Department of Applied Economics IV, University of the Basque Country UPV/EHU, Avd. Lehendakari Aguirre 83, 48015 Bilbao, Spain.
J Health Econ. 2012 Jul;31(4):578-83. doi: 10.1016/j.jhealeco.2012.02.006. Epub 2012 Apr 25.
In several economic fields, such as those related to health or education, the individuals' characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. In this note we propose a procedure to define indicators that measure equally the achievement and shortfall inequality. Specifically, we derive measures which are invariant under ratio-scale or translation transformations, and a decomposable measure is also obtained. As the indicators proposed depend on the distribution bounds, families of indices that guarantee the same inequality rankings regardless of the distribution maximal levels are identified.
在几个经济领域，如与健康或教育相关的领域，个体的特征是由有界变量来衡量的。因此，这些特征可能是由成就或不足来模糊地表示的。当需要评估不平等时，就会出现困难。人们可以关注成就或不足，但各自的不平等排名可能会导致矛盾的结果。在本说明中，我们提出了一种定义指标的方法，该指标可以平等地衡量成就和不足的不平等。具体来说，我们推导出了在比率尺度或平移变换下不变的度量，并且还得到了一个可分解的度量。由于所提出的指标取决于分布边界，因此确定了保证相同不平等排名的指数族，而与分布的最大水平无关。
