
Analyzing Multidimensional Well-Being
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"An indispensable reference for all researchers interested in the measurement of social welfare. . ."
-François Bourguignon, Emeritus Professor at Paris School of Economics, Former Chief Economist of the World Bank.
". . .a detailed, insightful, and pedagogical presentation of the theoretical grounds of multidimensional well-being, inequality, and poverty measurement. Any student, researcher, and practitioner interested in the multidimensional approach should begin their journey into such a fascinating theme with this wonderful book."
-François Maniquet, Professor, Catholic University of Louvain, Belgium.
A Review of the Multidimensional Approaches to the Measurement of Welfare, Inequality, and Poverty
Analyzing Multidimensional Well-Being: A Quantitative Approach offers a comprehensive approach to the measurement of well-being that includes characteristics such as income, health, literacy, and housing. The author presents a systematic comparison of the alternative approaches to the measurement of multidimensional welfare, inequality, poverty, and vulnerability. The text contains real-life applications of some multidimensional aggregations (most of which have been designed by international organizations such as the United Nations
Development Program and the Organization for Economic Co-operation and Development) that help to judge the performance of a country in the various dimensions of well-being.
The text offers an evaluation of how well a society is doing with respect to achievements of all the individuals in the dimensions considered and clearly investigates how achievements in the dimensions can be evaluated from different perspectives. The author includes a detailed scrutiny of alternative techniques for setting weights to individual dimensional metrics and offers an extensive analysis into both the descriptive and welfare theoretical approaches to the concerned multi-attribute measurement and related issues. This important resource:
. Contains a synthesis of multidimensional welfare, inequality, poverty, and vulnerability analysis
. Examines aggregations of achievement levels in the concerned dimensions of well-being from various standpoints
. Shows how to measure poverty using panel data instead of restricting attention to a single period and when we have imprecise information on dimensional achievements
. Argues that multidimensional analysis is intrinsically different from marginal distributions-based analysis
Written for students, teachers, researchers, and scholars, Analyzing Multidimensional Well-Being: A Quantitative Approach puts the focus on various approaches to the measurementof the many aspects of well-being and quality of life.
Satya R. Chakravarty is a Professor of Economics at the Indian Statistical Institute, Kolkata, India. He is an Editor of Social Choice and Welfare and a member of the Editorial Board of Journal of Economic Inequality.
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Satya R. Chakravarty is a Professor of Economics at the Indian Statistical Institute, Kolkata, India. He is an Editor of Social Choice and Welfare and a member of the Editorial Board of Journal of Economic Inequality.
Content
Preface xi
Endorsements xv
1 Well-Being as a Multidimensional Phenomenon 1
1.1 Introduction 1
1.2 Income as a Dimension ofWell-Being and Some Related Aggregations 4
1.3 Scales of Measurement: A Brief Exposition 10
1.4 Preliminaries for MultidimensionalWelfare Analysis 11
1.5 The Dashboard Approach andWeights on DimensionalMetrics in a Composite Index 14
1.6 MultidimensionalWelfare Function Axioms 17
1.6.1 Invariance Axioms 17
1.6.2 Distributional Axioms 19
1.7 MultidimensionalWelfare Functions 27
1.8 Concluding Remarks 37
References 38
2 An Overview of Multidimensional Economic Inequality 49
2.1 Introduction 49
2.2 A Review of One-DimensionalMeasurement 51
2.2.1 Normative One-Dimensional Inequality Indices 51
2.2.2 Subgroup-Decomposable Indices of Inequality 53
2.3 Multidimensional Inequality Indices 56
2.3.1 The Direct Approach 56
2.3.1.1 Axioms for a Multidimensional Inequality Index 56
2.3.1.2 Examples of Indices 60
2.3.2 The Inclusive Measure ofWell-being Approach 69
