Classical Horizontal Inequity and Reranking: an Integrated Approach

The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have generated two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson indices, and that allows a decomposition of the total redistributive effect of taxes and transfers in a vertical equity effect and a loss of redistribution due to either classical HI or reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across groups. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal which of reranking or classical HI is more important since this requires a judgement that is fundamentally normative in nature.Horizontal inequity, reranking, tax equity, inequality, Canadian tax system.

Classical Horizontal Inequity and Reranking: an Integrated Approach

The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have led to two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson index, and that allows a decomposition of the total redistributive effect of taxes and transfers into a vertical equity effect, a loss of redistribution due to classical HI, and a loss of redistribution due to reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across socio-economic groups and percentiles. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal whether reranking is more or less important than classical HI, since this requires a judgement that is fundamentally normative.Horizontal inequity, Reranking, Tax equity, Inequality, Canadian tax and transfer system

An Atkinson-Gini Family of Social Evaluation Functions

This is a significant revision of a paper which first appeared as Working Paper 98-26, CRÉFA, Département d’économique, Université Laval, Canada.We investigate the properties of a family of social evaluation functions and inequality indices which merge the features of the family of Atkinson (1970) and S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. Income inequality aversion is captured by decreasing marginal utilities, and aversion to rank inequality is captured by rank-dependent ethical weights, thus providing an ethically-flexible dual basis for the assessment of inequality and equity. These ocial evaluation functions can be interpreted as average utility corrected for the illfare of relative deprivation. They can alternatively be understood as averages of altruistic well-being in a population. They moreover have a simple graphical interpretation.We thank the Social Sciences and Humanities Research Council of Canada and the fonds pour la Formation des Chercheurs et l’Avancement de la Recherche of the government of Québec for their financial support

An Atkinson-Gini family of social evaluation functions

We investigate the properties of a family of social evaluation functions and inequality indices which merge the features of the family of Atkinson (1970) and S-Gini (Donaldson and Weymark (1980, 1983), Yitzhaki (1983) and Kakwani (1980)) indices. Income inequality aversion is captured by decreasing marginal utilities, and aversion to rank inequality is captured by rank-dependent ethical weights, thus providing an ethically-flexible dual basis for the assessment of inequality and equity. These ocial evaluation functions can be interpreted as average utility corrected for the illfare of relative deprivation. They can alternatively be understood as averages of altruistic well-being in a population. They moreover have a simple graphical interpretation

Social Classes, Inequality and Redistributive Policies in Canada

The social performance of fiscal redistributive mechanisms in Canada continues to receive a growing interest from politicians and research scientists. The aim of this paper is to assess the evolution of social classes in Canada and to check whether the market and governmental redistribution factors have affected their evolution during the last decade. We focus on the dynamic of inequality, polarization and progressivity of the fiscal system. The results of this study confirm the effectiveness of governmental redistributive mechanism to decrease inequality and polarization significantly and to maintain the middle social class at the detriment of the poorest one. The other evidence concerns the chronic increase in population share and wellbeing of the rich class. Finally, the progressivity of fiscal sytem has registered a significant increase during the last few years.Social classes, poverty, inequality, redistribution

Classical horizontal inequity and reranking : an integrated approach

The last 20 years have seen a significant evolution in the literature on horizontal inequity (HI) and have generated two major and "rival" methodological strands, namely, classical HI and reranking. We propose in this paper a class of ethically flexible tools that integrate these two strands. This is achieved using a measure of inequality that merges the well-known Gini coefficient and Atkinson indices, and that allows a decomposition of the total redistributive effect of taxes and transfers in a vertical equity effect and a loss of redistribution due to either classical HI or reranking. An inequality-change approach and a money-metric cost-of-inequality approach are developed. The latter approach makes aggregate classical HI decomposable across groups. As in recent work, equals are identified through a nonparametric estimation of the joint density of gross and net incomes. An illustration using Canadian data from 1981 to 1994 shows a substantial, and increasing, robust erosion of redistribution attributable both to classical HI and to reranking, but does not reveal which of reranking or classical HI is more important since this requires a judgement that is fundamentally normative in nature

On the Measurement of Long-Term Income Inequality and Income Mobility

This paper proposes a two-step aggregation method for measuring long-term income inequality and income mobility, where mobility is defined as an equalizer of long-term income. First, the income stream of each individual is aggregated into a measure of permanent income, which accounts for the costs associated with income fluctuations. Consequently, mobility will have an unambiguously positive impact on social welfare in the sense that for two societies that have identical short term income distributions, the social welfare will be greatest for the socie ty which exhibits most mobility. The second step consists of aggregating permanent incomes across individuals into measures of social welfare, inequality and mobility. To this end, we employ an axiomatic approach to justify the introduction of a generalized family of rank-dependent measures of inequality, where the distributional weights, as opposed to the Mehran-Yaari family, depend on income shares as well as on population shares. Moreover, a subfamily is shown to be associated with social welfare functions that have intuitively appealing interpretatio ns. Further, the generalized family of inequality measures provides several new interpretations of the Gini-coefficient. The proposed family of income mobility also proves to encompass standard measures of income mobility, depending on the assumptions made about the interpersonal preferences and the credit market.Income inequality, income mobility, social welfare, the Gini coefficient, permanent income, annuity.

Is an inequality-neutral flat tax reform really neutral?

Let us assume a revenue- and inequality-neutral flat tax reform shifting from a graduated-rate tax. Is this reform really distributional neutral? Traditionally, there has been a bias toward the inequality analysis, forgetting other relevant aspects of the income distribution. This kind of reforms implies a set of composite transfers, both progressive and regressive, even though inequality remains unchanged. This paper shows that polarization is a useful tool for characterizing this set of transfers caused by inequality-neutral tax reforms. A simulation exercise illustrates how polarization can be used to discriminate between two inequality-neutral tax alternatives.polarization, inequality, flat tax

On the Measurement of Long-Term Income Inequality and Income Mobility

This paper proposes a two-step aggregation method for measuring long-term income inequality and income mobility, where mobility is defined as an equalizer of long-term income. The first step consists of aggregating the income stream of each individual into a measure of permanent income, which accounts for the costs associated with income fluctuations and allows for credit market imperfections. The second step aggregates permanent incomes across individuals into measures of social welfare, inequality and mobility. To this end, we employ an axiomatic approach to justify the introduction of a generalized family of rank-dependent measures of inequality, where the distributional weights, as opposed to the Mehran-Yaari family, depend on income shares as well as on population shares. Moreover, a subfamily is shown to be associated with social welfare functions that have intuitively appealing interpretations. Further, the generalized family of inequality measures provides new interpretations of the Gini-coefficient.income inequality, income mobility, social welfare, Gini coefficient, permanent income, credit market, annuity

Comparisons of income mobility profiles

Methods are developed for income mobility comparisons between countries or between population subgroups based on the construction of mobility profiles. Mobility profiles provide an evocative picture of both the magnitude of income changes in a population, and its distribution across the income range. Comparisons of mobility profiles permit assessments in which mobility among the poor is given greater weight than mobility among the rich. Non-intersection of mobility profiles is shown to correspond with unambiguous rankings according to a large class of functions for the social evaluation of mobility. Particular focus is put on generalized Gini social evaluation functions from which summary indices are derived to obtain complete orderings. An empirical application based on the European Community Household Panel survey illustrates the usefulness of the methods and show how they can be used to shed new light on `pro-poor growth' issues.income mobility ; pro-poor growth ; dominance