Satya R. Chakravarty

The Measurement of Multidimensional Poverty

Many authors have insisted on the necessity of defining poverty as a multidimensional concept rather than relying on income or consumption expenditures per capita. Yet, not much has actually been done to include the various dimensions of deprivation into the practical definition and measurement of poverty. Existing attempts along that direction consist of aggregating various attributes into a single index through some arbitrary function and defining a poverty line and associated poverty measures on the basis of that index. This is merely redefining more generally the concept of poverty, which then essentially remains a one dimensional concept. The present paper suggests that an alternative way to take into account the multi-dimensionality of poverty is to specify a poverty line for each dimension of poverty and to consider that a person is poor if he/she falls below at least one of these various lines. The paper then explores how to combine these various poverty lines and associated one-dimensional gaps into multidimensional poverty measures. An application of these measures to the rural population in Brazil is also given with poverty defined on income and education.

Ethical social index numbers

1: On Quasi-Orderings of Income Profiles.- 1.1 Introduction.- 1.2 Social Evaluation (Welfare) Functions and their Arguments.- 1.3 Some Definitions.- 1.4 The Lorenz Quasi-Ordering.- 1.5 Some Alternative Quasi-Orderings.- 1.6 Concluding Remarks.- 2: Ethical Indices of Inequality.- 2.1 Introduction.- 2.2 Postulates for the Selection of an Index of Inequality.- 2.3 Cardinally Significant Ethical Indices of Relative Inequality.- 2.4 Cardinally Significant Ethical Indices of Absolute and Intermediate Inequality.- 2.5 Inequality as an Ordinal Concept.- 2.6 Decomposition of Inequality Indices by Population Subgroups and by Factor Components.- 2.7 Concluding Remarks.- 3: The Gini Indices of Inequality.- 3.1 Introduction.- 3.2 A Formal Definition of the Lorenz Curve for a Continuum of Population.- 3.3 A General Definition of the Lorenz Curve.- 3.4 An Extension of the Gini Index of Relative Inequality.- 3.5 Alternative Generalisations of the Gini Index.- 3.6 Empirical Estimation of Inequality Indices from Grouped Data.- 3.7 Concluding Remarks.- 4: Ethical Indices of Distance Between Income Profiles.- 4.1 Introduction.- 4.2 Ethically Coherent Distance Functions.- 4.3 A Characterisation Theorem.- 4.4 Concluding Remarks.- 5: The Measurement of Relative Deprivation.- 5.1 Introduction.- 5.2 A Simple Index of Relative Deprivation and the Implied Welfare Ordering.- 5.3 Ethical Indices of Relative Deprivation.- 5.4 Concluding Remarks.- 6: Ethically Flexible Indices of Poverty.- 6.1 Introduction.- 6.2 Properties for an Index of Poverty.- 6.3 Relative Indices of Poverty.- 6.4 Absolute Indices of Poverty.- 6.5 Concluding Remarks.- 7: Additively Decomposable Indices of Poverty.- 7.1 Introduction.- 7.2 Decomposability.- 7.3 Additively Decomposable Indices of Poverty.- 7.4 Empirical Estimation of Poverty Indices from Grouped Data.- 7.5 Concluding Remarks.- 8: Measurement of Tax Progressivity and Horizontal Inequity.- 8.1 Introduction.- 8.2 Indices of Local Progression.- 8.3 An Ethical Index of Global Tax Progressivity.- 8.4 Ethical Indices for the Measurement of Horizontal Inequity.- 8.5 Alternative Indices of Tax Progressivity and Horizontal Inequity.- 8.6 Concluding Remarks.- 9: Ethical Indices of Income Mobility.- 9.1 Introduction.- 9.2 Ethical Indices of Relative Mobility.- 9.3 Alternative Concepts of Mobility.- 9.4 Concluding Remarks.- Extended Bibliography.

A new index of poverty

This paper introduces a new index of poverty. The index satisfies all the axioms for ‘a good index of poverty’.

The Measurement of Social Exclusion

This paper develops an axiomatic approach to the measurement of social exclusion. At the individual level, social exclusion is viewed in terms of deprivation of the person concerned with respect to different functionings in the society. At the aggregate level we treat social exclusion as a function of individual exclusions. The class of subgroup decomposable social exclusion measures using a set of independent axioms is identified. We then look at the problem of ranking exclusion profiles by exclusion dominance principle under certain restrictions. Finally, applications of decomposable and non-decomposable measures suggested in the paper using European Union and Italian data are also considered.

A Generalized Human Development Index

The human development index indicates achievement in the living standard of a population in terms of attainment levels of different quality-of-life attributes, such as educational attainment and life expectancy at birth. This paper axiomatically characterizes a general measure of achievement. This achievement index, which contains the UNDP human development index as a special case, can be regarded as a generalized human development index. The general index allows calculation of the percentage contributions of individual attributes to overall achievement and hence to identify the attributes that are more/less susceptible to achievement. This kind of breakdown becomes important from a policy point of view. The paper provides an empirical illustration of the axiomatically characterized indices. Copyright Blackwell Publishing Ltd 2003

Ethical índices of Income Mobility

Ethical indices of income mobility measure the change in welfare resulting from mobility. The concept of mobility we explore consists of a welfare comparison between the actual time path of the income distribution with a hypothetical time path obtained by supposing that starting from the actual first-period distribution, the remaining income receipts exhibit complete immobility.

Multidimensional Poverty and Material Deprivation with Discrete Data

We propose a characterization of a popular index of multidimensional poverty which, as a special case, generates a measure of material deprivation. This index is the weighted sum of the functioning failures. The important feature of the variables that may be relevant for poverty assessments is that they are discrete in nature. Thus, poverty measures based on continuous variables are not suitable in this setting and the assumption of a discrete domain is mandatory. We apply the measure to European Union member states where the concept of material deprivation was initiated and illustrate how its recommendations differ from those obtained from poverty measures based exclusively on income considerations.

A Family of Multidimensional Poverty Measures

Relatively little research has been conducted until now on the multidimensional aspect of poverty measurement, that is poverty mesaures defined on various income and non-income attributes and their gaps with respect to pre-specified subsitence levels. The present paper investigates the properties of a family of poverty measures introduced by Foster, Greer and Thorbecke (1984) by aggregating the relative shortfalls of the various attributes from their respective subsistence quantities into a constant elasticity of substitution function.

INEQUALITY, POLARISATION AND WELFARE: THEORY AND APPLICATIONS

In this paper we explore the possibility of using the Atkinson (1970) – Kolm (1969) – Sen (1973) general ethical index in polarisation measurement. It is shown that though inequality and polarisation are two dissimilar concepts, different indices of inequality may be used to generate alternative indices of polarisation. A numerical illustration based on Indian household expenditure survey data is provided using several polarisation indices.

The Variance as a subgroup decomposable measure of inequality

An inequality index is called subgroup decomposable if it can be expressed as a weighted sum of inequality values calculated for population subgroups plus the contribution arising out of differences among subgroup means. Theil (1967) and Shorrocks (1980) pointed out two important requirements for subgroup decomposable inequality indices. Shorrocks (1980) has shown that Theils mean logarithmic deviation, for which the weights of subgroup terms are respective population shares, is the only relative inequality index that fulfils these two properties. In this paper we show that the variance is the only absolute inequality index to satisfy the population share weighted subgroup decomposability property, which in turn implies that it also meets the two properties suggested by Theil and Shorrocks. A numerical illustration of several inequality indices in also presented in the paper. JEL classification numbers:D31, D63.