Stéphane Mussard

• Ph.D.
• Professor (Full) at University of Nîmes

A family of single-parameter Atkinson–Shapley rules for TU-games is introduced. These rules are marginalist with a specific transformation of the marginal contributions depending on a parameter, which assesses how equality among payoffs fairly offsets inefficiency in the redistribution. This normative content is similar in spirit to that of Atkinso...

In this paper, we consider a new class of generalized Convex structure and we investigate their tropical limits. Some properties are pointing out such that translation homotheticity and others ones allowing to consider the case of discrete production sets that are related to some specific dual forms. Along this line a general class of mathematical...

Interpretability of predictive machine learning models is critical for numerous application contexts that require decisions to be understood by end-users. It can be studied through the lens of local explainability and attribution methods that focus on explaining a specific decision made by a model for a given input, by evaluating the contribution o...

A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation...

Under a technology based on the generalized mean of inputs and outputs with constant returns to scale (CRS), the firms have incentive to merge (in a firm game) in order to improve their technical efficiency. A directional complementarity property in inputs and in outputs is introduced. It is shown that the core of the firm game is non-void whenever...

This paper explores international tourism regarding Morocco’s leading touristic city Marrakech, and, more precisely, its two prominent public spaces, Jemaa el-Fna and the Medina. Following a web-scraping process of English reviews on TripAdvisor, a machine learning technique is proposed to gather insights into prominent topics in the data, and thei...

Predictive justice, which involves forecasting trial outcomes, presents significant challenges due to the complex structure of legal judgments. To address this, it is essential to first identify all claims across different categories before attempting to predict any result. This paper focuses on a classification task based on the detection of Artic...

The typical judicial pathway is made of a judgment by a tribunal followed by a decision of an appellate court. However, the link between both documents is sometimes difficult to establish because of missing, incorrect or badly formatted references, pseudonymization, or poor drafting specific to each jurisdiction. This paper first shows that it is p...

Scribe is a legal judgment annotation platform. Its objective is to improve dataset quality for machine learning models, to make annotation task faster and easier, and to boost interactions between annotators and developers. The platform manages 3 different classes of annotation: claims, named entities and sections. The platform facilitates the exp...

Interpretability of predictive machine learning models is critical for numerous application contexts that require decisions to be understood by end-users. It can be studied through the lens of local explainability and attribution methods that focus on explaining a specific decision made by a model for a given input, by evaluating the contribution o...

The widely used Prais–Winsten technique for estimating parameters of linear regression model with serial correlation is sensitive to outliers. In this paper, an alternative method based on Gini mean difference (GMD) is proposed. A Monte Carlo simulation is used to show that the Gini estimator is more robust than the general least squares one when t...

Nous étudions dans cet article les apports respectifs de différentes re-présentations de mots, de la méthode ensembliste et d'un transformer spécialisé que nous appelons CamemBERT judiciaire, sur la tâche de recherche d'entités nommées dans les décisions de justice françaises. Nous comparons les performances des modèles BiLSTM-CRFs entre eux, indiv...

Gini PCA github python : https://github.com/mussard974/Gini-PCA open access https://www.sciencedirect.com/science/article/pii/S0377221721000886

This paper proposes a two-parameter family of health indicators. First, these operational research indicators are axiomatically derived and allow a Boolean risk factor to be linked to different health dimensions. Second, the behavior of the social planner with respect to the risk factor (risk insensibility, risk sensibility and extreme risk sensibi...

This paper presents and compares several text classification models that can be used to extract the outcome of a judgment from justice decisions, i.e., legal documents summarizing the different rulings made by a judge. Such models can be used to gather important statistics about cases, e.g., success rate based on specific characteristics of cases’...

In this paper, a linear discriminant analysis (LDA) is performed in the Gini sense (GDA). Maximizing the generalized Gini gross between-group matrix allows the data to be projected onto discriminant axes. Different methods are investigated, the geometrical approach—based on a particular distance—and the probabilistic approach, which consists in emp...

Cooperation between firms can never improve the technical efficiency of any firm coalition. The directional distance function, by virtue of its additive nature, is a useful tool that outlines this impossibility. In this paper, the additive aggregation scheme of input/output vectors is generalized according to an aggregator. Accordingly, cooperation...

