The dual decomposition of aggregation functions and its application in welfare economics

Producción CientíficaIn this paper, we review the role of self-duality in the theory of aggregation functions, the dual decomposition of aggregation functions into a self-dual core and an anti-self-dual remainder, and some applications to welfare, inequality, and poverty measures.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

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

Bread and Social Justice: Measurement of Social Welfare and Inequalities Using Anthropometrics

We address the question of the measurement of pure health inequalities and achievement in the context of welfare decreasing variables. We adopt a general framework whereby the health variable is reported on an interval, from an optimum level to a critical survival threshold. There are two problems that require some departures from the usual framework used to measure inequality and social welfare. Firstly, we show that for welfare decreasing variables, the equally distributed equivalent value is decreasing in progressive transfers (instead of being increasing). Accordingly, appropriate achievement and inequality indices for welfare decreasing variables are introduced. Secondly, because the Lorenz curve and the associated inequality indices are not robust to alternative values of the survival threshold, we argue that the family of translation invariant social welfare functions and related absolute Lorenz curve allow us to undertake inequality comparisons between distributions that are robust to the chosen level of the survival threshold. An illustrative application of the methodology is provided

Could the World be Flat? Simulating Flat Tax Reforms in Western Europe

The flat tax idea has given rise to an ongoing debate both in academics and politics. Further on, it has recently been very successful, especially in transition countries in Eastern Europe. Although flat taxes are high on the political agenda in various Western European countries, they have not been implemented in these grown-up welfare states. The introduction of a flat tax with a basic tax allowance, a low uniform marginal tax rate, and a broad tax base as a reform of existing tax systems is supposed to have several advantages. Most importantly, positive effects on employment and GDP as well as reduced tax distortions are expected. In addition, flat tax reforms are thought to reduce administration and compliance costs as well as incentives for tax avoidance or evasion. However, the distributional effects seem to prevent a flat tax adoption in democracies with a well-established middle class. The motivation of this book is to identify hereby the driving forces behind the economic effects of a flat tax reform. There are two dimensions to be considered that are mutually interdependent: the details of the reform and the environment of its implementation. First, the flat tax design (e.g. parameters such as marginal rate and allowance, tax base simplification or cash flow corporate taxation) plays an important role for the results. Second, the results crucially depend on the country under observation. The underlying income distribution and demographic structure as well as the institutional background (i.e. the tax benefit system, welfare state) are decisive for the outcome of such a reform. The present book contributes to the existing literature in various ways. First, we provide a comprehensive survey of the state-of-the-art in simulation modelling for the ex-ante analysis of tax reform proposals. Second, we analyse and compare different types of welfare states and tax benefit systems especially with respect to the distribution and redistribution of income to explain differing results across countries. Third, we conduct an extensive analysis of the key sources of the economic outcomes of flat tax reforms. For this purpose, the extended methodology of simulation analysis is applied to analyse different hypothetical flat tax scenarios and the impact of their key elements (tax base simplification, marginal tax rate and basic allowance) on equity and efficiency for Germany and the other EU-15 countries in a common microeconometric framework. The analysis differs from the existing literature mainly by analysing the distributional effects as well as the effects on welfare and employment in a uniform simulation model and by applying a systematic approach for choosing the flat tax parameters. As stated above, the aim of this book is to identify the conditions which mainly influence the economic effects of a flat tax reform. The setup of this analysis is as follows. Chapter 2 introduces the methodology. Chapter 3 analyses the relevance of the flat tax design. In chapter 4, the European countries are compared regarding their institutional background and the underlying income distribution. In chapter 5, the role of these country specific aspects and their impact for possible flat tax reforms is investigated. Chapter 6 draws conclusions. At last, what can be learnt from our analysis is that the flatness of the tax schedule itself is not a key feature of the economic success of a tax reform. Other elements (simplification, increased compliance, corporate taxation) play a more important role. However, a flat tax reform can indeed overcome the fundamental equity efficiency trade-off. This is only true in two specific cases: first, for Mediterranean countries with highly polarised income distributions, and second, for Germany in the long-run if accounting for general equilibrium effects. Therefore, due to its adverse short-term distributional effects, the chances that the flat tax idea will invade the grown-up democracies of Western Europe are rather low. However, a further movement towards lower (marginal) tax rates with broader and simpler tax bases shall be observed. This, however, could eventually lead to tax benefit systems moving closer to linearity, albeit without an actual flat tax schedule

Classical inequality indices, welfare and illfare functions, and the dual decomposition

Producción CientíficaIn the traditional framework, social welfare functions depend on the mean income and on the income inequality. An alternative illfare framework has been developed to take into account the disutility of unfavorable variables. The illfare level is assumed to increase with the inequality of the distribution. In some social and economic fields, such as those related to employment, health, education, or deprivation, the characteristics of the individuals in the population are represented by bounded variables, which encode either achievements or shortfalls. Accordingly, both the social welfare and the social illfare levels may be assessed depending on the framework we focus on. In this paper we propose a unified dual framework in which welfare and illfare levels can both be investigated and analyzed in a natural way. The dual framework leads to the consistent measurement of achievements and shortfalls, thereby overcoming one important difficulty of the traditional approach, in which the focus on achievements or shortfalls often leads to different inequality rankings. A number of welfare functions associated with inequality indices are OWA operators. Specifically this paper considers the welfare functions associated with the classical inequality measures due to Gini, Bonferroni, and De Vergottini. These three indices incorporate different value judgments in the measurement of inequality, leading to different behavior under income transfers between individuals in the population. In the bounded variables representation, we examine the dual decomposition and the orness degree of the three classical welfare/illfare functions in the standard framework of aggregation functions on the domain. The dual decomposition of each welfare/illfare function into a self-dual central index and an anti-self-dual inequality index leads to the consistent measurement of achievements and shortfalls.Ministerio de Ciencia e Innovación (project ECO2009-11213)Ministerio de Ciencia e Innovación (project ECO2009-07332

Manufacturing sector productivity in South Africa in the 1980's : error and ideology in a contested terrain.

Thesis (Ph.D.)-Unversity of Natal, 1994.Estimates of the value of manufacturing sector output enter into many economic indices, especially those measuring productivity. The South African Central Statistical Services has twice made substantial errors in the output series. Revisions to correct the first of these raised the growth rate in manufacturing over the period 1970-80 from 2,6 per cent per annum (compound) to 5 per cent. This episode is not common knowledge. After examining the conceptual difficulties involved in producing output stimates, a practical technique for detecting errors in the series , the Euler Consistency Test, is presented. Developed, refined, and then applied to the South African data, it predicted, retrospectively, the first set of errors (using only the information available at the time those errors were made), then detected another set of errors , not previously known to exist. The study records the process by which the CSS was made to concede this second error. Acknowledgement only came after protracted correspondence and an examination conducted by a special committee formed to investigate my complaints. With 1979 set equal to 100, the output level in 1988 was originally given as 113,8. After investigation, the CSS raised this to 126,1. The magnitude of this second error is equivalent to the omission of the total output of the two SASOL plants commissioned during the early 1980s. Estimates of productivity growth by the National Productivity Institute using these incorrect figures are shown to have created a misleading picture of the sector's performance, especially in the sensitive debate over the relationship between wage and productivity growth. An attempt is made to lay the groundwork of an analytical framework for comprehending (from a Marxist point of view) the activities of ideological state apparatusses like the NPI. A review of the literature on theory choice is conducted, and the necessarily political nature of this activity is explored. The relative impotence of I science' in the face of ideology in a conflict-ridden society is considered. The question of the significance of disagreements between economists is examined, and prospects for convergence and consensus on certain issues are weighed