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 way poverty is measured is important for an understanding of what has happened to poverty as well as for anti-poverty policy evaluation. Sen's (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should satisfy certain properties or axioms and the desirability of a poverty measure should be evaluated by these axioms. During the last two decades, many researchers have adopted the axiomatic approach pioneered by Sen to propose additional axioms and develop alternative poverty measures. The objective of this survey is to provide a clarification on the extensive literature of aggregate poverty measures. In this survey, we first examine the desirability of each axiom, the properties of each poverty measure, and the interrelationships among axioms. The desirability of an axiom cannot be evaluated in isolation, and some combination of axioms may make it impossible to devise a satisfactory poverty measure; some axioms can be implied by other axioms combined and so are not independent; some others are ad hoc and are disqualified as axioms for poverty measurement. Based on the interactions among axioms, we identify the ‘core’ axioms which together have a strong implication on the functional form of a poverty measure. We then review poverty measures that have appeared in the literature, evaluating the interrelationships among different measures, and examining the properties of each measure. The axioms each measure satisfies/violates are also summarized in a tabular form. Several ‘good’ poverty measures, which have not been documented by previous surveys, are also included.

Aggregate Poverty Measures

Studies were performed in a long-term effort to develop clinically translatable, tissue engineered adipose constructs for reconstructive, correctional, and cosmetic indications. Rat preadipocytes were harvested, isolated, expanded ex vivo, and seeded within PLGA scaffolds. Preadipocyte-seeded and acellular (control) scaffolds were implanted for 1-12 months. Explanted scaffolds were stained with osmium tetroxide, processed, and counterstained using HE5:134) and demonstrate that adipose tissue can be formed in vivo using tissue engineering strategies. However, the long-term maintenance of adipose tissue remains elusive.

Long-term implantation of preadipocyte-seeded PLGA scaffolds.

Economists have long speculated that envy and malice play important roles in economic decisions. Surprisingly little empirical evidence has been offered in support of such claims. This paper uses experimental and multinomial logit techniques to estimate the effects of envy and malice in economic decisions involving Pareto efficiency. Envy and malice turn out to be powerful motivations with strong differential impacts across countries and relative positions. In some cases, opposition to Pareto gains reaches 60%. Behind a veil of ignorance, however, opposition falls to 10% overall. Pareto efficiency thus garners its greatest support under conditions which can lay claim to greatest legitimacy, those free of situational and personal bias. “... the greater part of human actions have their origin not in logical reasoning but in sentiment. This is particularly true for actions that are not motivated economically.... Man, although impelled to act by nonlogical motives, likes to tie his actions logically to certain principles; he therefore invents these a posteriori in order to justify his actions.” V. Pareto in The rise and fall of the elites (1968, p. 27)

Envy, malice and Pareto efficiency: An experimental examination

Mobility measurement,transition matrices and statistical inference

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Econometrics/Vol101.Issue2.2001/2193.pdf

Buhong Zheng

Papers

Aggregate Poverty Measures

Long-term implantation of preadipocyte-seeded PLGA scaffolds.

Envy, malice and Pareto efficiency: An experimental examination

Mobility measurement,transition matrices and statistical inference

Statistical inference for poverty measures with relative poverty lines