There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

This paper proposes a new methodology for multidimensional poverty measurement consisting of an identification method ρk that extends the traditional intersection and union approaches, and a class of poverty measures Mα. Our identification step employs two forms of cutoff: one within each dimension to determine whether a person is deprived in that dimension, and a second across dimensions that identifies the poor by ‘counting’ the dimensions in which a person is deprived. The aggregation step employs the FGT measures, appropriately adjusted to account for multidimensionality. The axioms are presented as joint restrictions on identification and the measures, and the methodology satisfies a range of desirable properties including decomposability. The identification method is particularly well suited for use with ordinal data, as is the first of our measures, the adjusted headcount ratio. We present some dominance results and an interpretation of the adjusted headcount ratio as a measure of unfreedom. Examples from the US and Indonesia illustrate our methodology.

Counting and Multidimensional Poverty Measurement

https://www.ophi.org.uk/wp-content/uploads/OPHI-wp32.pdf

Counting and multidimensional poverty measurement

Poverty and Famines: An Essay on Entitlement and Deprivation

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.

The Measurement of Multidimensional Poverty

Distribution-free statistical inference procedures for changes in Lorenz- and Gini-based indexes of tax progressivity are developed and applied. Related but distinct tests for the Reynolds–Smolensky index of residual progression and the Kakwani index of liability progression are provided. The inference procedures are illustrated by applying them to Luxembourg Income Study microdata for Sweden, the United Kingdom, and the United States before and after periods of tax reform. In each country a finding of significant change depends on the choice among progressivity indexes. No single index exhibits a consistent pattern of significant change in all countries across time.

Inference Tests for Gini-Based Tax Progressivity Indexes

Recently there has been increased interest in developing methods for measuring poverty in a way that takes into account the lifetime experience of individuals. We analyze some specific proposals that take the so-called spells approach and consider how they differ in the manner in which they address issues of lifetime poverty, most notably the measurement of chronic poverty. Comparing these specific measures by applying them to a US panel data set, we provide important insights for further research in conceptualizing and measuring lifetime poverty.

/pdf/empirical-issues-in-lifetime-poverty-measurement-59zpku5a6e.pdf

Empirical issues in lifetime poverty measurement

This note formally investigates the applicability of stochastic dominance (Lorenz dominance) to ordinal data such as self-reported health status. We confirm that for ordinal data distributions, stochastic dominance has limited applicability in ranking social welfare, while it has no applicability in ranking inequality.

Measuring inequality with ordinal data: a note

Simple random sampling has been assumed in most statistical inference procedures developed to test Lorenz dominance and other partial ordering conditions. This note, using the Bahadur representation, derives the (asymptotic) covariance structures of the Lorenz and generalized Lorenz ordinates for stratified, cluster and multistage samples. The comparison of these covariance structures illustrates the necessity of taking the sampling method into account in inference testing.

Testing lorenz curves with non-simple random samples

This paper characterizes unit-consistent poverty indices. The unit consistency axiom requires that poverty rankings (not poverty indices) remain unaffected when all incomes and the poverty lines are expressed in different measuring units. We consider two general frameworks of poverty measurement: the semi-individualistic framework that includes all decomposable indices and all rank-based indices; and the Dalton–Hagenaars framework that contains a subset of decomposable indices. Within the semi-individualistic framework, classes of unit-consistent poverty indices can be characterized for different value judgements about poverty measurement. Within the Dalton-Hagenaars framework, unit-consistent poverty indices are completely characterized without invoking any value judgement a priori.

Buhong Zheng

Papers

Inference Tests for Gini-Based Tax Progressivity Indexes

Empirical issues in lifetime poverty measurement

Measuring inequality with ordinal data: a note

Testing lorenz curves with non-simple random samples

Unit-consistent poverty indices