Quantitative Approaches to Multidimensional Poverty

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Quantitative Approaches to Multidimensional Poverty Measurement Also by Nanak Kakwani and Jacques Silber: Nanak Kakwani and Jacques Silber (editors) THE MANY DIMENSIONS OF POVERTY Also by Nanak Kakwani: Nanak Kakwani (author) INCOME INEQUALITY AND POVERTY Methods of Estimation and Policy Applications Nanak Kakwani (author) ANALYZING REDISTRIBUTION POLICIES A Study Using Australian Data Also by Jacques Silber: Jacques Silber (editor) HANDBOOK ON INCOME INEQUALITY MEASUREMENT Y. Flückiger and Jacques Silber (authors) THE MEASUREMENT OF SEGREGATION IN THE LABOR FORCE Quantitative Approaches to Multidimensional Poverty Measurement

Edited by Nanak Kakwani University of Sydney Former Director, International Poverty Centre, Brazil and Jacques Silber Bar-Ilan University, Israel

UNDP financial support to the International Poverty Centre for holding the International Conference on ‘The Many Dimensions of Poverty’ and the preparation of the papers in this volume is gratefully acknowledged. © United Nations Development Programme (UNDP) 2008 Softcover reprint of the hardcover 1st edition 2008 978-0-230-00489-4 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission.

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Library of Congress Cataloging-in-Publication Data Quantitative approaches to multidimensional poverty measurement

Edited by Nanak Kakwani and Jacques Silber. p. cm. Papers originally presented at an international conference in Brasilia on August 29–31, 2005. Includes bibliographical references and index. 1. Income distribution – Mathematical models – Congresses. 2. Poverty – Mathematical models – Congresses. I. Kakwani, Nanak. II. Silber, Jacques. HB523Q36 2007 339.4Ј6072 – dc22 2007022325

10987654321 17 16 15 14 13 12 11 10 09 08 Contents

List of Tables and Figures vii Foreword xii Nora Lustig Preface xiv Nanak Kakwani List of Contributors xvi Introduction: On Quantitative Approaches to Multidimensional Poverty Measurement xviii Nanak Kakwani and Jacques Silber

1 The Information Basis of Multivariate Poverty Assesments 1 Esfandiar Maasoumi and Maria Ana Lugo

2 The Fuzzy Set Approach to Multidimensional Poverty: the Case of Italy in the 1990s 30 Gianni Betti, Bruno Cheli, Achille Lemmi and Vijay Verma

3 The Rasch Model and Multidimensional Poverty Measurement 49 Alessio Fusco and Paul Dickes

4 A Cluster Analysis of Multidimensional Poverty in Switzerland 63 Giovanni Ferro Luzzi, Yves Flückiger and Sylvain Weber

5 Multidimensional Poverty and Multiple Correspondence Analysis 80 Louis-Marie Asselin and Vu Tuan Anh

6 Income, Consumption and Permanent Income: a MIMIC Approach to Multidimensional Poverty Measurement 104 Ramses Abul Naga and Enrico Bolzani

7 Multidimensional Measures of Poverty and Well-being Based on Latent Variable Models 118 Jaya Krishnakumar

8 A Multidimensional Approach to Subjective Poverty 135 Bernard M.S. van Praag and Ada Ferrer-i-Carbonell

9 Using Efficiency Analysis to Measure Individual Well-being With an Illustration for Catalonia 155 Xavier Ramos 10 Efficiency Analysis and the Lower Convex Hull Approach 176 Gordon Anderson, Ian Crawford and Andrew Leicester

v vi Contents

11 Measuring Multidimensional Poverty: The Axiomatic Approach 192 Satya R. Chakravarty and Jacques Silber

12 Determining the Parameters of Axiomatically Derived Multidimensional Poverty Indices: An Application Based on Reported Well-Being in Colombia 210 Carlos Eduardo Vélez and Marcos Robles

13 The Order of Acquisition of Durable Goods and the Measurement of Multidimensional Poverty 226 Joseph Deutsch and Jacques Silber

14 Using an Ordinal Approach to Multidimensional Poverty Analysis 244 Jean-Yves Duclos, David E. Sahn and Stephen D. Younger