A principal component analysis based on the generalized Gini correlation index is proposed (Gini PCA). The Gini PCA generalizes the standard PCA based on the variance. It is shown, in the Gaussian case, that the standard PCA is equivalent to the Gini PCA. It is also proven that the dimensionality reduction based on the generalized Gini correlation...

Court decisions are legal documents that undergo careful analysis by lawyers in order to understand how judges make decisions. Such analyses can indeed provide invaluable insight into application of the law for the purpose of conducting many types of studies. As an example, a decision analysis may facilitate the handling of future cases and detect...

In this paper, it is assumed that income does not have a linear correspondence with utility. Consequently, transfers of income and transfers of utility that could improve social welfare are studied. The conditions for the fulfillment of generalized income transfer principles, relevant to any given order of stochastic dominance, are determined. The...

We propose an Aitken estimator for Gini regression. The suggested A-Gini estimator is proven to be a U-statistics. Monte Carlo simulations are provided to deal with heteroskedasticity and to make some comparisons between the generalized least squares and the Gini regression. A Gini-White test is proposed and shows that a better power is obtained co...

This paper proposes an aggregable family of multidimensional concentration indices which is characterized in order to be consistent with a property of exogenous risk factors, i.e. health risks for which agents are not responsible for. It is shown that those indices are of interest when individuals face different risk factors, whereas traditional in...

Data contamination and excessive correlations between regressors (multicollinearity) constitute a standard and major problem in econometrics. Two techniques enable solving these problems, in separate ways: the Gini regression for the former, and the PLS (partial least squares) regression for the latter. Gini-PLS regressions are proposed in order to...

Data contamination and excessive correlations between regressors constitute a standard and major problem in econometrics. Two techniques enable solving these problems, in separate ways: the Gini regression for the former, and the PLS (partial least squares) regression for the latter. Gini-PLS regressions are proposed in order to treat extreme value...

This note provides a characterization of alpha-Gini inequality measures. These measures generalize the standard Gini index by including one sensitivity parameter \alpha, which captures different value judgments. The \alpha-Gini measures are shown to be weakly decomposable and unit-consistent. Weak decomposition provides within-group and between-gro...

In this paper, it is proven that the usual VAR models may be performed in the Gini sense, that is, on a ℓ1 metric space. The Gini regression is robust to outliers. As a consequence, when data are contaminated by extreme values, we show that semi-parametric VAR-Gini regressions may be used to obtain robust estimators. The inference about the estimat...

The purpose of this paper is to establish a topological relation between several known production models, precisely a link between $\mathbb B$-convex and Cobb-Douglas production models. The framework is based on the algebraic structures of the technology sets, issued from data envelopment, respecting either the assumption of constant elasticity of...

The purpose of this paper is to establish a topological relation between several known production models, precisely a link between -convex and Cobb–Douglas production models. The framework is based on the algebraic structures of the technology sets, issued from data envelopment, respecting either the assumption of constant elasticity of substituti...

Panel data, frequently employed in empirical investigations, provide estimators being strongly biased in the presence of atypical observations. The aim of this work is to propose a l(1) Gini regression for panel data. It is shown that the fixed effects within-group Gini estimator is more robust than the ordinary least squares one when the data are...

The aim of the paper is to investigate the interplay between both transfer principles defined on incomes and utilities. For instance, a social planner who respects an income transfer principle of a given order is not necessarily incline to support the utility transfer principle of the corresponding order. Utility transfer principles are useful to c...

Fixed effects; Gini regression; outliers

Fixed effects; Gini regressions; outliers; Gini decomposition

Gini regression; PLS regression, extreme values, extreme correlations

The concept of efficiency in groups postulates that a coalition of firms has to record a smaller distance toward the aggregate technology frontier compared with the sum of individual distances. Efficiency analysis (either allocative or technical) is defined with respect to cooperative firm game in order to provide operational distance functions, th...

Ce livre a pour objet de guider et d'aider les étudiants dans la résolution d'exercices concernant l'inférence statistique, le calcul des probabilités dans un contexte d'une algèbre de Boole (variables discrètes, continues, unidimensionnelles et bidimensionnelles), l'échantillonnage, les estimations (ponctuelles et par intervalle) et la théorie des...

In this book, Shlomo Yitzhaki and Edna Schechtman investigate the ”Gini methodology”. Both of the authors have dedicated an important part of their life to the development and the understanding of the Gini coefficient and its applications in Statistics, Econometrics, and Economics (welfare and inequality measurement). More generally, the authors ha...

