, 79, 81, 83, 101, 104, 108, 112, 113, 113n51, 114, 114n52, 115, 117, 121, 148n2, 149, 149n4, 208, 211, 256n1, 257n5, 257n6, 258, 258n6, 259, 283n21, 283n22, 284, 287, 289 Chang, R. 186n1 Chantreuil, F. 280n19 Cheli, B. 101, 103, 104, 105, 106, 108

Chen, S. 196n17

Cherchye, L. 234n2

Chiappero-Martinetti, E. 101, 101n35, 102, 102n36, 102n37, 103, 103n41, 104n43, 106, 106n46, 188n5

child poverty 129, 138-9, 143, 190, 221-2

Christiaensen, L. 90

chronic deprivation 284

chronic multidimensional poverty 282-94

Chung, K. H. 255

churning groups (poverty transitions) 293

Clark, C. R. 256n1

Clark, D. A. 7n14, 101, 188n5, 213n32

cluster analysis 71, 86, 87

Coady, D. 135

Cohen, A. 142

Cohen, G. A. 186n1

Cohen, L. 47

Colombia 2

Colombo, E. 74n3

complementarity/complements 62n59, 218, 224 association-decreasing rearrangement 62, 63, 64-5 axiomatic approach 114 dominance approach 83, 85

complementary cumulative distribution function (CCDF) 236-7, 247

composite indices 37, 70, 71, 73-5, 122, 210, 211, 234n2

Conconi, A. 2n1, 169, 177n17, 209n29 concordant/discordant pairs 239 conditional expectation 299, 300, 302, 304 CONEVAL 2n3, 3, 208n28, 214n34 confidence intervals 242-3, 244, 246, 247, 253 consensual/perceived deprivation approach 128, 133 consensus 203

consistent partial indices 161-8, 287-92

contingency tables 35, 76, 88, 96, 229-32

continuity 69

AF measures 116, 176

axiomatic approach 112, 113, 115, 116 headcount ratio 111

continuous variables 46-7, 84, 85

converse strong deprivation rearrangement 65

converse strong rearrangement 63, 65

converse weak deprivation rearrangement 65

converse weak rearrangement 62, 65, 114 conversion 6, 50

Core Welfare Indicator Questionnaire (CWIQ) 19, 20,

219

correlation 60, 73, 94, 97-8, 229-32

rank correlation 238-40

correlation coefficient 95, 231-2

see also Kendall's correlation coefficient; Pearson's correlation coefficient; Spearman's correlation coefficient

correlation/covariance matrix 88, 232 correspondence analysis (CA) 90, 95-6 Coste, J.

88, 94

counting approaches 123-43, 216

axiomatic approach 110-18, 120

building blocks 20, 22

censored achievement approach 149

chronic multidimensional poverty 283 comparability across people and dimensions 49-50 dimensional breakdown 68

dominance approach 83, 85

focus principles 56

fuzzy set approaches 100

identification and aggregation 33, 34

scales of measurement 47

see also Alkire and Foster (AF) methodology covariance 93, 94

Cowell, F. A. 120, 186, 253

Cramer's V measure 230, 231, 232 crisp set 103

cumulative distribution functions (CDFs) 34, 234, 236-7

dominance approach 79, 80, 81, 82 Curran, C. E. 3

Dag Hammarskjold Foundation 124n3

Dalton, H. 53n46

D'Ambrosio, C. 47n36, 51n42, 53n47, 54, 58n53, 68, 101, 115, 117, 121, 211, 258n6, 283n21, 283n22 dashboards 17, 18, 37, 70-1, 72-5, 122

Datt, G. 257n5

Davidson, R. 80n11, 235n4, 247n17, 253

Davies, R. 133

Deaton, A. 135n34, 196n17, 216n1, 219, 220, 222, 223, 223n7, 241,250n21

Decancq, K. 62n58, 62n59, 63n60, 77, 77n8, 132, 210n30, 210n31

deliberative/participatory exercise 202-3, 212, 213 Delors, J. 126

DelRio, C. 283n21

Demographic and Health Surveys (DHS) 19, 19n29, 20, 90, 219, 241, 243, 244, 245-6 demographic/sectoral effects 281-2

Deneulin, S. 6n9, 186n1

deprivation 3

Adjusted Headcount Ratio 21

associations across non-monetary deprivations 13-16

capability approach 5-6, 7, 8 comparability across people and dimensions 49-50 count 31, 116, 151, 174, 191,257, 285-6 counting approaches 128-33 cutoffs 31-4, 197, 199, 208-9

AdjustedHeadcountRatio 162, 167, 188 AF methodology 144, 145-6, 149-51, 154, 173-4, 184

axiomatic approach 111

comparability across people and dimensions 50 counting approaches 123, 134 fuzzy set approaches 100, 103, 109 marginal methods 37

Multidimensional Poverty Index 169 duration matrix 286, 291 FGT measures 28, 29 focus 52, 55-6, 59n55, 63

AF methodology 116, 118, 154, 176

axiomatic approach 110, 112, 113, 115, 116, 117, 118, 119

deprivation cutoffs 208

headcount ratio 111

statistical approaches 99 generalized means 38 indicators 10, 13-16 marginal 35, 37 matrix 31, 35, 36, 50

AdjustedHeadcountRatio 158, 160, 162, 164, 167

AFmethodology 150, 151-2, 153, 154-5 axiomatic approach 111, 116 censored see censored deprivation matrix chronic multidimensional poverty 284-5, 286 Multidimensional Poverty Index 170 monetary vs non-monetary 9-10 multidimensional poverty measurement 30, 31-4 policy 20-1 and poverty, difference between 55 scores 31, 200, 213

Adjusted Headcount Ratio 159, 162

AFmethodology 146, 150-1, 153-4, 155, 157 axiomatic approach 110 counting approaches 124, 128, 130, 132 inequality among the poor 258-9 Multidimensional Poverty Index 169-72 regression models 297 robustness analysis 234-5 status 50, 124, 150,211,213 trends 10-13 see also joint deprivations depth of poverty 28, 29, 78, 103n40, 146 d'Ercole, M. M. 132n29 Dercon, S. 51n42, 283n21

Desai, M. 137 descriptive methods 86-7 De-Shalit, A. 2, 3, 7, 10n16, 21, 186n1, 187, 204, 212 Deutsch, J. 5n8, 53n47, 54n48, 58n53, 62n58, 87n18, 90, 101, 104n43, 107n47