Index 262 List of Tables and Figures

Tables

1.1 Univariate poverty measurement by regions. Indonesia, 2000 12 1.A1 Summary statistics by regions. Indonesia, 2000 21 1.A2 Correlation coefficients: Indonesia, 2000 22 1.A3 Multivariate poverty measurement by regions. Indonesia, 2000 25 2.1 Membership functions of an individual in the four intersection sets 37 2.2 Situation of a generic individual i seen in fuzzy terms 38 2.3 Joint measures of deprivation (degrees of membership of individual i of fuzzy sets corresponding to two dimensions of deprivation) 38 2.4 Longitudinal measures of interest over two time periods 40 2.5 Conventional and fuzzy cross-sectional rates of income poverty: Italy and its macro-regions 1993–2000 42 2.6 Fuzzy measures of deprivation: monetary, non-monetary, and the two forms in combination 43 2.7 Longitudinal measures: traditional vs fuzzy approach 44 3.1 Analysis of the 29 items 57 3.2 Analysis of the nine items 58 3.3 Scale of poverty 59 3.4 Analysis of the five items of ‘durable goods’ 60 3.5 Scale of durable goods 60 4.1 Descriptive statistics for the variables used in factor analysis, SHP 2001 66 4.2 Rotated factor loadings (oblique rotation), 2001 69 4.3 Statistics for determining the number of clusters 71 4.4 Mean Scores on the four Factors, by cluster, 1999–2003 71 4.5 Complementary log-log model explaining multidimensional poverty 73 4.6 Complementary log-log model explaining financial poverty (Equivalized Income less than the half of the median income) 75 4.A1 Descriptive statistics for the variables used in cloglog estimation, SHP 2001 79 5.1 MIMAP Vietnam CBMS: first set of 13 poverty indicators (1999) 91 5.2 Mean poverty indicator by province (MIMAP CBMS) 92 5.3 The eight Vietnam-CBMS indicators found in VLSS surveys 93 6.1 Summary statistics 112 6.2 Parameters estimation 113 6.3 Prediction of permanent income 113 7.1 Results of the measurement model 130 7.2 Results of the structural equation model 131

vii viii List of Tables and Figures

8.1 A simple count of domain poverties for GSOEP 1996, West workers 145 8.2 Financial satisfaction GSOEP, 1996, West-workers, COLS 146 8.3 Domain variance/correlation matrix; GSOEP 1996 West workers 147 8.4 German general satisfaction explained (GSOEP, 1996 West workers), method: POLS 148 8.A1 Health satisfaction Germany, 1996 West-workers, POLS 152 8.A2 Job satisfaction GSOEP, 1996 West-workers, POLS 152 8.A3 Housing satisfaction GSOEP, 1996 West-workers, POLS 153 8.A4 Leisure satisfaction GSOEP, 1996 West-workers, POLS 153 8.A5 Environmental satisfaction GSOEP, 1996 West-workers, POLS 154 9.1 Summary statistics of well-being dimensions and overall well-being 163 9.2 Correlations between well-being dimensions, overall well-being and income 164 9.3 OLS regressions on well-being 166 9.4 Logit marginal effects on the well-being of the poor 168 9.A1 Variables used to estimate the dimensions 174 9.A2 Summary statistics of covariates used in Table 9.3 175 10.1 Welfare measures for hypothetical households 181 10.2 Distance measures to lowest and highest welfare households 184 10.3 Summary statistics for Human Development Index data 185 10.4 Deprivation indices summary statistics 186 10.5 Dominance tests 188 11.1 Poverty measurement with the Index P␪ 204

11.2 Multidimensional poverty measurement with the index Pr 205 12.1 Self-reported well-being: Colombia, 1997, 2003 212 12.2 Income-poverty measures: Colombia, 1997–2003 213 12.3 Poverty, unemployment and wages. Colombia, urban, 1996, 2000 214 12.4 Education poverty. Colombia, 1997–2003 215 12.5 Income-poverty measures taking into account public subsidies: Colombia, 1997–2003 216 12.6 Seven standard functional forms of MDP indexes and their main characteristics 217 12.7 Multidimensional measurements of poverty: Income, education and security, Colombia, 1997–2003 220 13.1 Ownership of durable goods by gender of head of household 228 13.2 Ownership of durable goods by household size 229 13.3 Ownership of durable goods by age of head of household 229 13.4 Ownership of durable goods by marital status of head of household 230 13.5 Ownership of durable goods by year of immigration of head of household 231 List of Tables and Figures ix

13.6 Ownership of durable goods by schooling level (years of schooling) of head of household 231 13.7 Ownership of durable goods by number of months worked by the head of the household during the last 12 months 232 13.8 Ownership of durable goods by status at work of head of household 232 13.9 Ownership of durable goods by place of residence of head of household 233 13.10 Ownership of durable goods by religion of head of household 234 13.11 List of possible orders of acquisition when there are three goods 235 13.12 Order of acquisition with highest proximity coefficient R (R ϭ 0.917) 238 13.13 Results of ordered logit regression (dependent variable ϭ latent variable measuring the level of deprivation) 239 13.14 Information on the bounds of the various ordered categories 240 13.15 Incidence of poverty by Gender of Head of Household 241 14.1 ⌸1,1 dominance test results for 1992 IHS and 1999 NHS 251 14.2 ⌸1,1 dominance tests for rural and urban areas in Toliara, Madagascar (differences between rural and urban dominance surfaces) 253 14.3 ⌸1,1 dominance tests for education and health in rural and urban Madagascar 255 14.4 ⌸2,2 dominance tests for education and health for males and females in Madagascar 256 14.5 Poverty comparisons for income and happiness, Great Britain, 1994 vs 2002 257

