www.ebook3000.com Multidimensional Poverty Measurement and Analysis www.ebook3000.com www.ebook3000.com Multidimensional Poverty Measurement and Analysis Sabina Alkire, James Foster, Suman Seth, Maria Emma Santos, José Manuel Roche, and Paola Ballón www.ebook3000.com Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries © Sabina Alkire, James Foster, Suman Seth, Maria Emma Santos, José Manuel Roche, and Paola Ballón 2015 The moral rights of the authors have been asserted First Edition published in 2015 Impression: All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2015931637 ISBN 978–0–19–968949–1 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only Oxford disclaims any responsibility for the materials contained in any third party website referenced in this work www.ebook3000.com ■ ACK N O W L E D G E M E N T S As authors and contributors to this book, we have worked as an intellectual team among ourselves and with colleagues and students Many techniques arose in conversation, and were developed by being passed around, critiqued, commented upon, improved, and reassessed iteratively, in theory and in practice, before they were written down systematically A sense of adventure and spirit of precision continued to the very end Among us, Ballón’s precise and clear contributions covered multivariate statistical methods, associations across indicators, standard errors, bootstrapping, and regression As the leader of the global MPI calculations 2011–13, Roche’s practical wisdom seeped into many parts; he contributed in particular to fuzzy set methods, poverty dynamics, standard errors, and data analysis Foster’s intellectual contributions are evident throughout the book as well as via less visible channels, given that Seth and Santos were his students Seth, Santos, and Alkire worked as a close-knit team across dozens of versions, covering very new ground in some cases, as well as revisiting and trying to distil for readers the key issues Each contributed deeply to this process of ongoing development of a public good, perhaps in the hope that our joint work might be of some practical use Many others also contributed definitive insights to this creative process The materials for this book developed greatly over a series of two-week intensive summer schools that we held in Delhi (2008), Lima (2009), Santiago and Amman (2010), Delft (2011), Jakarta (2012), Washington DC and Managua (2013), and Oxford (2014) We are grateful to our students, and to our other colleagues, for the learning that occurred together on those occasions We also presented materials from this book in our lunchtime seminar series, and in conferences and workshops, and benefited tremendously from the exchanges that ensued We received very helpful comments, corrections, improvements, and suggestions from many across the years, and are especially indebted to Tony Atkinson who read the full manuscript We are also grateful for direct comments from the following: Khalid Abu-Ismail, Sudhir Anand, Gordon Anderson, Roberto Angulo, Kaushik Basu, Francois Bourguignon, Cesar Calvo, Satya Chakravarty, Mihika Chatterjee, Adriana Conconi, Conchita D’Ambrosio, Jorge Davalos, Koen Decancq, Séverine Deneulin, Jean Drèze, Jean-Yves Duclos, Indranil Dutta, Marc Fleurbaey, Betti Gianni, Lu Gram, John Hammock, Bouba Housseini, Stephan Klasen, Jeni Klugman, Jaya Krishnakumar, Guy Lacroix, Achille Lemmi, Xavier Mancero, Enrica Chiappero Martinetti, Adib Nehmeh, Brian Nolan, Prasanta Pattanaik, Natalie Quinn, Amartya Sen, Jacques Silber, Frances Stewart, Joanne Tomkinson, Nicolas Van de Sijpe, Ana Vaz, Christopher Whelan, Gaston Yalonetzky, and Asad Zaman www.ebook3000.com vi ACKNOWLEDGEMENTS We have deeply appreciated the attentive and gentle support of Ann Barham, who corrected English and other matters throughout the whole text, and of Maarit Kivilo, who assembled the bibliography with exquisite precision and good humour Research assistants included Garima Sahai, who expertly processed dozens of literature searches and organized the pdf files at the start of this project, and Alejandro Olayo-Méndez SJ, who steered the project calmly to its conclusion Elizaveta Fouksman provided substantive and thoughtful pieces of analysis on a regular basis Timely, insightful, and very pertinent inputs came from research assistants, including Aparna John, Arif Naveed, Esther Kwan, Felipe Roa-Clavijo, Laurance Eschamps-Laporte, Maria Mancilla Garcia, Putu Natih, Saite Lu, and Franziska Mager A book is a team effort within a research centre such as the Oxford Poverty and