DHS Bangladesh 172n16

DHS Senegal 172n16 diagonal matrix 40 dichotomous variables 47

Dickerson, A. 139

dimensional breakdown 68

Adjusted Headcount Ratio 165-8, 256

AF methodology 116, 118, 147, 176

axiomatic approach 112, 113, 116, 117, 118, 119, 121 chronic multidimensional poverty 287 fuzzy set approaches 108

headcount ratio 111

inequality among the poor 256, 258, 259

Multidimensional Poverty Index 172-3 dimensional contribution 233n1, 270 dimensional cutoffs 31-3, 110, 118 dimensional deprivation index 37, 73, 74, 148 dimensional headcount ratio see multidimensional headcount ratio

dimensional monotonicity 58-9

AF methodology 116, 118, 147, 156n9, 157, 160, 171, 176

axiomatic approach 112, 113, 115, 116, 117, 118, 120, 121

chronic multidimensional poverty 287 dimensional rearrangement among the poor 66 dimensional transfer 52, 65-7, 117, 258 dimensions 186-7, 197, 201-6, 218

Adjusted Headcount Ratio 21

AF measures 176

comparability across 48-50 deprivation 18

deprivation cutoffs 31-3 dominance approach 82-3, 85 fuzzy set approaches 105-7 joint distribution 35 marginal methods 37

Multidimensional Poverty Index 168-9 multidimensional poverty measurement 30 quality of life 7

scales of measurement 43

unidimensional poverty measurement 25, 26

Venn diagrams 76-8 direct method 4, 125, 128, 131, 135-6, 138 discordant pairs 239 discrete variables 46-7, 84, 85 Di Tommaso, M. 91 Dobson, A. J. 298 Dollar, D. 298 dollar-twenty-five-a-day poverty 10-13, 72-3, 101, 196n18

dominance approach 70, 71, 78-86, 122

robustness analysis 234-8, 247 dominance curves 237 dominance properties 52, 57-67, 214 Donald, S. G. 247n17

Dreze, J. 5, 8, 16, 16n26, 17, 124n2, 139n41, 140 Dubois, D. 101

Dubois, W. E. B. 125n7 Duclos, J. Y. 2n2, 33n21, 59n54, 79, 80n11, 81, 82, 83, 83n14, 84, 84, 85, 86, 90, 235n4, 242, 244n15, 247n17, 281

Duflo, E. 196n17

duration of poverty 283, 286, 288, 289, 291, 292

Dworkin, R. 186n1

dynamic subgroups 273-82, 293

Echevin, D. 84 economic growth 16-17, 124

Efron, B. 253, 254, 255

Elbers, C. 135, 135n34

eligible population 222n5 empowerment 19, 21, 198, 219 ends 5

enter poverty 273-7, 280-1, 283

environment 8

episodes of poverty count vector 285 equivalence scales 49, 223

Erikson, R. 126, 132

EU-2020 74, 132

Eurobarometer 133

European Commission 126

European Community Household Panel (ECHP) 129, 131, 132

Eurostat 132, 132n29

EU-SILC 19, 129, 132

Evans, M. 139

exit poverty 273-7, 280-1, 283

factor analysis (FA) 71, 86, 87, 88, 89, 90, 91n23, 97-8, 99

confirmatory 97, 98, 100 exploratory 97, 98, 100

falling groups (poverty transitions) 293

Fattore, M. 74n3

Fay, M. 90

Feres, J. C. 134, 135

Ferreira, F. H. G. 2n2, 77, 177

Ferriss, A. 206n25

FGT measures 2, 27-9

AF methodology 145, 149, 156, 163, 175-6 axiomatic approach 112, 115, 119 dominance approach 81

fuzzy set approaches 103n40, 104n42, 108 macro regressions 295 statistical approaches 91

see also FGT measures

Fox, J. 301 Franke, C. H. 41n32 freedoms/unfreedoms

AdjustedHeadcountRatio 148, 160-1, 189-92 capability approach 5, 7, 8

functionings 148, 160-1, 184-185, 199, 218

Adjusted Headcount Ratio 188, 189 Fusco, A. 206n25 fuzzy set approaches 71, 100-9, 122

Gaie, J. B. R. 3 Gajdos, T. 63n60 Galtung, J. 126, 186n1 Gardiner, K. 139 Garnett, J. C. 97 Gassman, F. 77 GDP (gross domestic product) 16-17 Gekker, R. 189n8 Gender Empowerment Index (GEM) 74 generalized linear models (GLMs) 295-6, 298-303 for fractional data 296, 298, 308-9 logistic regression 306-7 logit models 302 probit models 302

Generalized Method of Moments 310 general mean 38-9, 74, 120

axiomatic approach 114-15, 117, 118 Gibbons, J. D. 238n7, 240 Gifi, A. 95n29 Gillie, A. 125 Glanville, J. L. 90 Glewwe, P. 219 GNP (gross national product) 9n16, 126 GOI 139, 139n41 Gonner, C. 141n44 goodness of fit 302-3 Gordon, D. 129, 129n19, 139, 206n25, 282n20 Gourieroux, C. 309 Grab, J. 84 Gradin, C. 2n2, 179, 283n21 Gravel, N. 84, 189n8

Greenacre, M. J. 87n17, 95, 95n29, 96n32 Greer, J. 24, 27, 27n9, 91, 112, 114, 145, 163, 256n1 Griffin, J. 186n1 Grimm, M. 84 Grosh, M. 135, 196n17, 219 gross domestic product (GDP) 16-17 Gross National Happiness Index (Bhutan) 2, 177 gross national product (GNP) 9n16, 126 Grusky, D. B. 196n17, 202 Guio, A.-C. 132, 206n25 Gunewardena, D. 196n21 Guttman, L. 48, 95n29 Gwatkin, D. R. 90

Hagenaars, A. 223n7 Hagerty, M. R. 206n25 Hallerod, B. 131 Hametner, M. 74 Hamilton, L. 124n4 Hansen, J. P. 47 happiness 2, 6-7, 177 Harriss-White, B. 10 Haughton, J. H. 196n17, 207n26, 296n3 headcount ratio 4, 120, 121, 194-5