Figures 1.1 Aggregate poverty line approach weak focus extreme poverty, equal weight 13 1.2 Aggregate poverty line approach weak focus extreme poverty, equal weight 13 1.3 Aggregate poverty line approach strong focus extreme poverty, equal weight 14 1.4 Aggregate poverty line approach strong focus extreme poverty, equal weight 14 1.5 Component poverty line approach strong focus extreme poverty, equal weight 15 1.6 Component poverty line approach strong focus extreme poverty, equal weight 15 1.7 Aggregate poverty line approach weak focus extreme poverty, equal weight. Magnified version of Figure 1.2 16 1.8 Aggregate poverty line approach strong focus extreme poverty, equal weight. Magnified version of Figure 1.4 16 x List of Tables and Figures

1.9 Component poverty line approach strong focus extreme poverty, equal weight. Magnified version of Figure 1.4 17 1.A1 CDFs for univariate distributions 23 1.A2 CDFs of aggregated well-being. First Approach (Weak Focus) – Equal weight 27 1.A3 CDFs of aggregated well-being. First Approach (Strong Focus) – Equal weight 28 1.A4 CDFs of aggregated well-being. Second Approach (Strong Focus) – Equal weight 29 2.1 Membership functions used by Cheli and Lemmi (1995), and Betti and Verma (1999) 33 4.A1 Scree diagram for 2001 factor analysis 78 4.A2 Dendrogram for 2001 cluster analysis 78 5.1a Mean Composite indicator by province/region MIMAP CBMS Survey 1999 92 5.1b Income per capita by province/region MIMAP CBMS Survey 1999 92 5.2a Vietnam consumption poverty rate, 1993–2002 95 5.2b Vietnam human & physical asset poverty rate, 1993–2002 95 5.2c Vietnam poverty rate, 1993–2002 95 5.2d Vietnam rural/urban poverty rate, 1993–2002 96 5.2e Northern Uplands poverty rate, 1993–2002 96 5.2f Red River Delta poverty rate, 1993–2002 97 5.2g North Central poverty rate, 1993–2002 97 5.2h Central Coast poverty rate, 1993–2002 97 5.2i Central Highlands poverty rate, 1993–2002 98 5.2j South East poverty rate, 1993–2002 98 5.2k Mekong River Delta poverty rate, 1993–2002 98 5.3 Regional poverty rate differentials, 1993–2002 99 5.4a Gini coefficient for consumption and composite indicators, 1992–2002 Vietnam 99 5.4b Gini coefficient for consumption and composite indicators, 1992–2002 Vietnam 99 5.4c Gini coefficient for consumption and composite indicators, 1992–2002 North Vietnam 100 5.4d Gini coefficient for consumption and composite poverty indicators, 1992–2002 Centre Vietnam 100 5.4e Gini coefficient for consumption and composite indicators, 1992–2002 South Vietnam 100 6.1 Identifying the poor using income, consumption and the multiple indicator index. A Venn diagram for 1990 data 114 6.2 Identifying the poor using income, consumption and the multiple indicator index. A Venn diagram for 1998 data 115 8.1 Satisfaction question module 138 8.2 The two-layer model 143 List of Tables and Figures xi

9.1 The output distance function 156 9.2 The input distance function 158 9.3 Density estimates of dimensions and well-being 163 9.4 Poverty (head-count) for various poverty line definitions 167 10.1 Two welfare measures for six hypothetical households 180 10.2 Distance measures to welfare of best- and worst-off household 181 10.3 Lower convex and upper monotone hulls for hypothetical data 183 10.4 Example of Rawlsian lower bound and poverty frontiers 185 10.5 Deprivation indices (–D) for 1997 and 2003 189 12.1 Homicide rate (per 100 thousand). Colombia, 1996–2005 214 14.1 Poverty incidence curves, urban and rural areas of Uganda, 1999 246 14.2 Bidimensional poverty dominance surface 248 14.3 Intersection, union, and intermediate dominance test domains 249 14.4 Aggregating with the human development index 253 14.5 Difference in two-dimensional dominance surfaces 255 Foreword

