Ranking Intersecting Lorenz Curves

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the best-off income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou-Dalton principle of transfers forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance. The dominance results for Lorenz curves do also apply to generalized Lorenz curves and thus provide convenient characterizations of the corresponding social welfare orderings.generalized Gini families of inequality measures, rank-dependent measures of inequality, Gini coefficient, partial orderings, Lorenz dominance, Lorenz curve, general principles of transfers

Robust inequality comparisons

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations Aaberge (2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves which was proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families and thus the least restrictive social preferences required to reach unambiguous ranking of a set of Lorenz curves. From the weight-functions of these inequality measures we obtain intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967-2005.The Lorenz curve, Lorenz dominance, rank-dependent measures of inequality, the Gini coefficient, generalized Gini families of inequality measures.

Robust Inequality Comparisons

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations Aaberge (2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves which was proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families and thus the least restrictive social preferences required to reach unambiguous ranking of a set of Lorenz curves. From the weight-functions of these inequality measures we obtain intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967-2005.Lorenz curve, Lorenz dominance, rank-dependent measures of inequality, Gini coefficient, generalized Gini families of inequality measures

Intersecting Lorenz curves and aversion to inverse downside inequality

From Springer Nature via Jisc Publications RouterHistory: received 2019-01-22, registration 2020-09-16, accepted 2020-09-16, pub-electronic 2020-10-02, online 2020-10-02, pub-print 2021-04Publication status: PublishedFunder: University of ManchesterAbstract: This paper defines and characterizes the concept of an increase in inverse downside inequality and show that, when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting inverse downside inequality aversion often depends on the relative strengths of its aversion to inverse downside inequality and inequality aversion. For the class of linear inequality indices, of which the Gini coefficient is a member, a measure characterizing the strength of an index’s aversion to inverse downside inequality against its own inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified

Income inequality and price elasticity of market demand: the case of crossing Lorenz curves

This paper extends Ibragimov and Ibragimov (Econ Theory 32:579–587, 2007) in which the effect of changes income inequality on the price elasticity of market demand is characterized for the class of income distribution changes occurring through non-intersecting Lorenz curve shifts. We derive sufficient conditions for increase/decrease in price elasticity of market demand, under general changes in income distribution, allowing Lorenz curves to intersect as they shift. We conclude by drawing out implications of different types of tax policy changes for demand elasticity

Effects of Flat Tax Reforms in Western Europe on Income Distribution and Work Incentives

The flat income tax has become increasingly popular recently, yet its implementation is limited to Eastern Europe. We analyse the distributional and efficiency effects of flat tax scenarios for Western European countries. Our simulations show that flat tax rates required to attain revenue neutrality with existing basic allowances improve labour supply incentives. However, they result in higher inequality and polarisation. Flat rates necessary to keep the inequality levels unchanged allow for some scope for flat taxes to increase both equity and efficiency. Our analysis suggests that Mediterranean countries are more likely to benefit from flat taxes.flat tax reform, income distribution, work incentives, microsimulation

Optimal Taxation According to Equality of Opportunity: a Microeconometric Simulation Analysis

The purpose of this paper is to introduce and adopt a generalised version of Roemer's (1998) Equality of Opportunity (EOp) framework for analysing optimal income taxation. EOp optimal tax rules seek to equalise income differentials arising from factors beyond the control of the individual. Unlike the pure EOp criterion of Roemer (1998) the generalised EOp criterion allows for alternative weighting profiles in the treatment of income differentials between and within types when types are defined by circumstances that are beyond people's control. An empirical microeconometric model of labour supply in Italy is used to simulate and identify optimal tax rules within classes of two- and three-parameter tax rules. A rather striking result of the analysis is that the optimal tax rule turns out to be the pure lump-sum tax, under Roemer's pure EOp criterion as well as under the generalised EOp criterion with moderate degrees of aversion to within-type inequality. A high degree of within-type inequality aversion instead produces EOp-optimal rules with positive marginal tax rates. When the EOp-version of the Gini welfare function is adopted as Eop criterion, the optimal tax rule turns out to be close to the actual 1993 Italian tax system, if not for the important difference of prescribing a universal lump-sum positive transfer of 3,500,000 ITL, which has no comparable counterpart in the actual system. On the other hand, when using the conventional equality of outcome (EO) criterion, the pure lump-sum tax always turns out to be optimal, at least with respect to the classes of two- and three-parameter rules. We also compute second-best solutions, namely we exclude lump-sum taxes. Overall, the results do not conform to the perhaps common expectation that the EO criterion is more supportive of “interventionist” (redistributive) policies than an EOp approach.

