Inequality decomposition by population subgroups for ordinal data

Abstract

We present a class of decomposable inequality indices for ordinal data (e.g. self-reported health survey). It is characterized by well-known inequality axioms (e.g. scale invariance) and a decomposability axiom which states that an index can be represented as a function of inequality values in subgroups and subgroup sizes. The only decomposable indices are strictly monotonic transformations of the weighted average of frequencies in categories. Among the indices proposed in the literature only the absolute value index (Abul Naga and Yalcin, 2008; Apouey, 2007) is decomposable. As an empirical illustration we calculate regional contributions to overall health inequality in Switzerland.

Statistical Inference for a Novel Health Inequality Index

“…This dataset was also analyzed by [3] and [6]. We do not include the distributions of SHS in the seven regions in this paper, this information can be found in [6].…”

“…This dataset was also analyzed by [3] and [6]. We do not include the distributions of SHS in the seven regions in this paper, this information can be found in [6]. We use the Due to the reason of random sampling of the data set, it is natural to ask questions, like, do East and Ticino have different health inequalities in fact?…”

“…[5] proposed a method using income-health matrix to measure socioeconomic inequality in health. [6] introduced a family of sub-group decomposable indices and investigated the decomposability of the indices. [7] conducted an empirical study of the health inequality index for ordinal data from China.…”

Estimation of inequality indices of the cumulative distribution function

“…Let m ∈ {1, ..., k} denote the median response state in some given distribution P ∈ D. First, to give an example of an inequality index that is linear in the cumulative distribution function, consider the family of sub-group decomposable indices of Kobus and Miłoś (2012):…”

“…Let m ∈ {1, ..., k} denote the median response state in some given distribution P = (P 1 , ..., P n ) ∈ D and return to the class (1.1) of sub-group decomposable inequality indices of the cumulative distribution, introduced by Kobus and Miłoś (2012). As a corollary to Proposition 2, we derive the form of the Jacobian vector in relation to (1.1): Corollary 3 For the class of inequality indices of the cumulative distribution function (1.1) that are decomposable by population sub-groups, the Jacobian vector J evaluated at some distribution P ∈ D takes the form…”