The International Poverty Centre (IPC) is one of the three global thematic facilities that has been established by the United Nations Development Programme (UNDP) to bring knowledge-based development services closer to country partners around the world. The IPC has been built on a partnership between UNDP and the Government of Brazil’s Institute of Applied Economic Research (IPEA). Its main goals are to expand the knowledge and capacity of developing countries to design and implement effective human development policies, to facilitate knowledge sharing through South–South cooperation for the reduction of poverty and to pro- mote global debates to improve our understanding of development and the achieve- ments of the Millennium Development Goals. The IPC, which is almost three years old, is fully immersed in a global agenda aim- ing to reduce poverty. It took a major initiative in organizing an international conference on ‘Many Dimensions of Poverty’, which took place in Brasilia on 29–31 August 2005. More than forty papers were presented by participants from all parts of the world. Although the majority of the papers were of very high quality, the IPC could only publish selected 26 papers in two books. The present book, entitled ‘Quantitative Approaches to Multidimensional Poverty Measurement’, offers the reader quite a complete review of the various techniques to derive multidimensional measures of poverty, while the other book is mainly focused on the conceptual issues one faces when defining the dimensions of poverty. Amartya Sen’s seminal 1976 paper should certainly be considered as the study which launched the field of poverty measurement, although clearly poverty indices such as the headcount, the income gap ratio and even Watts’ (1968) index were used before Sen proposed his measure. Following Sen’s paper numerous studies, whether theoretical or empirical, have attempted to measure poverty, the one with the great- est impact being probably the famous Foster, Greer and Thorbecke (1984) paper. It is only much later that attempts were made to derive multidimensional measures of poverty. Such a shift of emphasis could not have taken place without Sen’s (1985) conceptual framework for a multidimensional approach to poverty, stressing the notions of functionings and capabilities. Such a move towards a multidimensional approach to poverty measurement was, however, made easier by progress that took place in the field of multidimensional inequality measurement (see, for example, the contributions of Kolm, 1977; Atkinson and Bourguignon, 1982; and Maasoumi, 1986). The chapters in this book cannot represent the final state of the art in the field of multidimensional poverty measurement because there is presently a growing amount of research devoted to this issue and one may expect that important new advances will take place in the coming years. This book is, however, unique in that it offers the reader a very wide coverage of the various approaches that have appeared in the literature. I am quite convinced that even people working in the field will

xii Foreword xiii discover techniques they were hitherto unaware of. This, for example, could be the case of the Rasch model of which people who are not psychologists may have never heard, or even of the fuzzy approach to poverty which for many years has been popular in Italy but much less so in the Anglo-Saxon world. The application of efficiency analysis to poverty measurement may also be new for some readers who have not closely followed the literature on productivity measurement. I believe therefore that a book on the ‘Multidimensional Approaches to Poverty Measurement’ is first of all timely because it offers a survey of so many different approaches to multidimensional poverty measurement. Such a book should also provide a unique opportunity for researchers in the field to compare the various approaches so that eventually a consensus will emerge to determine the most attract- ive approach. Reading this book is hence a ‘must’ for anybody working in the field.

NORA LUSTIG SHAPIRO VISITING PROFESSOR ELLIOTT SCHOOL OF INTERNATIONAL AFFAIRS GEORGE WASHINGTON UNIVERSITY DIRECTOR, POVERTY GROUP BUREAU OF DEVELOPMENT POLICY UNITED NATIONS DEVELOPMENT PROGRAMME Preface

Poverty reduction has become an overriding goal of development policy. To inform policy, research on poverty has focused on income or consumption-based poverty measures. But the most important development of poverty research in recent years is certainly the shift of emphasis from a uni- to a multi-dimensional approach to poverty. Poverty is now defined as a human condition that reflects failures in many dimensions of human life such as hunger, ill health, malnutri- tion, unemployment, inadequate shelter, lack of education, vulnerability, power- lessness, social exclusion and so on. Poverty is not only multidimensional but also multidisciplinary. Recognising the importance of multidimensional and multidisciplinary nature of poverty, the International Poverty Centre took a major initiative in organizing an international conference on ‘The Many Dimensions of Poverty’, which took place in Brasilia on 29–31 August 2005. The initial idea of holding such a conference came from Professor Jacques Silber and I, as Director of the International Poverty Centre, implemented it. I wish to express my gratitude to Jacques, who put enormous efforts in bringing together a group of about fifty internationally renowned scholars in the field. More than forty papers were presented by participants from all parts of the world. Although the majority of papers were of very high quality and often reported on very original research, we could only publish 26 selected papers in two books. The present book, entitled ‘Quantitative Approaches to Multidimensional Poverty Measurement’, offers the reader quite a complete review of the various techniques allowing deriving multidimensional measures of poverty while the other book is mainly focused on conceptual issues one faces when defining the dimensions of poverty. The UNDP requires that all its publications be peer reviewed. I am grateful to Professor Daniel Slottje for providing an excellent overall review of this book. He made very thoughtful comments on every paper. The earlier versions of the papers presented at the conference have been revised in the light of comments made by the reviewer. In his review, Professor Slottje writes that ‘this book brings together, in one place, diverse empirical approaches to measuring and analyzing multidimensional poverty. This book should certainly be published. The collection of international contributors is superb and representative of a true world body. The quality of the papers is almost uniformly excellent and reflects, as one would expect it to, top flight work by top flight academics and researchers.’ The organization of an international conference is a major undertaking. I am indeed grateful to many people, who put wholehearted efforts in the organization of the conference on ‘Many Dimensions of Poverty’. I owe special thanks to Eduardo Zepeda, Sandra Viergever, Marcelo Medeuros, Hyun Son, Fabiane Florencio, Fabio Veras, Rafael Osorio, Andre Lyra, Francisco Filho, Joana Costa and Dimitri Silva.