We propose a generalization of the decomposition by population subgroups of the α-Gini index, the so-called multi-level subgroup decomposition. We demonstrate that all components obtained from the decomposition, can integrate in their functional form a parameter of inequality sensitivity being either related to overall inequalities (α) or to betwee...

We introduce the special issue in memory of our late colleague Bernard Philippe of the University of Perpignan. We would like to acknowledge Bernard for the many things he gave us before leaving: scientific rigor, the importance of teaching, open-mindedness, and generosity.

In this article we show that the Gini coefficient is simultaneously decomposable both by sources of income and by populations of income receivers for nonoverlapping income distributions: the so-called first-best Gini multi-decomposition. We show that this multidimensional decomposition is useful for many reasons: (i) it is related to the degree of...

This article proposes a unified technique of the Gini decomposition. The Gini multi-decomposition is a combination of the income source decomposition and the subgroup decomposition. This technique is applied on reference situation and simulated scenarios for partial trade liberalisation in Philippines, and is extended to different orderings to capt...

This article combines computable general equilibrium (CGE) micro-simulation modeling and the Gini multi-decomposition analysis. The CGE-micro-simulation approach enables one to generate endogenous income distributions following government policy interventions. The introduction of these endogenous distributions into the Gini multi-decomposition, tha...

Following Milanovic's (1997) paper, we propose a simple way to compute the Gini index when income y is a quadratic function of its rank among n individuals.

In this paper, we investigate the analytical links between the rate of unemployment, monetary creation and how individuals share the value added in an economy with three types of agents: capital owners, managers and employees. This relationship relies on the fact that the rate of unemployment depends on many macroeconomic characteristics such as: c...

In the second half of the period'1961-2000, the unemployment rate trended down in the United States and the United Kingdom, and trended up steadily in Germany, France, and Italy. Can we explain this divergence by assuming that the impact of wage demands on the value-added breakdown was more restrained in the U.S. and U.K. than in the three continen...

En tendance, durant la seconde partie de la période 1961/2000, le taux de chômage reflue aux États-Unis et au Royaume-Uni, il continue à croître en Allemagne, en France et en Italie. Est-il possible d’expliquer cette divergence d’évolution en supposant que les effets de la revendication salariale sur le partage de la valeur ajoutée ont été mieux ma...

The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, baed on the Shapley Value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that m...

Afin de lutter contre le chômage « ...qui, en dehors de courts intervalles d’emballement, est une conséquence, et à notre avis une conséquence inévitable, de l’individualisme tel qu’il apparaît dans le régime capitaliste moderne. » (Keynes J.M., 1968, p. 394-395), Keynes propose de réguler le fonctionnement de la composante marché des capitaux des...

Four axioms are introduced in order to characterize the family of pair-based decomposable inequality measures, which is embraced in the class of weakly decomposable inequality measures. Three axioms, namely, normalization by pairs, aggregation by pairs, and decomposition by pairs enable the pair-based family of inequality measures to be deduced and...

We show in this paper that the growth rate of the Sen index is multi-decomposable, that is, decomposable simultaneously by groups and income sources. The multi-decomposition of the poverty growth yields respectively: the growth rate of the poverty incidence (poverty rate) decomposed by groups, the growth rate of the poverty depth (poverty gap ratio...

The rate of unemployment in period t depends on GDP and inflation rate in period t − 1. We then show that GDP is related to money creation, and subsequently that the rate of unemployment is a decreasing function of this creation.

Macro/micro-economic modelling has emerged as a rigorous instrument to link policy reforms with changes in income distribution. Indeed, this approach enables one to capture directly the general equilibrium effect of policy reforms upon changes in household welfare. These endogenous distributions combined with the Gini multi-decomposition provide po...

Dans la Théorie générale, le chômage peut être considéré comme la conséquence d’une défaillance de la procédure de détermination des prix. Dans le cadre du modèle WS/PS, il peut être considéré comme la conséquence de l'utilisation de cette procédure par une minorité. Nous proposons une esquisse qui permet de combiner ces deux idées, tout en évitant...

This paper develops a multi-country overlapping-generations general equilibrium model to gauge the economic impacts of demographic changes in the global economy and its transmission effects on different countries. Although severe demographic pressures contribute to significantly lower real GDP per capita across several regions in the world, globali...