AF methodology 146, 147, 149, 160

chronic multidimensional poverty 283, 294 contingency tables 230-1 counting approaches 127, 131 deprivation cutoffs 209 dominance approach 80 FGT measures 28, 29 macro regressions 295 robustness analysis 234

intertemporal changes by dynamic subgroups 276-7 see also Adjusted Headcount Ratio; incidence of poverty; multidimensional headcount ratio height-for-age 46 Hemming, R. 256n1 Hentschel, J. 196n17 Herrera, A. O. 124n3 Hicks, J. 5 Hicks, N. 3, 72 Hidalgo-Capitan, A. 3 High-Level Panel 19 Hirschfeld, H. O. 95n29 Hirway, I. 139n41 Hoddinott, J. 135 Hollen Lees, L. 125n6 Horowitz, A. W. 2n2, 179 Hotelling, H. 91 household surveys 141, 217, 219, 220, 222-3 Howard, J. 3, 196n20, 202 Hoy, M. 51n42, 283n21 Hoyland, B. 234n2 Hugo, V. 1, 3 Hulme, D. 101, 196n20, 283n22, 293n23 Human Development Index (HDI) 9n16, 74, 195,

Human Poverty Index (HPI) 74

human rights 3, 5, 13n22

Huppi, M. 281

hypothesis testing 243-6, 247

one-sample test 243-4, 245

one-tailed test 244, 245, 247

two-sample test 244-6

two-tailed test 244, 245

identification of poverty 122, 196-7, 199-201

AdjustedHeadcountRatio 159, 188, 189

AF methodology 115, 144-6, 148-56, 159-60, 173, 174, 176

axiomatic approach 110, 111, 115, 120

chronic multidimensional poverty 283-4, 285-6, 292

composite indices 74-5

counting approaches 123, 127-9, 137, 140-1, 143 dashboards 73, 74, 75

deprivation 31-2

dimensional breakdown 68

dominance approach 81-2, 83

fuzzy set approaches 100, 102, 107-8, 109 multidimensional poverty measurement 32-4, 51-2, 56, 63

non-monetary indicators 9

unidimensional poverty measurement 26-7 unit of identification 121, 220, 221-6

value-added of joint distribution of deprivations 18-19

Venn diagrams 78

IISD 207

ILO 124n3

imputation 228

incidence effect 281

incidence-intensity decompositions 280-2 incidence of poverty 4, 28n11

Adjusted Headcount Ratio 156-7, 159, 160, 161-2

AF methodology 148, 174, 175, 185

chronic multidimensional poverty 288

inequality among the poor 256

Multidimensional Poverty Index 171, 172 regression models 296, 298, 302, 308-10 intertemporal changes by dynamic subgroups 276-82

see also headcount ratio; multidimensional headcount ratio

income method 4, 70

counting approaches 125, 131, 133, 136, 140 income poverty/monetary poverty

counting approaches 130, 132n30, 133-4, 136-7, 138, 141

economic growth and social indicators 17

FGT approach 2

headcount ratio 4, 194-5

imputation 228

indicators 207-8

joint distribution of deprivations 18

linear regression analysis 298 measures 9-10

trends 10-13

unidimensional measurement 26-9

INDEC 133, 134

India

counting approaches 139-40

Demographic and Health Surveys 241, 243, 244, 245-6

economic growth and social indicators 16-17 household surveys 219

monetary vs non-monetary household deprivations 10

National Family Health Survey (NFHS) 14 population subgroup decomposability 271, 272 indicators 216, 218

Adjusted Headcount Ratio 21

AF methodology 145-6 capability poverty 7-8 comparability across 48, 49, 50 counting approaches 123-4, 128, 130, 132-8, 140-1,

143

deprivation 10, 13-16

design 219-28

factor analysis 89

limitations 20

marginal methods 37

Multidimensional Poverty Index 168-9 non-monetary 8-9

normative choices 186, 188-9, 192, 193, 197, 199, 201-2, 206-8

poverty 21 relationships among 228-32 resources 6

scales of measurement 40, 43, 44, 48 transformation to match unit of identification 221-2

inequality among the poor 55, 59, 60, 256-64 information theory approach 114, 118-20 instrumental value 5, 6

instrumental variable method 297, 310 integrated method to measure poverty 136-8, 143 intensity effect 281 intensity of poverty

Adjusted Headcount Ratio 157, 159, 160, 161-2

AF methodology 145, 146, 147, 148, 174, 175, 185 chronic multidimensional poverty 283, 288, 289, 291, 292, 294

counting approaches 127

inequality among the poor 256, 259, 263-4

Multidimensional Poverty Index 171, 172 regression models 298 statistical inference 242 intertemporal changes

descriptive analysis 265-6, 266-8, 272 by dynamic subgroups 273, 274-82 interaction effect 280, 281

intermediate criterion 33, 152

Adjusted Headcount Ratio 236

AF methodology 115, 153-4 axiomatic approach 115 counting approaches 124 focus principles 56 poverty frontier 81-2, 83 intersection criterion 33, 152

Adjusted Headcount Ratio 236

AF methodology 115, 153-4 axiomatic approach 110, 115 counting approaches 124 focus principles 56 fuzzy set approaches 106-7 poverty frontier 81-2, 83 Venn diagrams 75, 76 interval scales 41, 42, 44-5, 47, 48 intrinsic value 5, 6 invariance properties 41n30, 43, 52-7, 99

Jaeger, D. A. 297n6 Jain, S. K. 139n41 Jalan, J. 139n41, 283n21 Jamieson, S. 47 Janvry, A. de 298n9 Japan Commission on Measuring Well-being (JCMW) 196n21

Jayaraj, D. 117 Jencks, C. 133 Jenkins, S. P. 5, 79, 196n17 Joe, H. 238n7

Johansson, S. 126, 126n8 joint deprivations 34, 35, 36, 220

axiomatic approach 120

cluster analysis 71 dashboard approach 73 fuzzy set approach 71 missing values 228 Venn diagrams 75-7 joint distribution 17-19, 21, 34-6, 37, 60, 70, 71, 122, 220

AF methodology 145, 149, 221 axiomatic approach 120 composite indices approach 74, 75 contingency tables 229, 230 dashboard approach 73, 75 deprivation cutoffs 208 dominance approach 82, 83, 85 fuzzy set approaches 108 missing values 228 statistical approaches 86, 88 Venn diagrams 76, 78 joint restrictions 51, 56 Jolliffe, I. T. 87n17, 91n22, 91n23, 94 Jones, S. 2n2, 180 Joreskog, K. G. 97, 98 Jung, E. 132, 178