xiv Preface xv

I am particularly grateful to Roberto Astorino, who provided excellent expert assist- ance in taking care of the technical aspects of the book. Finally, I express my gratitude to Nora Lustig and Terry McKinley for supporting the publication of this book.

NANAK KAKWANI List of Contributors

Ramses Abul Naga, University of Lausanne, Lausanne, Switzerland

Gordon Anderson, University of Toronto, Toronto, Canada

Louis-Marie Asselin, Institut de Mathématique C.F. Gauss and CIRPÉE Centre, Laval, Canada

Enrico Bolzani, Swiss Federal Department of Foreign Affairs, Bern, Switzerland

Gianni Betti, University of Siena, Siena, Italy

Bruno Cheli, University of Pisa, Siena, Italy

Satya R. Chakravarty, Indian Statistical Institute, Kolkata, India

Ian Crawford, University of Surrey, Guildford, Surrey, and Institute for Fiscal Studies, London, UK

Joseph Deutsch, Bar-Ilan University, Ramat-Gan, Israel

Paul Dickes, University of Nancy II, Nancy, France

Jean-Yves Duclos, Department of Economics, Université Laval, Ste-Foy, Canada

Ada Ferrer-I-Carbonell, Institucio Catalana de Recerca i Estudis, Barcelona and Institut d’Anàlis: Econòmica (CSIC), Bellaterra (Barcelona), Spain

Giovanni Ferro Luzzi, University of Geneva, Geneva, Switzerland

Yves Flückiger, University of Geneva, Geneva, Switzerland

Alessio Fusco, CEPS/INSTEAD, Luxembourg

Jaya Krishnakumar, University of Geneva, Geneva, Switzerland

Andrew Leicester, Institute for Fiscal Studies, London, UK

Achille Lemmi, University of Siena, Siena, Italy

Ana Lugo Maria, University of Oxford, Oxford, UK

xvi List of Contributors xvii

Esfandiar Maasoumi, Southern Methodist University, Dallas, USA

Bernard van Praag, University of Amsterdam, Amsterdam, The Netherlands

Xavi Ramos, Universitat Autònoma de Barcelona, Bellaterra (Barcelona) Spain

Marco Robles, Inter-American Development Bank, Washington DC, USA

David Sahn, Cornell University, Ithaca, NY, USA

Carlos Eduardo Vélez, Inter-American Development Bank, Washington DC, USA

Vijay Verma, University of Siena, Siena, Italy

Vu Tuan Anh, Vietnam Institute of Economics, Vietnam

Sylvain Weber, Geneva School of Business Administration (HEG), Geneva, Switzerland, and University of Applied Sciences of Western Switzerland (HES SO), Switzerland

Stephen D. Younger, Cornell University, Ithaca, NY, USA Introduction: On Quantitative Approaches to Multidimensional Poverty Measurement Nanak Kakwani and Jacques Silber

On 29–31 August 2005 took place in Brasilia an international Conference on The Many Dimensions of Poverty. This conference was organized by the International Poverty Centre (IPC), one of the three global thematic facilities created by the United Nations Development Programme (UNDP) to bring knowledge-based development services closer to country partners around the world. Most of the chapters in the present book are updated versions of some of the papers that were given at this conference, although three chapters cover material which was not available at that time. As should be clear from the title, the goal of this book is to give the reader an account as complete as possible of the various quantitative approaches that have appeared hitherto in the literature on the measurement of multidimensional poverty. Thorbecke (2007) has argued that ‘most of the remaining unresolved issues in poverty analysis are related directly or indirectly to the multi-dimensional nature and dynamics of poverty. Before the Development Community can become more successful in designing and implementing poverty-alleviation strategies, within the context of growth, we need to identify and understand better the various dimensions of poverty and how the latter interact over time and across space.’ There can be no better way of emphasizing the importance of multidimensional poverty measurement. Thorbecke (2007), however, does not hide the difficulties one faces when attempting to provide measures of multidimensional poverty. In his words,

to ascertain poverty and make poverty comparisons within a multi-dimensional framework require the approximation of a welfare function that includes the specification of the relative welfare weights and conveys information about the direct marginal benefits of each attribute and about the interaction among these attributes. In particular this last requirement represents a tall order. It is difficult enough estimating the direct (individual) benefits, let alone the multiple and often complex interactions among sets of attributes. The latter can be substitutes or complements. On the one hand, if dimensions are substitutes, it means that a person can trade-off one attribute for another (say more food for less clothing) and remain on the same iso-utility curve. On the other hand, if attributes are complements, an increase in the amount of one raises the marginal utility of the other (more education increases the present discounted value of the future stream of income). It is also possible that some combinations of poverty dimensions are neither substitutes nor complements.