Human Development Initiative (OPHI) So we are more than usually grateful for the diligent backstopping by our colleagues as we addressed this book project and they took leadership in other areas Heartfelt thanks to Mauricio Apablaza, Mihika Chatterjee, Adriana Conconi, Paddy Coulter, Emma Feeny, Lara Fleischer, Heidi Fletcher, Natasha Francis, John Hammock, Bouba Housseini, Usha Kanagaratnam, Thomas Morgan, Laura O’Mahony, Christian Oldiges, Kim Samuel, Moizza Sarwar, Tery van Taack, Joanne Tomkinson, Ana Vaz, and Diego Zavaleta The authors warmly acknowledge and thank ESRC-DFID RES-167-25 ES/1032827/1 for research support, and Santos thanks ANPCyT-PICT 1888 for research support Finally, we thank our families and friends for their enduring patience and kind support throughout this process The usual disclaimers apply www.ebook3000.com ■ C O NTEN TS LIST OF FIGURES ix LIST OF TABLES x LIST OF BOXES xii Introduction 1.1 1.2 1.3 1.4 1.5 Normative motivation Empirical motivations Policy motivation Content and structure How to use this book 20 22 23 The framework 24 2.1 Review of unidimensional measurement and FGT measures 2.2 Notation and preliminaries for multidimensional poverty measurement 2.3 Scales of measurement: Ordinal and cardinal data 2.4 Comparability across people and dimensions 2.5 Properties for multidimensional poverty measures 30 40 48 50 Overview of methods for multidimensional poverty assessment 70 3.1 3.2 3.3 3.4 3.5 3.6 Dashboard of indicators and composite indices Venn diagrams The dominance approach Statistical approaches Fuzzy set approaches Axiomatic measures 24 72 75 78 86 100 109 Counting approaches: Definitions, origins, and implementations 123 4.1 Definition and origins 4.2 Measures of deprivation in Europe and their influence 4.3 Measures of unsatisfied basic needs in Latin America and beyond 4.4 Counting approaches in targeting 4.5 Final comments on counting approaches 123 128 www.ebook3000.com 133 139 143 viii CONTENTS The Alkire–Foster counting methodology 5.1 5.2 5.3 5.4 5.5 The AF class of poverty measures: Overview and practicality Identification of the poor: The dual-cutoff approach Aggregation: The adjusted headcount ratio Distinctive characteristics of the adjusted headcount ratio The set of partial and consistent sub-indices of the adjusted headcount ratio 5.6 A case study: The global multidimensional poverty index (MPI) 5.7 AF class measures used with cardinal variables 5.8 Some implementations of the AF methodology Normative choices in measurement design 6.1 6.2 6.3 6.4 The adjusted headcount ratio: A measure of capability poverty? Normative choices Elements of measurement design Concluding reflections Data and analysis Robustness analysis and statistical inference 8.1 Robustness analysis 8.2 Statistical inference 8.3 Robustness analysis with statistical inference Distribution and dynamics Inequality among the poor Descriptive analysis of changes over time Changes over time by dynamic subgroups Chronic multidimensional poverty 10 Some regression models for AF measures 10.1 10.2 10.3 10.4 145 148 156 159 161 168 173 177 186 188 192 196 214 216 7.1 Data for multidimensional poverty measurement 7.2 Issues in indicator design 7.3 Relationships among indicators 9.1 9.2 9.3 9.4 144 Micro and macro regressions Generalized linear models Micro regression models with AF measures Macro regression models for M0 and H 216 219 228 233 234 240 246 256 256 264 273 282 295 296 298 304 308 REFERENCES 311 INDEX 343 www.ebook3000.com ■ LIST OF FIGURES 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 Complementary CDFs and poverty dominance 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 Logistic regression curve—West Java 307 www.ebook3000.com 342 REFERENCES WHO Programme of Nutrition (1997) Global Database on Child Growth and Malnutrition, compiled by M de Onis and M Blössner Geneva: World Health Organization WHO Multicentre Growth Reference Study Group (2006) WHO Child Growth Standards: Length/Height-for-Age, Weight-for-Age, Weight-for- Length, Weight-for-Height and Body Mass Index-for-Age: Methods and Development Geneva: World Health Organization Wiggins, D (1998) Needs, Values, Truth, 3rd edn Oxford: Clarendon Press Wolff, H., Chong, H., and Auffhammer, M (2011) ‘Classification, Detection and Consequences of Data Error: Evidence from the Human Development Index’, The Economic Journal, 121(553): 843–70 Wolff, J and De-Shalit, A (2007) Disadvantage Oxford: Oxford University Press World Bank (1990) World Development Report 1990: Poverty Washington, DC: World Bank World Bank (2000) World Development Report 2000/2001 Washington, DC: World Bank World Bank (2013) Global Monitoring Report 2013: Monitoring the MDGs Washington, DC: World Bank, , accessed April 2014 World Bank (2014) World Development Indicators Washington, DC: World Bank, Wright, G (2008) Findings from the Indicators of Poverty and Social Exclusion Project: A Profile of Poverty Using the Socially Perceived Necessities Approach, Key Report Pretoria: Department of Social Development, Republic of South Africa Yalonetzky, G (2009) ‘Testing for Stochastic Dominance Among Additive, Multivariate Welfare Functions with Discrete Variables’, OPHI Research in Progress 9a, University of Oxford Yalonetzky, G (2011) ‘A Note on the Standard Errors of the Members of the Alkire–Foster Family and its Components’, OPHI Research in Progress 25a, University of Oxford Yalonetzky, G (2012) ‘Poverty Measurement with Ordinal Variables: A Generalization of a Recent Contribution’, ECINEQ Working Papers 246, Society for the Study of Economic Inequality Yalonetzky, G (2013) ‘Stochastic Dominance with Ordinal Variables: Conditions and a Test’, Econometric Reviews, 32(1): 126–63 Yalonetzky, G (2014) ‘Conditions for the Most Robust Multidimensional Poverty Comparisons Using Counting Measures and Ordinal Variables’, Social Choice and Welfare, 43(4): 773–807 Yu, J (2013) ‘Multidimensional Poverty in China: Findings Based on the CHNS’, Social Indicators Research, 112(2): 315–36 Zadeh, L A (1965) ‘Fuzzy Sets’, Information and Control, 8(3): 338–53 Zaidi, A and Burchardt, T (2005) ‘Comparing Incomes When Needs Differ: Equivalization for the Extra Costs of Disability in the UK’, Review of Income and Wealth, 51(1): 89–114 Zavaleta, D., Samuel, K., and Mills, C (2014) ‘Social Isolation: A Conceptual and Measurement Proposal’, OPHI Working Paper 67, University of Oxford Zheng, B (1997) ‘Aggregate Poverty Measures’, Journal of Economic Surveys, 11(2): 123–62 Zheng, B (2007) ‘Unit-Consistent Poverty Indices’, Economic Theory, 31: 113–42 Zumbo, B D (ed.) (1998) ‘Validity Theory and the Methods Used in Validation: Perspectives from the Social and Behavioral Sciences’, Social Indicators Research, 45(1): 1–509 ■ INDEX Aaberge, R 116, 258n6 Abe, A 133 absolute rate of change 264–5, 266, 269 achievement matrix 25–6, 35, 49 Adjusted Headcount Ratio 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 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 Adjusted Poverty Gap (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 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 344 INDEX 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 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 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 Benzécri, 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 90 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 INDEX 345 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 Adjusted Headcount Ratio 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 cardinal variables/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 fuzzy set approaches 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 Adjusted Headcount Ratio 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 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 238–40 346 INDEX 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 Dag Hammarskjöld 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 Del Rio, 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 Adjusted Headcount Ratio 21 associations across non-monetary deprivations 13–16 capability approach 5–6, 7, 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 Adjusted Headcount Ratio 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 Adjusted Headcount Ratio 158, 160, 162, 164, 167 AF methodology 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 AF methodology 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 INDEX 347 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 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 Drèze, 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 Échevin, 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 enter poverty 273–7, 280–1, 283 environment 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 Adjusted Headcount Ratio Fields, G S 79n9 Filmer, D 90 Finch, N 10, 10n16 Finnis, J 186n1 first-order stochastic dominance (FSD) 79–80, 81, 83, 234, 236, 237–8 Firth, D 298, 302n15 Fisher, R A 95n29 Fiszbein, A 135n33 Fitoussi, J.