Trannoy
Alain Trannoy
Publications
Disaggregation arises when broad categories like households budget units are divided into elementary units as individual income recipients. We study the preservation of stochastic dominance for every order beyond two after disaggregation: If we observe a dominance relation among household income distributions, it is also true at the individual level. We find necessary and sufficient conditions satisfied by the common sharing rule adopted by households to divide the cake among individuals. The sharing function, which maps the household income into the outcome of the disadvantaged individual, must have derivatives of the same sign as the utility function characterizing the stochastic order of interest. In addition, the household has to follow a compensating rule, meaning that at the margin the distribution should be in favor of the disadvantaged individual.
Deux méthodes sont généralement envisagées pour l'évaluation des politiques de santé. L'approche coût-bénéfice s'appuie sur la somme des consentements individuels à payer : elle respecte les préférences individuelles mais elle donne une priorité aux préférences des plus riches car leurs consentements à payer sont en général plus élevés. L'approche coût-efficacité sélectionne les politiques assurant le gain le plus élevé en matière de santé globale, à coût total donné. Elle n'avantage pas les individus à revenu élevé, mais elle peut avoir d'autres effets indésirables : par exemple favoriser le traitement d'une affection bénigne qui profitera au plus grand nombre par rapport à une affection grave touchant peu de personnes. Une variante de l'analyse coût-bénéfice évite ces différents écueils. Elle consiste à pondérer les consentements à payer par des coefficients qui varient en sens inverse d'un indicateur de bien-être individuel combinant revenu et état de santé. L'indicateur choisi est le revenu équivalent santé : il s'agit du revenu effectif de l'individu diminué du montant auquel il serait prêt à renoncer pour être en parfaite santé. À revenu donné, il décroit donc quand la santé se détériore. Contrairement à des indices d'utilité subjective, il a l'avantage de ne s'appuyer que sur les préférences ordinales des individus. Cette approche est mise en œuvre à l'aide d'une enquête conduite sur un échantillon représentatif de la population française. Compte tenu de leurs contraintes financières, les personnes à bas revenu accordent moins d'importance relative à leur état de santé. Mais les coefficients obtenus permettent néanmoins de surpondérer les individus les moins favorisés cumulant faible revenu, mauvaise santé et forte préférence pour l'amélioration de cette santé. Ces coefficients sont ensuite mobilisables pour l'évaluation de toute politique pour laquelle on connaitrait les consentements individuels à payer.
Purpose:
We analyze equality of opportunity for earnings acquisition in France between 1973 and 1993 defining individual circumstances by parental earnings. We compare two different definitions of circumstances. In the first one they are measured by the father's earnings level, in the second one by the father's rank in the earnings distribution.
Methodology:
First we use stochastic dominance tools. Then we decompose the evolution of inequality of opportunity using the mean logarithmic deviation and the results of regressions of descendants’ earnings on their parents’ earnings.
Findings:
Inequality of opportunity has remained stable when conditioning on the earnings level of the father, whereas it has diminished when conditioning on his rank in the earnings distribution. The former result is explained by the stable intergenerational earnings elasticity. The latter by the decreasing wage inequality in the previous generation.
Originality:
Our analysis emphasizes that the assessment of equality of opportunity and its evolution is very sensitive to the partition of circumstances used. Moreover, it stresses the complementarity between the discrete and the continuous approaches for measuring inequality of opportunity.
This paper proposes a dominance approach to study inequality of well-being across countries. We consider a class of well-being indices based on the three attributes used in the HDI (Human Development Index). Indices are required to satisfy: preference for egalitarian marginal distributions of income, health and education, ALEP substitution of attributes and priority to poor countries in allocating funds to enhance health and education. We exhibit sufficient conditions for checking dominance over the defined class of well-being indices. We apply our method to country data from 2000 to 2005. The deterioration in health conditions in poor countries is why welfare improvements at the world level cannot be ascertained.
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No abstract is available for this item.
This paper presents a general procedure inspired by the Shapley value for decomposing any inequality indices by factor components or by sub-populations. To do so we define an inequality game. Despite the fact that the characteristic function is not super-additive in general and that the linearity assumption of the space of inequality game does not hold, an axiomatization of the Shapley value is given in this context by using the Potential function pioneered by HART and MAS-COLELL [1989]. This result proves to be useful in illustrating a trade-off between the desirable properties of consistency and marginality. A comparison of such decomposition with the decomposition method investigated by SHORROCKS [1982] is provided in the case of factor component decomposition. Refinement of the Shapley decomposition is investigated when the set of income sources is nested. Furthermore, an application to the sub-population decomposition problem is also investigated.