xviii Introduction xix

The obstacles to multidimensional poverty measurement that have just been men- tioned do certainly not represent an exhaustive list of all the difficulties faced by researchers in this field. The present book is nevertheless testimony to the fact that during the past decade or so important progress has been made. The first chapter in this book is devoted to the potential contribution of information theory to multidimensional poverty measurement. As indicated by the authors, Esfandiar Maasoumi and Maria Ana Lugo, measures of multivariate well- being (or ill-being), such as poverty or inequality, are scalar functions of matrices of several attributes associated with a number of individuals or households. This entails ‘aggregation’ over individuals as well as attributes and hence implies that a set of weights be attached to each individual, and normative decisions be taken about the weight to be given to each attribute, as well as the relation between the attributes as, perhaps, substitutes or complements. For Maasoumi and Lugo information theory aggregation methods have the advantage of being explicit about such normative choices. Furthermore according to axiomatically well developed measures of divergence in information theory, the measures such an approach proposes should be considered as ‘ideal’. A completely different view is taken by Gianni Betti, Bruno Cheli, Achille Lemmi and Vijay Verma in the second chapter of this volume which offers a survey of the so-called ‘Fuzzy’ approach to multidimensional poverty measurement that started in the early 1990s. The idea is that defining as poor those who are below some poverty line and as non-poor those that are above, implies a binary classification that cannot take into account borderline cases, those whose income or expenditures are close to the poverty line. Once the population is no longer divided into poor and non-poor individuals, particular attention has to be given to the concept of membership function, that is, to the degree of poverty of every individual in each dimension of poverty. The authors discuss the important issues of correctly defining the complementarity between and the intersection, union and aggregation of the various dimensions of poverty. They also stress the need to appropriately charac- terize longitudinal measures of poverty, making a distinction between the persistent or transient nature of poverty and movement into and out of the state of poverty. An empirical illustration based on Italian data complements their analysis. The following five chapters of this volume cover various latent variables approaches to multidimensional poverty measurement. Chapter 3, written by Alessio Fusco and Paul Dickes, shows how the so-called Rasch model, which is commonly used in the field of psychometrics, can be applied to poverty measurement. They devote particular attention to two important aspects of poverty measurement, the number of dimensions to be selected and the nature of the underlying continuum. They first argue that the Rasch model offers a way of confirming or rejecting the hypothesis that poverty is unidimensional. Then they discuss the question of the nature of the continuum, asking whether the relationship between the items in each dimension is homogeneous or hierarchical. In the latter case it would imply that poverty consists in accumulating disadvantages so that if a person suffers from a very severe deprivation, he/she will also suffer from other, less severe deprivations. Here again they show that the Rasch model helps verifying the hierarchical and xx Introduction cumulative nature of the relationship between the items. An empirical illustration, based on a data set from Luxembourg, confirms in fact the multidimensional nature of poverty. Chapter 4, written by Yves Flückiger, Sylvain Weber and Giovanni Ferro Luzzi, shows how Factor and Cluster Analysis can be used to analyse multidimensional poverty. Factor analysis is used in a first step to construct poverty indicators based on many possible dimensions without posing too many a priori restrictions. The base variables are thus combined to produce common factors which convey some aspect of multidimensional poverty. By ascribing individual scores on each factor, the authors, in a second stage, use cluster analysis to determine population sub- groups that are unevenly affected by the various dimensions of poverty, what allows them to identify the poor. A logit regression is finally estimated to find the determinants of poverty. The empirical illustration is based on five waves (1999 to 2003) of the Swiss Household Panel (SHP) which is very similar to the European Community Household Survey. In Chapter 5, Louis-Marie Asselin and Vu Tuan Anh describe another latent variable approach, the so-called Multiple Correspondence Analysis (MCA). Their idea is that since concepts of multidimensional poverty are frequently measured with qualitative ordinal indicators, for which traditional principal components analysis (PCA) is a priori not an optimal approach, looking for a similar but more appro- priate factorial technique is justified. This Multiple Correspondence Analysis, designed in the 1960s and 1970s, goes beyond the principal component analysis approach by providing more powerful description tools of the hidden structure in a set of qualitative variables. The chapter shows how this technique may be used to construct a composite indicator from multiple primary poverty indicators and then to compute poverty indices on the basis of this composite indicator. This methodology is then applied to Vietnamese data to analyze the dynamics of poverty during the period 1992–2002. In Chapter 6, Ramses Abul Naga and Enrico Bolzani explain how another latent variable approach, the so-called multiple indicators and multiple causes model (MIMIC), may be used to measure poverty. They use a traditional life-cycle model consumption to obtain