2.4 Concluding Remarks 77
References 78
3 A Synthesis of Multidimensional Poverty 85
3.1 Introduction 85
3.2 A Brief Review of One-Dimensional Analysis 89
3.3 Preliminaries for Multidimensional Poverty Analysis 93
3.4 Identification of the Poor and Deprivation Counting 95
3.5 Axioms for a Multidimensional Poverty Metric 99
3.5.1 Invariance Axioms 100
3.5.2 Distributional Axioms 103
3.5.3 Decomposability Axioms 108
3.5.4 Threshold Limit Sensitivity Axiom 111
3.5.5 Technical Axioms 112
3.6 Multidimensional Poverty Measurement 113
3.6.1 The Dashboard Approach 113
3.6.2 The Direct Approach 117
3.6.3 The Inclusive Measure ofWell-being Approach 123
3.7 Multidimensional Poverty Orderings 125
3.7.1 A Brief Outline of One-Dimensional Orderings 126
3.7.2 Multidimensional Orderings 129
3.8 Dimensions ofWell-Being with Ordinal Significance and Multidimensional Poverty 131
3.9 Orderings Based on Deprivations Counts 134
3.10 Multidimensional Material Deprivation 138
3.11 Concluding Remarks 142
References 143
4 Fuzzy Set Approaches to the Measurement of Multidimensional Poverty 163
4.1 Introduction 163
4.2 Fuzzy Membership Function 165
4.3 Axioms for a Fuzzy Multidimensional Poverty Index 173
4.3.1 Invariance Axioms 175
4.3.1.1 Fuzzy Strong Ratio Scale Invariance 175
4.3.1.2 Fuzzy Strong Translation Scale Invariance 177
4.3.1.3 FuzzyWeak Focus 177
4.3.1.4 Fuzzy Strong Focus 178
4.3.1.5 Fuzzy Symmetry 178
4.3.1.6 Fuzzy Population Replication Invariance 179
4.3.2 Distributional Axioms 179
4.3.2.1 Fuzzy Monotonicity 179
4.3.2.2 Fuzzy Monotonicity Sensitivity 180
4.3.2.3 Fuzzy DimensionalMonotonicity 181
4.3.2.4 Fuzzy Transfer 182
4.3.2.5 Increasing Fuzzy Poverty under Correlation-Increasing Switch 184
4.3.3 Decomposability Axioms 185
4.3.3.1 Fuzzy Subgroup Decomposability 185
4.3.3.2 Fuzzy Factor Decomposability 185
4.3.4 Fuzzy Sensitivity Axiom 186
4.3.4.1 Increasing Fuzzy Poverty for Increased Membership Function 186
4.3.5 Technical Axioms 187
4.3.5.1 Fuzzy Boundedness 187
4.3.5.2 Fuzzy Continuity 187
4.4 Fuzzy Multidimensional Poverty Indices 187
4.5 Fuzzy Poverty Orderings 191
4.6 Concluding Remarks 195
References 195
5 Poverty and Time: A Multidimensional Appraisal 201
5.1 Introduction 201
5.2 Preliminaries 207
5.3 The Block Approach 208
5.3.1 IndividualMultidimensional Intertemporal Poverty Index 208
5.3.2 Aggregate Multidimensional Intertemporal Poverty Index 218
5.3.3 A Review of Some Related One-Dimensional Proposals 220
5.4 An Exploration of the Counting Approaches to Multidimensional
Intertemporal Deprivations 226
5.5 The Multidimensional Duration Approach 229
5.5.1 A Review of One-Dimensional Duration-Reliant Offers 229
5.5.2 Axioms for a Chronic Multidimensional Poverty Quantifier 231
5.5.3 The Bourguignon-Chakravarty Approach to Chronic Multidimensional Poverty Measurement 240
5.6 Intertemporal Poverty Orderings 243
5.7 Concluding Remarks 245
References 246
6 Vulnerability to Poverty: A Multidimensional Evaluation 251
6.1 Introduction 251
6.2 A Review of One-DimensionalMeasurement 254
6.3 Multidimensional Representation of Vulnerability to Poverty: An Axiomatic Investigation 262
6.4 Concluding Remarks 269
References 271
7 An Exploration of Some Composite and Individualistic Indices 277
7.1 Introduction 277
7.2 Human Development Index 278
7.3 Human Poverty Index 284
7.4 Gender Inequality Index 286
7.5 Better Life Index 288
7.6 Active Citizenship Composite Index 291
7.7 Measuring Human Opportunity: A Counting Approach 293
7.8 Assessment of Progress toward Achievements in Millennium Development Goals 295
7.9 Air Quality Index 301
7.10 Concluding Remarks 303
References 304
Index 311
Chapter 1
Well-Being as a Multidimensional Phenomenon
1.1 Introduction
The choice of income as the only attribute or dimension of well-being of a population is inappropriate since it ignores heterogeneity across individuals in many other dimensions of living conditions. Each dimension represents a particular aspect of life about which people care. Examples of such dimensions include health, literacy, and housing. A person's achievement in a dimension indicates the extent of his performance in the dimension, for instance, how healthy he is, how friendly he is, how much is his monthly income, and so on.