Effects of flat tax reforms in Western Europe on equity and efficiency

The flat income tax has become increasingly popular recently, yet its implementation is limited to Eastern Europe. We analyse the distributional and e? ciency effects of flat tax scenarios for Western European countries. Our simulations show that flat tax rates required to attain revenue neutrality with existing basic allowances improve labour supply incentives. However, they result in higher inequality and polarisation. Flat rates necessary to keep the inequality levels unchanged allow for some scope for flat taxes to increase both equity and e? ciency. Our analysis suggests that Mediterranean countries are more likely to benefit from flat taxes. --Flat tax reform,income distribution,work incentives,microsimulation

Measuring unidimensional inequality: practical framework for the choice of an appropriate measure

The final publication is available at Springer via http://dx.doi.org/10.1007/s11205-020-02268-0Inequality and its analysis have received increasing attention in the literature over the last decades, which has led to the development of a large number of inequality measurement methodologies. In the analysis of inequality, results rely heavily on the choice of a measurement methodology and, very often, different methodologies do not lead to the same rankings. Therefore, in the assessment of inequality, the choice of an appropriate measure is crucial. Important as this choice may be, to the best of the authors’ knowledge, there exists no research on the development of a systematic and unified framework for the selection of an adequate inequality measure depending on the context. In consideration of the foregoing, this paper provides a framework with practical guidelines for researchers and practitioners to facilitate the task of choosing the most appropriate inequality measure for their specific needs. The proposed guidelines are based on seven main properties of inequality indexes and are preceded by a comprehensive review of the different methods developed so far, focusing specifically on the advantages and drawbacks of each. Besides, they are accompanied by an empirical application of the different methodologies reviewed in order to better illustrate the various properties of the different inequality measures.Peer ReviewedPostprint (author's final draft

The redistributive effects of fiscal policies in Turkey, 2003

This thesis investigates redistributive impacts of fiscal policies at household level in a middle income developing country, Turkey, in 2003. It utilizes the benefit and tax incidence methodologies and applies the welfare dominance analysis and summary indices of progressivity to assess the distributional impacts of the fiscal policies. The 2003 Household Income and Consumption Expenditures Survey from the Turkish Statistical Institute is used for this purpose. Chapter 2 reviews the theoretical and empirical literature for measuring inequality and progressivity. The aim of the chapter is to review and discuss the measures used in the thesis. This is followed by the three empirical studies that form the core of the thesis. Chapter 3 and 4 examine redistributive impacts of publicly provided education, health, infrastructure services and social cash and in kind transfers. The key findings show that apart from primary education, none of the social services in question are well targeted to the poor, although the incidence of the services is progressive. In Chapter 5, attention is paid to direct and indirect tax policies in Turkey. Indirect taxes dominate tax revenues in Turkey. The results of the standard tax incidence analysis show that direct taxes are progressive thanks to personal income tax and property taxes. In the context of indirect taxes, redistributive power of indirect taxes is limited. The incidence of indirect taxes is sensitive to the welfare indicator chosen. While the indirect taxes reduce expenditure inequality, they increase income inequality. Effective indirect tax rates estimated by using input-output tables prove the importance of taxation on imported goods and intermediate goods, which are ignored by the standard tax incidence analysis. The incidence with effective indirect taxes is less progressive in the case of expenditure as the welfare indicator and more regressive in the case of income. The net fiscal incidence indicates that the fiscal policies have a positive redistributive impact on both expenditure and income inequality, and this positive impact is mainly driven by the public benefits