Kakwani, N. 86n16

Kanbur, R. 196n17, 196n20, 202, 283n22

Kannai, Y. 62n59

Kast, M. 133

Kaztman, R. 10, 135, 136, 136n35

Kearns, A. 142

Kelly, E. 6n11

Kendall, M. G. 238n7, 239, 240

Kendall's correlation coefficient 11n20, 238, 239, 240

Kent, J. T. 86n16, 93n25, 100

Khan, S. N. 142

Khandker, S. R. 196n17, 207n26, 296n3

Khera, R. 139n41, 140

Klasen, S. 10n16, 18, 91

Klemisch-Ahlert, M. 189n8

Klugman, J. 196n17

Kobus, M. 84

Kolm, S. C. 54n49, 59, 257

Kozel, V. 220

Kraay, A. 298

Krishnakumar, J. 89, 89n21, 91, 98

Kuga, K. 120

Kuklys, W 6, 91

Kullback, S. 119

Labar, K. 84

Lambert, P. J. 79

Land, K. C. 206n25

Lanjouw, J. O. 135

Lanjouw, P. 135, 196n17, 223n7

Lansley, S. 128-9, 129n18, 130, 131, 133

Larochelle, C. 2n2, 177

Lasso de la Vega, M. C. 215n35, 236 latent class analysis (LCA) 86, 87 Latin America 17, 125, 133-9

Lawley, D. N. 98

Lawson, D. 283n21

Layard, R. 6n13

Layte, R. 10, 10n16, 130n26, 131

League of Arab States 138, 142n46

Leavy, J. 3, 196n20, 202

Lee, S. 255

Leibler, R. A. 119

Lelli, S. 90, 101

Lemmi, A. 101, 102, 103, 104, 105, 106, 108

Lenoir, R. 126

Lewis, C. I. 75n6

Likert, R. 47

Likert scales 47

Limam, M. 101

linear predictor 300, 301

linear regression model 295, 298-300

link function 301-2, 304, 309

logit 304-5, 306

probit 304-5

Living Standard Measurement Survey (LSMS) 19,

20, 219

long-term groups (poverty transitions) 293

Lopez-Calva, L. F. 6n9

Lord, F. M. 48

Luce, R. D. 44, 44n34, 47

Lugo, M. A. 2n2, 62n58, 63n60, 77, 114, 118, 119, 120, 177,210n31,211,258n6

M_a measures 145-8, 160, 173, 175-7, 211

see also Adjusted Headcount Ratio; Adjusted Poverty Gap; Adjusted Squared Poverty Gap/FGT Measure

Maasoumi, E. 114, 118, 118n56, 119, 120, 211, 258n6

Mack, J. 128-9, 129n18, 130, 131, 133 macro data 217

Maggino, F. 74n3, 86, 207

Maitre, B. 10, 10n16, 130n26, 131, 132, 206n25

Makdissi, P. 101

Mancero, X. 134, 135

Maniquet, F. O. 77, 186n1, 210n30

Maquet, I. E. 132

Marcus-Roberts, H. 41, 41n32

Mardia, K. V. 86n16, 93n25, 100

marginal deprivations 35

marginal distribution 34, 35, 36, 37, 83

marginal methods 36-7, 70-1, 73

Marlier, E. 3, 126, 206n25, 207

Marshall, A. W. 59

Marx, K. 5

Masset, E. 283n22

matches/mismatches 229-30

Mather, M. 217

Matoussi, M. S. 101

matrix operations 37-40

Mauro, V. 2n2, 139, 181

Maxwell, A. E. 98

Mayer, S. E. 133

McCullagh, P. 296n1, 298, 301, 303n16, 309

McGillivray, M. 9n16, 101, 234n2

McKay, A. 283n21

McKenzie, D. 90

meaningfulness 211

Adjusted Headcount Ratio 159n10 comparability across people and dimensions 49 non-monetary indicators 8-9

ordinality 56

scales of measurement 40, 41, 45, 48 means 5

Meinzen-Dick, R. 2n2, 177, 200

membership functions 71, 102-5, 107, 108, 109 Mendez, F. 2n2, 179

metadata 217

Metz, T. 3

Mexico 2, 194, 196, 214n34

Michalos, A. C. 196n21, 206n25

Micklewright, J. 5, 196n17

micro data 122, 217

Mill, J. S. 5

Millennium Development Goals (MDGs) 1 dashboard approach 72 data 19

drinkable water sources 44

economic growth 17 marginal methods 37 trends 10-13

Mills, A. M. 253 Minujin, A. 136, 139 Mishra, A. 2n2 missing values 227-8 Mitra, S. 2n2, 179, 215n35, 244n14 MkNelly, B. 133 model-based methods 86-7

Molina, S. 133 moments

first-order 99

second-order 88, 99 monetary poverty see income poverty/monetary poverty

Monfort, A. 309 monitoring 3, 21, 68, 72, 125, 127, 130, 132, 142, 161, 162, 163, 193, 197-8, 199, 203, 212, 217, 218, 258, 273, 274, 280 monotonicity 52, 57-8

AF methodology 175

axiomatic approach 112, 113, 115

FGT measures 28, 29 fuzzy set approaches 108 headcount ratio 111 ordinal scales 43 statistical approaches 99

Moore, K. 293n23 Morales, E. 223n7 Morduch, J. 280n19 Morris, M. D. 74 mortality rate 11n19, 12, 17, 37, 72, 217 MoSA 138, 142n46 Moustaki, I. 98 movers 276-9 movers effect 278-9 MPDC 138, 142n46 Muellbauer, J. 223n7 Muffels, R. 130

Mukherjee, D. 51n42, 53n47, 54n48, 55n50, 58n53, 68, 112, 113n51, 211, 257n6

Mukherjee, N. 139n41 Mukhopadhyay, A. 84 multidimensional dominance 81-6 multidimensional headcount ratio 118