an empirical framework for the joint dependence of household income and consumption on permanent income. Predictors of the latter variable are obtained using welfare indicators, determinants of long-run income and sociodemographic variables. For their empirical investigation they employ data from two household surveys carried out by the Swiss Federal Statistical Office, a household consumption survey carried out in 1990 and a follow-up survey carried out in 1998. The methodology yields interesting insights about the sensitivity of resource definitions when it comes to the identification of the poor population. Although there is a substantial share of the poor population which household income, consumption and permanent income jointly identify as being poor, it is also the case that each separate indicator identifies groups of households as being in poverty when these same households cross the poverty line in other dimensions of well-being. This is the case for the two mostly commonly used indicators of well-being, namely income and consumption, but also for the permanent income Introduction xxi indicators discussed in this chapter. The authors conclude that there is hence some potentially new information about the incidence of poverty to be obtained from permanent income indices. Chapter 7, written by Jaya Krishnakumar, is the final chapter in this volume to take a latent variables approach to multidimensional poverty measurement. Krishnakumar begins by a review of the theory and practice of multidimensional indices of human development (or deprivation) based on latent variable models, summarizing simple procedures like factor analysis as well as more complex for- mulations such as the structural equations model. She argues, in fact, that the structural equations model is the most suitable framework for representing the interdependent nature of the different dimensions of well-being while accounting for the impossibility of their direct measurement. Applications of these method- ologies, in particular of the structural equations model, in the field of welfare and poverty measurement are discussed, highlighting their main features and findings. The approach taken in Chapter 8 is quite different. Its authors, Bernard van Praag and Ada Ferrer-i-Carbonell, address two key issues in modern policy-oriented poverty research. First, they consider that poverty is an individual feeling and not an objective status, describable in terms of commands over goods. This leads them to derive an operational definition of subjective poverty as being below a certain degree of satisfaction with the situation one is in. Secondly, they distinguish several domains of life, and consequently, several types of poverty, each pertaining to a specific life domain. To implement their approach the authors recommend using an Ordered Probit- related method that makes use of the cardinal information that can be derived from the satisfaction questions. They thus argue that if somebody is evaluating his satisfaction level by a ‘7’, one may assume that this ‘7’ has a cardinal significance, in the sense that all respondents who are satisfied for a 7 feel satisfied for 70 per cent compared to the best conceivable situation, assuming a scale from zero to ten. Van Praag and Ferrer-i-Carbonell analysed poverty with respect to six domains of satisfaction and thus defined an overall poverty concept as an amalgam of domain poverties. The proposed methodology is applied to German panel data (GSOEP) and the authors found that, although the chance of being poor on one domain enhances the chances of being poor in another domain, it is justified to see poverty as a multidimensional concept. They conclude that satisfaction ‘with life as a whole’ can be seen as an aggregate of satisfactions with life domains, so that poverty ‘with life as a whole’ may be decomposed into poverty components with respect to life domains. The next two chapters in this book discuss a completely different approach which is borrowed from production theory and called efficiency analysis. In Chapter 9 Xavier Ramos shows how distance functions, a tool typically employed in production economics to measure the distance between a set of inputs and a set of outputs, can be employed to approximate a composite measure encompassing the many dimensions of well-being. The analysis is conducted in two stages. First, to estimate the level of achievement in a given dimension of well-being input distance functions are used, the inputs being variables that are supposed to determine the corresponding dimension of well-being. Then, in a second stage, the overall xxii Introduction level of well-being is estimated via an output function whose components are the various dimensions of well-being estimated in the previous stage. Econometric techniques such as corrected least squares are used to derive the levels of well- being in the various dimensions as well as the overall level of well-being. The empirical illustration uses data from Catalonia, the extent of poverty being com- puted on the basis of the distribution of the variable measuring overall well-being. The results are compared with those obtained when using income alone to estimate poverty. Efficiency analysis is also the angle under which Gordon Anderson, Ian Crawford and Andrew Liecester look at well-being in Chapter 10. They use, however, a different technique called the Lower Convex Hull Approach. A deprivation index relative to the lower convex hull of the joint distribution of a collection of characteristics or goods is constructed which provides some insights into the notion of multivariate relative welfare and poverty. The lower convex hull has a useful interpretation in the poverty context as the ‘Rawlsian’ frontier in the sense that no agent can be found that would be poorer than those defined by the lower convex hull. This technique is then applied by the authors to World Bank data on the