A note on the 'Natural Rate of Subjective Inequality' hypothesis and the approximate relationship between the Gini coefficient and the Atkinson index

In a recent paper in this journal, Lambert et al (2003) sought to establish the Natural Rate of Subjective Inequality (NRSI) hypothesis. In this note, their test of the NRSI hypothesis is critically evaluated and an alternative reason is offered as to why their empirics appeared to support it. The findings, based on simulation, do not overturn the NRSI hypothesis, but indicate the need for deeper and more thorough analysis if this insightful and potentially far-reaching hypothesis is to be established.Natural rate of subjective inequality; inequality indices; simulation

Copula-based orderings of multivariate dependence

In this paper I investigate the problem of defining a multivariate dependence ordering. First, I provide a characterization of the concordance dependence ordering between multivariate random vectors with fixed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vectors with non-fixed margins, I impose a scale invariance principle which leads to a copula-based concordance dependence ordering. Finally, a wide family of copula-based measures of dependence is characterized to which Spearman’s rank correlation coefficient belongs.copula, concordance ordering, dependence measures, dependence orderings, multivariate stochastic dominance, supermodular ordering.

Copula-based orderings of multivariate dependence

In this paper I investigate the problem of defining a multivariate dependence ordering. First, I provide a characterization of the concordance dependence ordering between multivariate random vectors with fixed margins. Central to the characterization is a multivariate generalization of a well-known bivariate elementary dependence increasing rearrangement. Second, to order multivariate random vectors with non- fixed margins, I impose a scale invariance principle which leads to a copula-based concordance dependence ordering. Finally, a wide family of copula-based measures of dependence is characterized to which Spearmanís rank correlation coefficient belongs.copula, concordance ordering, dependence measures, dependence orderings, multivariate stochastic dominance, supermodular ordering

Copula-based measurement of dependence between dimensions of well-being

Well-being consists of many dimensions such as income, health and education. A society exhibits greater dependence between its dimensions of well-being when the positions of the individuals in the different dimensions are more aligned or correlated. Differences in dependence may lead to very different societies, even when the dimension-wise distributions are identical. I propose to use a copula-based framework to order societies with respect to their dependence. A class of measures of dependence is derived to which the multidimensional rank correlation coefficient belongs. I illustrate the usefulness of the approach by showing that Russian dependence between three dimensions of well-being has increased significantly between 1995 and 2003. Unfortunately, the aspect of dependence is missed by all composite well-being measures based on dimension-specific summary statistics such as the popular Human Development Index (HDI).copula, complex inequality, concordance, HDI, multidimensional inequality, Russia, well-being.

Progressivity comparisons

Analysts should correct for distributional differences before undertaking local progressivity comparisons between income tax or tax and benefit schedules. A transplant-and-compare procedure is advocated, involving 'importation' of the schedule from one regime into another, or from both into a reference scenario. The residual progression ordering over transplanted schedules then assures a global ordering of original regimes by Lorenz or Suits curves. The algorithm is advocated for use only when transplantation functions are isoelastic, and is illustrated for the Canadian, Israeli and UK tax and benefit systems.

Copula-based measurement of dependence between dimensions of well-being.

Well-being consists of many dimensions such as income, health and education. A society exhibits greater dependence between its dimensions of well-being when the positions of the individuals in the different dimensions are more aligned or correlated. Differences in dependence may lead to very different societies, even when the dimension-wise distributions are identical. I propose to use a copula-based framework to order societies with respect to their dependence. A class of measures of dependence is derived to which the multidimensional rank correlation coefficient belongs. I illustrate the usefulness of the approach by showing that Russian dependence between three dimensions of well-being has increased significantly between 1995 and 2003. Unfortunately, the aspect of dependence is missed by all composite well-being measures based on dimension-specific summary statistics such as the popular Human Development Index (HDI).

Stochastic Frontier Models With Correlated Error Components

In the productivity modelling literature, the disturbances U (representing technical inefficiency) and V (representing noise) of the composite error W=V-U of the stochastic frontier model are assumed to be independent random variables. By employing the copula approach to statistical modelling, the joint behaviour of U and V can be parameterised thereby allowing the data the opportunity to determine the adequacy of the independence assumption. In this context, three examples of the copula approach are given: the first is algebraic (the Logistic-Exponential stochastic frontier model with margins bound by the Fairlie-Gumbel-Morgenstern copula) and the second and third are empirically oriented, using data sets well-known in productivity analysis. Analysed are a cross-section of cost data sampled from the US electrical power industry, and an unbalanced panel of data sampled from the US airline industryStochastic Frontier model; Copula; Copula approach; Sklar's theorem; Families of copulas; Spearman's rho.

Kakwani decomposition of redistributive effect: Origins, critics and upgrades

Kakwani decomposition of redistributive effect into vertical and reranking terms is one of the most widely used tools in measurement of income redistribution. This paper describes how the decomposition has emerged, how its proponents managed to expand and upgrade it, and how extensively it has been employed in empirical research. However, the arguments are presented that the decomposition features certain methodological problems and it is therefore called for its reinterpretation.income redistribution, Kakwani decomposition, reranking, horizontal inequity, progressivity

Coupling couples with copulas: analysis of assortative matching on risk attitude

We investigate patterns of assortative matching on risk attitude, using self‐reported (ordinal) data on risk attitudes for males and females within married couples, from the German Socio‐Economic Panel over the period 2004–2012. We apply a novel copula‐based bivariate panel ordinal model. Estimation is in two steps: first, a copula‐based Markov model is used to relate the marginal distribution of the response in different time periods, separately for males and females; second, another copula is used to couple the males' and females' conditional (on the past) distributions. We find positive dependence, both in the middle of the distribution, and in the joint tails, and we interpret this as positive assortative matching (PAM). Hence we reject standard assortative matching theories based on risk‐sharing assumptions, and favor models based on alternative assumptions such as the ability of agents to control income risk. We also find evidence of “assimilation”; that is, PAM appearing to increase with years of marriage. (JEL C33, C51, D81