Only income-dependent well-being quantifiers assume that individuals with the same level of income are regarded as equally well-off irrespective of their positions in such nonincome dimensions. In their report, prepared for the Commission on the Measurement of Economic Performance and Social Progress, constituted under a French Government initiative, Stiglitz et al. (2009, p. 14) wrote "To define what wellbeing means, a multidimensional definition has to be used. Based on academic research and a number of concrete initiatives developed around the world, the Commission has identified the following key dimensions that should be taken into account. At least in principle, these dimensions should be considered simultaneously: (i) Material living standards (income, consumption and wealth); (ii) Health; (iii) Education; (iv) Personal activities including work; (v) Political voice and governance; (vi) Social connections and relationships; (vii) Environment (present and future conditions); (viii) Insecurity, of an economic as well as a physical nature. All these dimensions shape people's wellbeing, and yet many of them are missed by conventional income measures."
The need for analysis of well-being from multidimensional perspectives has also been argued in many contributions to the literature, including those of Rawls (1971); Kolm (1977); Townsend (1979); Streeten (1981); Atkinson and Bourguignon (1982); Sen (1985); Stewart (1985); Doyal and Gough (1991); Ramsay (1992); Tsui (1995); Cummins (1996); Ravallion (1996); Brandolini and D'Alessio (1998); Narayan (2000); Nussbaum (2000); Osberg and Sharpe (2002); Atkinson (2003); Bourguignon and Chakravarty (2003); Savaglio (2006a,b); Weymark (2006); Thorbecke (2008), Lasso de la Vega et al. (2009), Fleurbaey and Blanchet (2013); Aaberge and Brandolini (2015), Alkire et al. (2015); Duclos and Tiberti (2016).1
Nonmonetary dimensions of well-being are not unambiguously perfectly correlated with income. Consider a situation where, in some municipality of a developing country, there is a suboptimal supply of a local public good, say, mosquito control program. A person with a high income may not be able to trade off his income to improve his position in this nonmarketed, nonincome dimension of well-being (see Chakravarty and Lugo, 2016 and Decancq and Schokkaert, 2016).
In the capability-functioning approach, the notion of human well-being is intrinsically multidimensional (Sen, 1985, 1992; Sen and Nussbaum, 1993; Nussbaum, 2000; Pogge, 2002; Robeyns, 2009). Following John Stuart Mill, Adam Smith, and Aristotle, in the last 30 years or so, it has been reinterpreted and popularized by Sen in a series of contributions. In this approach, the traditional notions of commodity and utility are replaced respectively with functioning and capability.
Any kind of activity done or a state acquired by a person and a characteristic related to full description of the person can be regarded as a functioning. Examples include being well nourished, being healthy, being educated, and interaction with friends. Such a list can be formally represented by a vector of functionings. Capability may be defined as a set of functioning vectors that the person could have achieved.
It is possible to make a distinction between a good and functioning on the basis of operational difference. Of two persons, each owning a bicycle, the one who is physically handicapped cannot use the bike to go to the workplace as fast as the other person can. The bicycle is a good, but possessing the skill to ride it as per convenience is a functioning. This indicates that a functioning can be enacted by a good, but they are distinct concepts. Consequently, these two persons, each owning a bicycle, are not able to attain the same functioning (see Basu and López-Calva, 2011). Since the physically handicapped person, who lacks sufficient freedom to ride the bike as per desire, has a smaller capability set than the other person.