components of the Human Development Index for the years 1997 and 2003 for a panel of 170 countries. Anderson, Crawford and Liecester conclude that, excluding the extremely poor nations, there have been improvements in the plight of poor countries. The next two chapters discuss and use axiomatically derived multidimensional poverty indices. In Chapter 11 Satya Chakravarty and Jacques Silber first present the basic axioms that are used in deriving multidimensional poverty indices. They then discuss some important indices that have appeared in the literature such as the multidimensional generalizations of the Foster-Greer and Thorbecke (FGT), the Chakravarty and the Watts unidimensional poverty indices. Particular attention is devoted to the decomposability properties of these indices. A characterization of a multidimensional extension of the Watts (1968) index is also provided. The chapter ends by giving an empirical illustration based on world data on per capita GDP, life expectancy and literacy rates for the years 1993 and 2002. The data, taken from the Human Development Reports, were available for 169 countries. As ‘poverty thresholds’ the authors selected $3 and $5 a day for the per capita GDP and 60 and 70 years for the life expectancy. Various weights were also given to these two dimensions. Chakravarty and Silber conclude that among what the Human Development Reports defines as Low Human Development countries poverty is higher when a greater weight is given to the life expectancy dimension. It is also higher when the per capita GDP threshold is raised from $3 to $5 a day than when the life expectancy threshold rises from 60 to 70 years. Chapter 12 was written by Carlos Eduardo Velez and Marcos Robles. To measure multidimensional poverty, the authors use the same indices as those discussed in the previous chapter. What makes their approach original is that they suggest a technique that may help choose the value of the parameters describing the degree of aversion to extreme poverty or inequality and of complementarity or substitu- tion between the different dimensions of poverty and deprivation. Their idea is to Introduction xxiii select the parameters that correspond to the cases where the multidimensional poverty indices they use will show changes in poverty that will be similar to those one would infer on the basis of the evolution of self-reported well-being. The empirical illustration is based on Colombian data for the period 1997–2003 and uses three dimensions of poverty – income poverty, education and a variable describing how safe the individuals feel in the area in which they live. The authors conclude that the negative effects on well-being induced by the lower per capita consumption which followed the economic recession of the late 1990s were more than compensated by the increasing progressiveness of the implicit subsidies afforded by the social programmes and the improvement in the educational endowments of household heads. They also conjecture that the substantial security improvements that took place after 2003 have been discounted by Colombians and this could explain the remaining gap between what self-reports on well-being and multidimensional poverty measures indicate. Chapter 13 was written by Joseph Deutsch and Jacques Silber. Their proposition is to measure the wealth of households on the basis of the order of acquisition of durable goods or, more generally, assets. This idea was originally suggested in the mid-1960s, but the authors combine it with an ordered logit regression type of analysis to derive the determinants of multidimensional poverty. The empirical illustration is based on the 1995 Census of the Israeli population. The technique presented in this chapter should be relevant to development economists who use an asset approach to poverty. It might also be relevant to researchers interested in checking whether there exists also an order of ‘dis-acquisition’ of assets and/or of ‘dis-connection’ from society when a process of impoverishment and of deterioration of the social status of the individuals leads them to become ‘socially excluded’. The last chapter of this volume, written by Jean-Yves Duclos, David Sahn and Stephen Younger, explains how to make poverty comparisons using multidimensional indicators of well-being. It shows, in particular, how to check whether the comparisons are robust to aggregation procedures and to the choice of multidimensional poverty lines. The proposed method applies equally well to what can be defined as ‘union’, ‘intersection’ and ‘intermediate’ approaches to dealing with multidimensional indicators of well-being. The authors derive also the sampling distribution of various multidimensional poverty estimators, including estimators of the ‘critical’ poverty frontiers outside which multidimensional poverty comparisons can no longer be deemed to be ethically robust. The results are illustrated using data from various developing countries. The papers in this volume are not a survey of a definitive state of the art in the field. It is likely that the competition of ideas and some evolutionary process will lead to a situation, a few years from now, where some of the techniques developed in this book will have been considered as inadequate for the task at hand. Our goal is simply to contribute to the debate concerning multidimensional poverty measurement. Progress in this domain will not be possible if the various approaches available are not known to those working in the field. Unfortunately, it is our belief that several of them have been completely ignored by many specialists. This xxiv Introduction volume represents therefore a unique opportunity to become familiar with the present state of the knowledge.

Reference

Thorbecke, E. (2007) ‘Multi-dimensional Poverty: Conceptual and Measurement Issues’, in Nanak Kakwani and Jacques Silber (eds), The Many Dimensions of Poverty. Basingstoke: Palgrave Macmillan.