65 research outputs found
ANALYSIS OF INDICES OF ECONOMIC INEQUALITY FROM A MATHEMATICAL POINT OF VIEW
A number of indices of economic inequality have been proposed in the literature. Their constructions are based on various econometric motives and justifications such as axioms of fairness. In this paper we analize the indices stepping slightly aside from their econometric meanings and adopting a mathematical approach that treats the indices as distances ā in some functional spaces ā between the egalitarian and actual Lorenz curves. More specifically, starting with, and being guided by, the econometric definitions of various indices, we modify the indices in such a way that the resulting ones become natural from the mathematical point of view. It turns out that some of the new āmathematicalā indices coincide with the corresponding well known āeconometricā ones, some appear to be only asymptotically equivalent, and some turn out to have different asymptotic behaviour when the sample size indefinitely increases.Dominance; Lagrangian Multiplier; Likelihood Ratio Test; MSE; Non-central Chisquare and F; Ridge Regression; Superiority; Wald Test.
Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references
The underlying idea behind the construction of indices of economic inequality
is based on measuring deviations of various portions of low incomes from
certain references or benchmarks, that could be point measures like population
mean or median, or curves like the hypotenuse of the right triangle where every
Lorenz curve falls into. In this paper we argue that by appropriately choosing
population-based references, called societal references, and distributions of
personal positions, called gambles, which are random, we can meaningfully unify
classical and contemporary indices of economic inequality, as well as various
measures of risk. To illustrate the herein proposed approach, we put forward
and explore a risk measure that takes into account the relativity of large
risks with respect to small ones.Comment: 29 pages, 4 figure
Consistent Testing for Poverty Dominance
poverty, stochastic dominance, random poverty line, bootstrap
Measuring association via lack of co-monotonicity: the LOC index and a problem of educational assessment
Measuring association, or the lack of it, between variables plays an
important role in a variety of research areas, including education, which is of
our primary interest in this paper. Given, for example, student marks on
several study subjects, we may for a number of reasons be interested in
measuring the lack of co-monotonicity (LOC) between the marks, which rarely
follow monotone, let alone linear, patterns. For this purpose, in this paper we
explore a novel approach based on a LOC index, which is related to, yet
substantially different from, Eckhard Liebscher's recently suggested
coefficient of monotonically increasing dependence. To illustrate the new
technique, we analyze a data-set of student marks on mathematics, reading and
spelling
Zengaās new index of economic inequality, its estimation, and an analysis of incomes in Italy
For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their diļ¬erences with respect to geographic regions, and changes over time periods. It is a challenging area due to a number of reasons, one of them being the fact that diļ¬erent measures, or indices, are needed to reveal diļ¬erent features of income distributions. Keeping also in mind that the notions of āpoorā and ārichā are relative to each other, M. Zenga has recently proposed a new index of economic inequality. The index is remarkably insightful and useful, but deriving statistical inferential results has been a challenge. For example, unlike many other indices, Zengaās new index does not fall into the classes of L-, U-, and V -statistics. In this paper we derive desired statistical inferential results, explore their performance in a simulation study, and then employ the results to analyze data from the Bank of Italyās Survey on Household Income and Wealth.Zenga index, lower conditional expectation, upper conditional expectation, conļ¬dence interval, Bonferroni curve, Lorenz curve, Vervaat process.
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