Adjusted Headcount Ratio 156, 157 axiomatic approach 111 chronic multidimensional poverty 287-9, 291, 292, 293

inequality among the poor 259, 263-4 Multidimensional Poverty Index 171 robustness analysis 234, 236, 238 standard errors 249, 250, 251, 252 multidimensional headcount ratio (cont.) statistical inference 242, 243 intertemporal changes

descriptive analysis 264-73

by dynamic subgroups 273-4, 276-7, 279, 280 see also incidence of poverty

multidimensional poverty 1-3 capability approach 5-6, 7, 8 data and computational techniques 19-20 design 5

indicators 9

joint distribution of deprivations 18 Multidimensional Poverty Index (MPI) 2, 168-73, 177, 225, 226

associations across non-monetary deprivations 14 Bhutan 18

India 245-6

inequality among the poor 263-4 robustness analysis 239-40, 247-8 intertemporal changes, descriptive analysis 266-8, 269-71

multidimensional poverty methodology 21-2, 33-4 multiple correspondence analysis (MCA) 71, 86, 87,

88-9, 90, 94n26, 95-6, 98-9, 100

Multiple Indicator Cluster Survey (MICS) 19, 20, 219 Murgai, R. 139n41

Murteira, J. M. 309 Muthen, B. O. 97

Muthen, L. K. 97

Naga, R. H. A. 77 Nagar, A. 98

Nandy, S. 139

Narayan, D. 1, 3, 196n20, 202, 205, 213n32, 293n23 Nardo, M. 74n3, 86, 206n25, 234n2

National Statistics Bureau, Royal Government of Bhutan 2n3, 18

Nehmeh, A. 138, 142n46

Nelder, J. A. 296n1, 298, 301, 303n16, 309 Nelson, J. 223n7

Neubourg, C. de 77, 139 Neumann, D. 77n8

Newcombe, R. G. 253n22 Nicholas, A. 2n2, 180, 283n22

Nolan, B. 1, 8-9, 10n16, 18, 126n9, 127n12, 130,

130n23, 130n25, 130n26, 132, 133, 214n34 Noll, H.-H. 201

nominal scales 41, 42, 43, 44, 45, 47 non-linear functional form 104, 309, 310 non-normalized/numbered weights 151-2, 158, 176-7 non-triviality 69, 112, 113

normalization 69

axiomatic approach 112, 113, 117, 118 in inequality measurement 260-1 normalized gap matrix 111-12, 173-4 normalized income gap 104n42

AF methodology 146

axiomatic approach 113, 114, 119

chronic multidimensional poverty 287

counting approaches 137

multidimensional poverty measurement 32-3, 48 unidimensional poverty measurement 27, 28, 29 normalized weights 30, 151-2

Norman, G. 47, 48

Notten, G. 2n2, 180, 298n9

Nteziyaremye, A. 133

Nussbaum, M. 6n9, 180, 186n1, 203n24 Nussbaumer, P. 2n2

Nygard, F. 253

Ocampo, J. P. 179

O'Donnell, O. 46

OECD 223n7

Olkin, I. 59

ongoing poor 273-8, 280, 283

opportunities 5, 8 ordinal variables/data 40-8, 56-7, 122, 199

AdjustedHeadcountRatio 159-60, 176, 191, 258

AF methodology 118, 144, 148, 148n2, 154 axiomatic approach 110, 111, 112, 116-18, 120, 121 chronic multidimensional poverty 286, 287 counting approaches 137, 138, 139, 142, 143 fuzzy set approaches 101, 109

unidimensional poverty measurement 25n3 overlap, measure of 230-2

Pagani, A. 125n7

pairwise comparisons 233, 234-9, 240, 247, 263 Papke, L. E. 309

Parfit, D. 186n1

Pattanaik, P. K. 36n27, 37, 160-1, 189, 189n8, 191n10,

191

Pearson, K. 91

Pearson's correlation coefficient 11n20, 99-100

Peichl, A. 2n2, 180

Peluso, E. 116, 258n6

percentage contributions 166, 167-8, 172-3, 290 period-specific partial indices 291

Permanyer, I. 234n2

permissible statistics 41-3, 44n33, 48 permutation matrix 39-40

Pestel, N. 2n2, 180

Petesch, P. 196n20, 213n32, 293n23

Pett, M. A. 47

Physical Quality of Life Index 74

Poi, B. P. 255

policy 3, 186-7, 193, 195, 200-1, 233

Adjusted Headcount Ratio 160, 162

AF methodology 147

axiomatic approach 121

chronic multidimensional poverty 287

counting approaches 125-6, 135, 138, 139, 143 FGT measures 29

fuzzy set approaches 101

motivation 20-2

poverty and welfare, link between 4-5

poverty cutoffs 213-14

intertemporal changes by dynamic subgroups 278 Popli, G. 139

population effect 11, 25, 30, 53, 99, 165, 241-2, 250 population growth 268

population subgroup decomposability 67-8, 271-3

Adjusted Headcount Ratio 163-5

AF methodology 116, 118, 147, 176

axiomatic approach 112, 113, 115, 116, 117, 118, 119 chronic multidimensional poverty 287

fuzzy set approaches 108 headcount ratio 111

Multidimensional Poverty Index 171-2

Porter, C. 51n42, 283n22

Posarac, A. 2n2, 179 post-identification dimensional deprivations 34, 37 poverty

comparisons 256

cutoffs 32-3, 196, 197, 213-14 AdjustedHeadcountRatio 163, 166, 188, 189 AFmethodology 144, 146, 147, 149, 152-3, 154, 155, 174, 185

axiomatic approach 110 counting approaches 124, 127n13, 128, 129-30, 131, 137

fuzzy set approaches 100, 103, 109 inequality among the poor 258 robustness analysis 234-8, 247 statistical approaches 100 statistical inference 247

effect 280-1

focus 52, 55, 56, 63

AF methodology 116, 118, 147, 154, 176 axiomatic approach 112, 113, 115, 116, 117, 118, 119

headcount ratio 111

frontiers 33n21, 81-2, 83, 85

gap measure 27, 28, 29

index 33

axiomatic approach 112-14, 121

fuzzy set approaches 108 properties for multidimensional poverty measures 52

statistical approaches 87, 90, 99, 100

lines 4, 148n2, 213

AF methodology 155n7

axiomatic approach 110, 119 counting approaches 125, 128, 130-1, 134, 136, 137, 139-40

dominance approach 79, 80, 81 fuzzy set approaches 103n39 multidimensional poverty measurement 33 unidimensional poverty measurement 26-7, 28, 29, 32

scorecard 141-2, 143

Prade, H. 101

Pradhan, M. 141n44 prevalence of poverty 28n11 prices 148n2, 187n3 primary goods 6, 127n11, 187n2 principal component analysis (PCA) 71, 86, 87, 88-9, 90,91-5, 98-9, 100

principal components 91-5

standardized 95

principles see axioms; properties

Pritchett, L. H. 90 progressive transfer 257 properties 8

AF methodology 21

chronic multidimensional poverty 287

inequality among the poor 260-1

for multidimensional poverty measures 50-69

see also axioms

Proschan, F. 61n57, 61n58, 238n7 public reasoning 8, 74, 202, 203, 211 Purchasing Power Parity (PPP) 196, 310