This article presents a new synthetic methodology that gauges simultaneously the inequalities in multidimensional poverty within and between groups of population and the dimensions that tend to increase inequality in poverty.

The purpose of this article is to show that the Gini index of equality is decomposable: (i) both by subgroup and income source and (ii) into a parametric configuration permitting statistical inference on equality components. We demonstrate that the Gini index of equality decompositions imply those of the Gini index of inequality. These results sugg...

This paper develops a multi-country overlapping-generations general equilibrium model to gauge the economic impacts of demographic changes in the global economy and its transmission effects on different countries. Although severe demographic pressures contribute to significantly lower real GDP per capita across several regions in the world, globali...

In this article we show that the Gini coefficient is simultaneously decomposable both by sources of income and by populations of income receivers for non-overlapping income distributions: the so-called first-best Gini multi-decomposition. We show that this multidimensional decomposition is useful for many reasons: (i) it is related to the degree of...

The purpose of this paper is to show that the Gini index of equality is: (i) subgroup decomposable throughout interpersonal comparisons; (ii) decomposable by income source; (iii) decomposable both by subgroup and income source; (iv) and decomposable in a multidimensional context permitting statistical inference on equality components. These results...

For any given order of inverse stochastic dominance, standard concentration curves are decomposed into three components, called contribution curves. Those components correspond to within-group inequalities, between-group inequalities, and transvariational inequalities. We prove, for all orders, that contribution curve dominance implies systematical...

The aim of this paper is to offer new risk indicators that enable one to classify securities of a portfolio according to their risk degrees. These indexes are issued from a new method of the covariance decomposition based on the Shapley Value. The risk indicators are computed via the well-known Gini coefficient, which is viewed as a new risk measur...

Au cours de la période 1961/2000, pourquoi la tendance à la hausse des taux de chômage s’est-elle inversée dans des économies « anglo-saxonnes » comme les États-Unis et le Royaume-Uni et pas dans des économies « continentales » telles que l’Allemagne, la France et l’Italie ? Nous soutenons que cette inversion ne peut pas être imputée au fait que ce...

Les mesures d’inégalité du revenu rassemblent deux types d’indicateurs décomposables : les indices décomposables en sous-populations et les indices décomposables en sources de revenu. Les premiers permettent de partager l’inégalité totale en une inégalité intragroupe et une inégalité intergroupe et les seconds d’attribuer à chaque facteur de revenu...

This paper introduces the concept of Pigou-Dalton transfers between populations of income receivers. Gini's mean difference and Dagum's Gini index between populations are axiomatically derived in order to gauge the impact of within- and between-group Pigou-Dalton transfers on Dagum's measure. We show its sensitiveness for any given transfer in the...

Income inequality measures involve two sub-classes of decomposable measures: those decomposed by sub-groups and those decomposed by income source. The former enables one to compute between- and within-group indices. The latter allows for gauging the inequality related to each factor of income (labour income, capital income, social taxes, etc.). The...

Résumé La lecture de la littérature indique que la mesure des inégalités de revenus s’est largement développée depuis les années 1970. L’étude des inégalités mesurées sur les revenus des individus est nécessaire mais non suffisante pour appréhender la complexité des déterminants des inégalités. En ce sens, les techniques de décompositions des mesur...

In this paper, we propose the conception of within-group CD-curve, to apprehend the impact of indirect tax reforms on truncated distributions of consumption expenditures. This confers decision makers the ability to perform within-group transfers as well as between-group transfers to reduce poverty in particular groups or to obtain an overall povert...

Nous soutenons que pour étudier le fonctionnement réel des économies capitalistes, il ne suffit pas de considérer l'innovation comme un processus de destruction créatrice. Il est aussi nécessaire de supposer que les agents de ces économies adoptent une institution ou règle nommée système de paiement. Cette hypothèse permet de proposer deux conclusi...

The purpose of this note is twofold. First, it proposes a multi-decomposition of the Luenberger productivity index, that is, a combined decomposition both by attribute, which is characterized by technical change or efficiency change, and by firm. Second, it applies this technique to the European Union to measure the most important contributions to...

In 1990, Cerioli and Zani introduced an operational multivariate method to analyse and measure poverty, aiming at incorporating several dimensions of poverty. As Dagum and Costa [2004] showed, this study applies the fuzzy set theoretic approach and thus making quantitatively operational the French Social Exclusion Theory and Sen’s analysis of funct...