-P 7, 21, 124n2, 197–8, 218 Flachaire, E 253 Fleurbaey, M 6n13, 8, 8n15, 59n54, 74n3, 77, 186n1, 189n8, 210n30 348 INDEX Flórez, C E 101 focus 108, 109 see also deprivation: focus; poverty: focus Foster, J E 2n2, 4n5, 8, 16n26, 24, 26n4, 27, 27n7, 27n8, 27n9, 28, 29, 31, 36, 36n27, 51, 51n42, 52n44, 53n47, 56, 58, 58n53, 63n60, 67n62, 68n63, 72, 74n4, 75, 79, 79n10, 81, 81n12, 90, 91, 109, 110, 112, 113, 114, 115, 116, 116n53, 118n55, 120, 121, 122, 124, 144, 145, 147, 152, 158, 161n11, 163, 165, 176, 177, 179, 183, 188n4, 190, 191, 193–4, 195, 196n17, 196n18, 196n19, 206, 207n26, 210, 213, 215n35, 225, 234n2, 236, 256n1, 257–8, 257n4, 283n21, 284, 287, 298 Foster–Greer–Thorbecke (FGT) methodology see also FGT measures Fox, J 301 Franke, C H 41n32 freedoms/unfreedoms Adjusted Headcount Ratio 148, 160–1, 189–92 capability approach 5, 7, 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 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 Gönner, C 141n44 goodness of fit 302–3 Gordon, D 129, 129n19, 139, 206n25, 282n20 Gourieroux, C 309 Gräb, 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 Halleröd, 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 Hicks, N 3, 72 Hidalgo-Capitán, A 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 Høyland, B 234n2 Hugo, V 1, Hulme, D 101, 196n20, 283n22, 293n23 Human Development Index (HDI) 9n16, 74, 195, 210 INDEX 349 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 Adjusted Headcount Ratio 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 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 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 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, 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, 281 350 INDEX 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, 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 INDEX 351 long-term groups (poverty transitions) 293 López-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 Mα 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 Mtre, 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 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 Meinzen-Dick, R 2n2, 177, 200 membership functions 71, 102–5, 107, 108, 109 Méndez, F 2n2, 179 metadata 217 Metz, T Mexico 2, 194, 196, 214n34 Michalos, A C 196n21, 206n25 Micklewright, J 5, 196n17 micro data 122, 217 Mill, J S Millennium Development Goals (MDGs) 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, 252 352 INDEX 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, data and computational techniques 19–20 design indicators 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 Muthén, B O 97 Muthén, 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 Nygård, F 253 Ocampo, J P 179 O’Donnell, O 46 OECD 223n7 Olkin, I 59 ongoing poor 273–8, 280, 283 opportunities 5, ordinal variables/data 40–8, 56–7, 122, 199 Adjusted Headcount Ratio 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 INDEX 353 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 Adjusted Headcount Ratio 163, 166, 188, 189 AF methodology 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 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 Ramsey RESET 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 108 354 INDEX 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, 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 Sanström, 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 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 INDEX 355 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 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 Székely, 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 Fuzzy and Relative (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 AF methodology 115, 116, 118, 153–4, 155, 176 axiomatic approach 110, 111, 112, 115, 116, 118, 120 356 INDEX 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 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 Wooldridge, J M 309 World Bank 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 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 ... Alkire and Santos (2009) 30 MULTIDIMENSIONAL POVERTY MEASUREMENT AND ANALYSIS 2.2 Notation and Preliminaries for Multidimensional Poverty Measurement We now extend the notation to the multidimensional. . .Multidimensional Poverty Measurement and Analysis www.ebook3000.com www.ebook3000.com Multidimensional Poverty Measurement and Analysis Sabina Alkire, James Foster,... and inequality (section 6.2) Ruggeri-Laderchi, Saith, and Stewart (2003), Deutsch and Silber (2005, 2008) 6 MULTIDIMENSIONAL POVERTY MEASUREMENT AND ANALYSIS This plurality applies also to poverty