Qizilbash, M. 101, 102, 102n36, 102n38 quasi-maximum likelihood estimator (QML) 309 Quigley, W. 125n6

Quinn, N. 51n42, 283n22

Qutub, S. 142

Rabe-Hesketh, S. 296n3

Ragin, C. C. 101n34

Rahman, T. 89

Ramalho, E. A. 309

Ramalho, J. J. 309

RamseyRESET test 310

Ranade, R. R. 51n42, 53n47, 54n48, 55n50, 58n53, 68, 112, 113n51, 211, 257n6

rank correlation 238-40

rank robustness 233, 234, 238-40, 247-8

ratio scale 41, 42, 45, 47, 47, 48, 199

comparability across people and dimensions 50n40 weights 211

Ravallion, M. 2n2, 16n26, 27n9, 72n2, 74, 81n12, 177, 186, 196n17, 207n26, 210n31, 211, 213n32, 218n4, 223n7, 281, 283n21, 298

Rawls, J. 6, 6n11, 124n4, 186n1, 187n2

Ray, R. 2n2, 180, 283n22

Raz, J. 186n1

Reader, S. 124n4, 186n1

rearrangement 52, 60-6

axiomatic approach 113, 119, 120

headcount ratio 111

Reddy, S. 36n27

redundancy 229-32 regression models 295-310

determinants of AF poverty measures 295-310 macro regressions 295, 296-8, 308-10 micro regressions 295, 296-8, 304-8 regressive transfer 108 relative rate of change 265-6, 267 Rencher, A. C. 92, 94 replication 39 replication invariance 52, 53

AF measures 116, 118, 176 axiomatic approach 112, 113, 115, 116, 117, 118, 119 fuzzy set approaches 108 headcount ratio 111

in inequality measurement 260 resources

capability approach 5, 6, 7 counting approaches 125, 127 unidimensional poverty measurement 27, 29 well-being 49n39

Ringen, S. 130, 130n23

Rio Group 134 Rippin, N. 258 rising groups (poverty transitions) 293

Robano, V. 142

Roberts, F. S. 41, 41n31, 41n32, 47, 159n10 Robeyns, I. 6n11, 8n15, 186n1, 188n5, 203n24 Robles, M. 2n2, 142, 178 robustness 196, 210, 214, 215, 233-40, 246-8 counting approaches 137 fuzzy set approaches 105, 109 statistical approaches 100

Roche, J. M. 2n1, 2n2, 90, 101n35, 139, 169, 172, 173,

177n17, 180, 188n5, 259n7, 263, 264n10, 266, 267, 268, 270, 271, 279, 280, 281, 282, 282n20 Roelen, K. 2n2, 77, 180, 298n9

Roemer, J. E. 186n1 Room, G. 126n9

Rowntree, B. S. 26n5, 70n1, 125 Roy, I. 139n41, 140

Ruger, J. P. 190n9 Ruggeri Laderchi, C. 5n8, 10, 10n16, 148n2

Sadoulet, E. 298n9

Sahn, D. E. 33n21, 79, 81, 82, 83, 83n14, 84, 85, 86, 90 Saisana, M. 142, 234n2

Saith, R. 5n8, 10, 148n2

Saltelli, A. 142 Samman, E. 19 sample design 207, 264, 283 sampling 219, 240-2

simple random 248-50

stratified 250-3

Sanstrom, A. 253 Santos, G. 74n3

Santos, M. E. 2n1, 29n14, 38n28, 51n42, 72, 74n3,

74n4, 75, 125n5, 138, 144, 168, 168n15, 169,

177n17, 180, 200, 208n28, 209, 213, 215n35, 225, 226-8, 226n10, 237, 240, 241, 247, 283n21 Sarle, W. S. 41

Sarwar, M. 74n3 Sastry, N. 90 scaled deviance statistic 303, 307-8 scale invariance 52, 54-5

AF measures 116, 118, 176 axiomatic approach 112, 113, 115, 116, 117, 118, 119 fuzzy set approaches 108 headcount ratio 111

scales of measurement 40-8

Schady, N. 135n33 Schellenberg, J. A. 90 Schreiner, M. 141-2, 141n45, 143 second-order stochastic dominance 80-1, 237 Segal, P. 207n26

Sen, A. K. 1-2, 3, 5-8, 6n9, 6n10, 6n12, 7, 16, 16n26,

17, 21, 26, 26n3, 27, 27n8, 28, 29, 32, 34, 41, 44, 48, 49n38, 49n39, 51, 51n42, 53n47, 74, 85, 101, 101n33, 108, 110, 120, 123, 124n2, 125, 126, 127n11, 128, 144, 148n2, 161, 185, 187, 187n3, 189-90, 189n7, 190n9, 192, 193, 194, 194n15, 195, 195n16, 197-8, 198n22, 199, 201, 202-3, 203n24, 206, 210, 211-12, 213, 213n33, 218, 256, 257n4

Seta, M. Del 189n8 Seth, S. 2n1, 2n2, 4n5, 27n8, 36n27, 62n58, 63n60, 66n60, 74n4, 75n5, 77, 79n10, 81n12, 139, 139n41, 140, 140n42, 142-3, 169, 172, 173, 177n17, 178, 196n17, 207n26, 209n29, 215n35, 234n2, 243, 246, 246n16, 250n21, 257, 259, 259n7, 260, 263, 264, 271, 272

Shaffer, P. 196n20

Shah, A. 137

Shannon, C. E. 119 Shapiro, J. 283n21 Sharan, M. R. 140 Shepherd, A. 283n22, 293n23 Shorrocks, A. F. 67n62, 79, 81, 120, 196n18, 256n1, 280, 280n19, 281

