Un cadre général pour le calcul des élasticités inégalités de la pauvreté

Many authors have recently emphasized the crucial role of income inequalities in the design of efficient policies aimed at reducing poverty. However, the link between variations of the degree of inequality and variations of poverty are not well documented. The literature, for instance, does not provide any satisfying tool for predicting how a small relative variation of the Gini index can be associated to a variation of the headcount index. In the present paper, we define a family of Lorenz curve transformations that can directly be interpreted in terms of relative variations of known inequality measures. Then, we extend pcitet{kakwani-93} methodology for the calculation of inequality elasticities of poverty. Improvements are threefold with respect to pcitet{kakwani-93} works. First, our formulas do not confine to the sole Gini index. Secondly, they embrace the uncertainty and the complexity of the mechanical link between inequality and poverty. Third, using some flexible functional form, one can easily perform an accurate estimation of the point inequality elasticities of poverty corresponding to observed variations of a given income distribution. Finally, we propose a simple measure that may be helpful to assess how ``pro-poor'' are inequality variations by comparing the observed elasticities with the set of theoretical elasticities that could be obtained from the initial income distribution.