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

The coefficient of variation, stochastic dominance and inequality: A new interpretation

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Econometrics/Vol101.Issue2.2001/2192.pdf

Statistical inference for testing inequality indices with dependent samples

This article derives large-sample properties and provides asymptotically distribution-free statistical inference procedures for an alternative approach to inequality orderings—normalized stochastic dominance (NSD). NSD is a straightforward extension of standard dominance techniques. As such, it can be generalized to higher orders of dominance, thereby providing a more powerful technique for ranking distributions. We illustrate the NSD method by applying it to Current Population Survey data for 1970–1990.

Inequality Orderings, Normalized Stochastic Dominance, and Statistical Inference

The paper examines the implications of the newly proposed unit consistency axiom for partial inequality orderings. We first show that some intermediate Lorenz dominance conditions violate the axiom. We then characterize a class of intermediate Lorenz orderings and demonstrate that the only unit-consistent member is the one related to Krtscha (Models and measurement of welfare and inequality. Springer, Heidelberg, 1994)’s intermediate notion of inequality which has recently been investigated by Zoli (A surplus sharing approach to the measurement of inequality. Discussion paper no. 98/25, University of York, 1998; Logic, game, theory and social choice. Tilburg University Press, Tilburg, 1999) and Yoshida (Soc Choice Welf 24:557–574, 2005). Finally, we provide a general characterization for unit-consistent Lorenz orderings and the Krtscha-type dominance again turns out to be the only one that is intermediate and unit-consistent.

Buhong Zheng

Papers

The coefficient of variation, stochastic dominance and inequality: A new interpretation

Statistical inference for testing inequality indices with dependent samples

Inequality Orderings, Normalized Stochastic Dominance, and Statistical Inference

Inequality orderings and unit consistency

Fuzzy ranking of human development: A proposal