Siani Tchouametieu, J. R. 2n2, 181

Siegel, M. 2n2, 181 Silber, J. 5n8, 53n47, 54n48, 58n53, 62n58, 86n16, 90, 101, 104n43, 107n47, 117n54, 258n6

Silver, H. 126n9 similarity 228 Siminski, P. 2n2, 177 Simpson, G. G. 230n13 Sinclair, T. 280n19 Sinha, K. 283n22 Sirgy, M. J. 206n25 Skrondal, A. 296n3 Smith, A. 5

Smith, S. C. 2n2, 142, 177

Smith, W. 133 Smithson, M. 101n34 social exclusion/inclusion 117, 207

counting approaches 125, 126-7, 128, 132, 143 Sorbom, D. 97, 98

South Asia 140

Spearman, C. 97

Spearman's correlation coefficient 11n20, 238, 239, 240 squared gap matrix 174 squared poverty gap 28, 29

standard errors 241-2, 243, 244, 245, 246, 248-55 statistical approaches 70, 71, 86-100, 122 statistical inference 233-4, 238, 240-8 stayers 276-9

stayers effect 278-9

Stecklov, G. 90

Stevens, S. S. 41, 41n29, 41n30, 41n31, 42, 43, 44n33, 45, 46, 47

Stewart, F. 3, 5n8, 10, 124n4, 125, 126, 136n35, 148n2, 186n1, 260, 262

Stifel, D. 90

Stigler, G. J. 219

Stiglitz, J. E. 7, 21, 71, 73, 124n2, 197-8, 207n26, 218 Stiglitz-Sen-Fitoussi Commission 7, 21, 197-8, 218 stochastic dominance 79-81, 83, 90

robustness analysis 234-5, 236, 237-8

Stock, J. H. 297n6

Streeten, P. 3, 72, 125, 186n1

strong deprivation rearrangement 65

axiomatic approach 112, 113, 115 inequality among the poor 257

strong monotonicity

AF measures 116, 118, 176

axiomatic approach 116, 118, 119

strong rearrangement 63

AF measures 118

axiomatic approach 118, 121

structural equation models (SEM) 71, 87, 89, 91,

97-8

stunting 46

subgroup consistency 67-8

axiomatic approach 117, 118

chronic multidimensional poverty 287 fuzzy set approaches 108

subgroup properties 28, 52, 67-8 subjective wellbeing 6-7 subnational disparity 263-4

Subramanian, S. 117 substitutability/substitutes 62n59 association-decreasing rearrangement 62, 63, 64-5 axiomatic approach 114, 119

counting approaches 137, 139, 142 deprivation focus 55 dominance approach 83, 85

Sundaram, K. 139n41

Sunstein, C. R. 190n9

sustainable development 8

Svedberg, P. 193

Swanepoel, J. W. H. 255

symmetry 52-3

AF measures 116, 118, 176

axiomatic approach 112, 113, 115, 116, 117, 118, 119

fuzzy set approaches 108 headcount ratio 111

inequality among the poor 258

Szekely, M. 16n26, 20, 194, 298

targeting 135, 139-43, 160, 187, 198

Tarozzi, A. 135n34

technical properties 52, 70

Theil, H. 119

Thomas, B. K. 139n41, 140

Thon, D. 27, 256n1

Thorbecke, E. 24, 27, 27n9, 91, 112, 114, 145, 163,

256n1

Thurstone, L. L. 97

Tibshirani, R. 253, 254, 255

time monotonicity 287

Tonmoy Islam, T. M. 2n2, 181

Totally FuzzyandRelative (TFR) approach 104, 105 Tout, H. 125n7

Townsend, J. 125n6

Townsend, P. 26n5, 125, 125n7, 128, 133 trade-offs 74, 120,121,211

Trani, J.-F. 2n2, 139, 181

Trannoy, A. 280n19 transfer 52, 57n52, 59-60

AF measures 116, 176

axiomatic approach 112, 113, 115, 116, 119

FGT measures 28, 29

fuzzy set approaches 108, 109 headcount ratio 111

in inequality measurement 261

translation invariance 54n49, 260

Trognon, A. 309

Tsui, K.-Y. 36n27, 51n42, 54n48, 55n50, 58n53, 59n55,

62, 62n58, 63n60, 113, 113n51, 114, 121, 148n2, 149n4, 211, 213, 257n6

Tukey, J. W. 48

Type I error 242n11

Type II error 188, 233-4

Tzamourani, P. 98

Ulph, D. 256n1

UN 217

uncensored headcount ratio 265, 267, 269-71, 273

UNCTAD 124

underweight 46

UNDESA 11, 196n17, 268

UNDG 205

UNDP 2, 2n1, 3, 74, 138, 142n46, 177n17

UNEP 124

unfreedoms see freedoms/unfreedoms

UNICEF 139

unidimensional poverty measurement 24-9, 32 comparability 49

dominance approach 79-81 fuzzy set approaches 101 monotonicity principle 58 normative choices 196

transfer principle 57n52, 60

union criterion 33, 149, 152

Adjusted Headcount Ratio 166, 236 AFmethodology 115, 116, 118, 153-4, 155, 176 axiomatic approach 110, 111, 112, 115, 116, 118, 120 union criterion (cont.)