As Sen argued in several contributions, there is a clear distinction between starvation and fasting. Two persons may be in the same nutritional state, but one person fasting on some religious ground, say, is better off than the other person who is starving because he is poor. Since the former person has the freedom not to starve, his capability set is larger than that of the poor person (see also Fleurbaey, 2006a). Consequently, capabilities become closely related to freedom, opportunity, and favorable circumstances.2
Once the identification step, the selection of dimensions for determining human well-being, is over, at the next stage, we face the aggregation problem. The second step involves the construction of a comprehensive measure of well-being by aggregating the dimensional attainments of all individuals in the society. One simple approach can be dimension-by-dimension evaluation, resulting in a dashboard of dimensional metrics. A dashboard is a portfolio of dimension-wise well-being indictors (see Atkinson et al., 2002).3 A dashboard can be employed to monitor each dimension in separation. But the dashboard approach has some disadvantages as well. In the words of Stiglitz et al. (2009, p. 63), "dashboards suffer because of their heterogeneity, at least in the case of very large and eclectic ones, and most lackindications about.hierarchies among the indicators used. Furthermore, as communications instruments, one frequent criticism is that they lack what has made GDP a success: the powerful attraction of a single headline figure that allows simple comparisons of socio-economic performance over time or across countries." The problem of heterogeneity across dimensional metrics can be taken care of by aggregating the dashboard-based measures into a composite index. The main disadvantage of this aggregation criterion is that it completely ignores relationships across dimensions. An alternative way to proceed toward building an all-inclusive measure of well-being is by clustering dimensional achievements across persons in terms of a real number. (See Ravallion, 2011, 2012, for a systematic comparison.)
The objective of this chapter is to evaluate how well a society is doing with respect to achievements of all the individuals in different dimensions. This is done using a social welfare function, which informs how well the society is doing when the distributions of dimensional achievements across different persons are considered. A social welfare function is regarded as a fundamental instrument in theoretical welfare economics. It has many policy-related applications. Examples include targeted equitable redistribution of income, assessment of environmental change, evaluation of health policy, cost-benefit analysis of a desired change, optimal provision of a public good, promoting goodness for future generations, assessment of legal affairs, and targeted poverty evaluation (see, among others, Balckorby et al., 2005; Adler, 2012, 2016; Boadway, 2016; Broome, 2016, and Weymark, 2016).
In order to make the chapter self-contained, in the next section, there will be a brief survey of univariate welfare measurement. Section 1.3 addresses the measurability problem of dimensional achievements. In other words, this section clearly investigates how achievements in different dimensions can be measured. Some basics for multivariate analysis of welfare are presented in Section 1.4. The concern of Section 1.5 is the dashboard approach to the evaluation of well-being. There will be a detailed scrutiny of alternative techniques for setting weights to individual dimensional metrics. In Section 1.6, there will be an analytical discussion on axioms for a multivariate welfare function. Each axiom is a representation of a property of a welfare measure that can be defended on its own merits. Often, axioms become helpful in narrowing down the choice of welfare measures. Section 1.7 studies welfare functions, including their information requirements, which have been proposed in the literature to assess multivariate distributions of well-being. Finally, Section 1.8 concludes the discussion.
1.2 Income as a Dimension of Well-Being and Some Related Aggregations
The measurement of multidimensional welfare originates from its univariate counterpart. In consequence, a short analytical treatment of one-dimensional welfare measurement at the outset will prepare the stage for our expositions in the following sections.
It is assumed before all else that no ambiguity arises with respect to definitions and related issues of the primary elements of the analysis. For instance, should the variable on which the analysis relies be income or expenditure? How is expenditure defined? What should be the reference period of observation of incomes/expenditure? How is the threshold income that represents a minimal standard of living determined (see Chapter 2)4? Generally, income data are collected at the household level. Income at the individual level can be obtained from the household income by employing an...
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