La littérature montre que la mesure des inégalités de revenu n’est pas suffisante pour appréhender les déterminants des inégalités. Les sources de rémunération, leurs corrélations au revenu global, leurs parts dans le revenu global, rentrent en compte dans la décomposition de la mesure de Gini, faisant aussi apparaître la mesure du pseudo-Gini. Les...

Given the multiplicative decomposition of the Sen index into three commonly used poverty statistics – the poverty rate (poverty incidence), poverty gap ratio (poverty depth) and 1 plus the Gini index of poverty gap ratios of the poor (inequality of poverty) – the index becomes much easier to use and to interpret for economists, policy analysts and...

The aim of this paper is to provide an application of the Shapley Value to decompose financial portfolio risk. Decomposing the sample covariance risk measure yields relative measures, which enable securities of a portfolio to be classified according to risk scales.

Gini and entropy are the most use measures to gauge income inequalities. We show that each measure yields different subgroup decomposition techniques into within-group inequalities and between-group inequalities. Then, we show that the Gini index has been decomposed into many ways to bring out a third measure of income inequalities.scales.

The aim of this paper is threefold. First, we propose a bidimensional decomposition of the Gini ratio that combines two decomposition techniques of inequality measurement in a bivariate distribution context. Usually decomposed measures of inequality are gauged to be significant or not, using non-stratified bootstrap techniques. Second, we show, wit...

In this paper, we show that the rate of unemployment in period t depends on GDP and inflation rate in period t-1. We then show that GDP is related to money creation, and subsequently that the rate of unemployment is a decreasing function of this creation.

The purpose of this paper is to demonstrate the multi-decomposition of the aggregate Malmquist productivity index, that is, a combined decomposition both by attribute, which is characterized by technical change or efficiency change, and by firm.

Nous proposons une nouvelle méthode de décomposition. La multi-décomposition de l'indicateur de Gini combine deux méthodes de décomposition: la décomposition en sous-groupes et la décomposition en sources de revenu. La technique retenue est mise en œuvre dans le cadre d'une étude concernant les revenus italiens des années 1989 et 2000. Elle permet...

The inequalities of net annual wages, estimated via the Gini ratio, declined by about 8% between 1976 and 2000. The indicator fell from 0.322 to 0.296. By using the Gini decomposition and dividing the French population by age group, gender, occupational category, and geographic area, we can estimate the distribution of inequalities over the period.

De 1976à2000,lesinégalitésderémunérationnetteannuelle,mesuréesàl’aidedel’indicedeGini,ontconnuunebaissenotablede 8%. L’indice est passé de 0,322 à 0,296. En effectuant des découpages de la population par âge, sexe, professions et catégorie socioprofessionnelle et région, il est possible, par l’intermédiaire de la décomposition de l’indice de Gini,...

This paper proposes many indicators of vertical and horizontal redistribution throughout a generalized technique of Gini decomposition. Using the TD/BU micro-simulation models with externalities, we simulate income distributions and income source distributions for seven educational groups in Philippines in order to measure the inequality variations...

Cette recherche étend l’approche de Dagum C. et Costa M. [“Analysis and Measurement of Poverty. Univariate and Multivariate Approaches and their Policy Implications. A case of Study: Italy”, dans Dagum C. et Ferrari G. (ed.), Household Behaviour, Equivalence Scales, Welfare and Poverty, Springer Verlag, Germany, p. 221-271, 2004]. Nous développons...

The purpose of this paper is to extend Dagum’s Gini decomposition (“A New Approach to the Decomposition of the Gini Income Inequality Ratio”, Empirical Economics 22(4), 515-531, 1997a) following three types of theoretical modelisation. The first one deals with a “poor/non-poor” decomposition within a sub-group multilevel framework. The second one e...

This article extends the paper of Dagum C. and Costa M. (“Analysis and Measurement of Poverty. Univariate and Multivariate Approaches and their Policy Implications. A case of Study: Italy”, In Dagum C. and Ferrari G. (eds.), Household Behaviour, Equivalence Scales, Welfare and Poverty, Springer Verlag, Germany, 221-271, 2004). We further develop th...

Le but de cet article est de démontrer que l’indice de Malmquist agrégé satisfait la propriété de multi-décomposabilité. Cette dernière permet de combiner la décomposition par firme et la décomposition par attribut qui est caractérisée par le progrès technique et la variation d’efficacité.