chronic multidimensional poverty 292

composite indices 74-5

counting approaches 124, 128, 132, 134, 140, 141 dimensional breakdown 68

focus principles 56

fuzzy set approaches 106

poverty frontier 81-2, 83

unit consistency 54, 115

unit of identification 121, 220, 221-6

UNRISD 3

Ura, K. 2, 177, 234

utility 5, 6-7, 25, 26-7

validity 23, 128, 193, 206, 207, 209, 216, 247, 297

Van Ootegem, L. 188n5, 210n31

variance 89, 92-4, 96

Vaz, A. 263, 264n10, 266, 267, 268, 270, 271, 279 vector operations 37-40

Veen, R. J. van der 8n15

Velleman, P. F. 45, 48

Venn, J. 75, 75n6, 75n7, 78

Venn diagrams 70, 71, 75-8, 122

Verdier-Chouchane, A. 101

Verhofstadt, E. 188n5, 210n31

Verkuilen, J. 101n34, 104n43

Verma, V 101, 104, 104n43, 106, 107n47

Verme, P. 90

Vero, J. 107n47

Vick, B. 179

Vizard, P. 203n24

Vogel, J. 126

Voices of the Poor 1, 204-5

Volkert, J. 188n5

Vranken, J. 132

Vriens, M. 130

Wagle, U. R. 2n2, 91, 181, 196n21

Wagner, J. 309

Waidler, J. 2n2, 181

wasting 46

Watts, H. W. 29, 51n41, 113

weak deprivation rearrangement 65

AF measures 116, 176

axiomatic approach 112, 113, 116, 117, 118

weak dimensional monotonicity 59, 111

weak monotonicity 58

AF measures 118

axiomatic approach 112, 113, 118, 121

fuzzy set approaches 108 headcount ratio 111

weak rearrangement 62

AF measures 118

axiomatic approach 118

headcount ratio 111

inequality among the poor 257n6

weak transfer 59-60

AF measures 118 axiomatic approach 112, 113, 115, 118 fuzzy set approaches 108 headcount ratio 111

Wedderburn, R. W M. 296n1, 298 weighted deprivation matrix 151-2, 158, 176 weight-for-age 46 weight-for-height 46 weights 197, 206, 210-13

comparability across people and dimensions 50 normalized 30, 151-2

notation 30

well-being/welfare

association-decreasing rearrangement 62

axiomatic approach 110

capability approach 5, 6-7

counting approaches 126 dominance approach 81, 84

Gross National Happiness Index (Bhutan) 2, 177 measurement 55 and poverty, link between 4-5 poverty as shortfall from 3-4 resources 49n39

unidimensional poverty measurement 25-6 Weymark, J. A. 63n60

Whelan, C. T. 1, 8-9, 10, 10n16, 18, 126n9, 127n12, 130, 130n23, 130n25, 130n26, 131, 132, 133, 206n25, 214n34

WHO 46

WHO Multicentre Growth Reference Study Group 46 Wiggins, D. 186n1

Wilkinson, L. 45, 48

within-group inequality 260, 261, 262, 262n9 within-group mean independence 260 Wodon, Q. 101

Wolff, H. 2, 3, 7, 10n16, 21, 186n1, 187, 204, 212, 234n2

Women's Empowerment in Agriculture Index 2 Wooldridge, J. M. 309

WorldBank 11n21, 13, 196n17

Wright, G. 133

Wright, J. H. 297n6

Xu, Y. 36n27, 160-1, 189, 189n8, 191n10, 191

Yalonetzky, G. 84, 117n54, 139, 215n35, 235n3, 241n9,

258n6, 280, 281, 283n21, 284, 287, 289

Yap, D. B. 2n2, 179

Yerokhin, O. 2n2, 177

Yogo, M. 297n6

Younger, S. D. 33n21, 79, 81, 82, 83, 83n14, 84, 85, 86 Yu, J. 181

Zadeh, L. A. 101, 106, 106n46

Zaidi, A. 6

Zandvakili, S. 253

Zani, S. 101, 103, 104, 105, 106, 107, 108

Zheng, B. 27n8, 51n42, 54, 283n21

z-score 45, 46

Zumbo, B. D. 86, 206n25, 207

An alternative way of linking poverty and welfare is to follow a more conceptual approach and consider whether the various trade-offs implied by a poverty measure are broadly consistent with some underlying notion of social welfare. This is indeed a reasonable route, but one whose conclusions are often ignored in practice. For example, the so-called headcount ratio, which is simply the proportion of people considered poor in a population, is the most commonly used measure in traditional poverty measurement exercises (the income approach) as well as in the basic needs tradition (the direct approach). However, such a measure has the interesting property that a decrease of any size in the income (or unmet basic needs) of a poor person paired with a corresponding increase for a non-poor person will leave poverty unchanged. This, of course, is rather untenable from many welfare perspectives. Likewise, a decrease in the income of a poor person (no matter how large the decrease) paired with an increase in the income of another poor person sufficient to lift that person to the income poverty line (no matter how small the increase) will decrease poverty. Again, this would appear to be inconsistent with any reasonable welfare function censored at the poverty line.

Note, though, that the fact that these trade-offs are not justified in welfare terms has not forced the removal of the headcount ratio income poverty measure from consideration. This brings us to the third consideration of policy. For in fact other considerations also apply—such as comprehensibility, which a measure needs in order to advance welfare in practice. The level and composition of poverty must be communicated relatively accurately to journalists, non-specialist decision-makers, activists, and disadvantaged communities to motivate action. The headcount ratio is a remarkably intuitive, if somewhat crude, measure that takes the identification process very seriously and reports a meaningful number: the incidence of poverty. The fact that it is at odds with notions of welfare appears to be of second-order importance, because users have not found a comparably meaningful number with better welfare properties to highlight as the 'headline' statistic. So the welfare implications of poverty measures need to be considered alongside political economy and operational considerations of such measures, such as their communicability. We adopt this wider approach—which

⁴ Note that when referring to welfare here (and throughout the book) we do not refer to any particular so-called welfare programme, but rather to the concept of well-being. We do so because a body of economic literature developed in the twentieth century, namely ‘welfare economics’, is a conversation partner for multidimensional poverty measurement (Atkinson 2003).

⁵ For example, the Watts unidimensional poverty measure is related to the geometric mean—one of Atkinson’s social welfare functions. See Alkire and Foster (2011b); cf. Foster, Seth, et al. (2013).

⁶ See section 6.3.7 and section 2.3.

Consider^{* * 28} two distributionsy andy' with the following distribution of achievements in a particular dimension: y = (2,6,7) and y' = (1,5,9). We first show how to calculate μβ(y) for certain values of β and then compare two distributions with a graph where β ranges from —2 to 2. In this example, we assume that all dimensions are equally weighted: w₁ = w₂ = w₃ = 1 /3.

Arithmetic Mean: The arithmetic mean (β = 1) of distribution y is μ₁(y) = (2 + 6 + 7)/3 = 5.

²⁸ Alkire and Santos (2009).

¹⁸ These bounds are theoretically possible lower and upper bounds. Further research using panel datasets is required to investigate the likelihood of these bounds.

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Source: Alkire S., FosterJ., Seth S. et al.. Multidimensional Poverty Measurement and Analysis. Oxford University Press,2015. — 368 p.. 2015

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