Department of Economics, University of Oregon, Eugene, OR 97403-1285, USA.
J Health Econ. 2011 Jan;30(1):214-9. doi: 10.1016/j.jhealeco.2010.10.008. Epub 2010 Nov 10.
In measuring inequality of a bounded variable such as health status, one can focus on attainments or shortfalls. However, rankings of social states by attainment and shortfall inequality do not necessarily mirror one another. We propose a requirement, that attainment inequality and shortfall inequality be measured consistently, and we examine the performance of partial orderings and indices of inequality in this respect. For relative inequality and all currently documented intermediate inequality concepts, the orderings fail our consistency requirement, as do all indices which respect these orderings. However, the absolute inequality partial ordering satisfies consistency. We identify two classes of indices of absolute inequality, one containing rank-independent and the other rank-dependent indices, which measure attainment and shortfall inequality consistently (in fact identically). The only subgroup decomposable inequality index, of any type, which measures attainment and shortfall inequality consistently is the variance. We discuss implications for the study of pure health inequality.
在衡量健康等有界变量的不平等时，可以关注实现程度或差距。然而，实现程度和差距不平等的社会状态排名不一定相互反映。我们提出了一个要求，即实现程度不平等和差距不平等的衡量应保持一致，并在这方面检验了部分排序和不平等指数的性能。对于相对不平等和所有目前记录的中间不平等概念，排序不符合我们的一致性要求，所有尊重这些排序的指数也是如此。然而，绝对不平等的部分排序满足一致性。我们确定了两类绝对不平等指数，一类包含独立于排名的指数，另一类包含依赖于排名的指数，它们一致地（实际上是相同地）衡量实现程度和差距不平等。任何类型的唯一可分组分解不平等指数，一致地衡量实现程度和差距不平等的指数是方差。我们讨论了对纯健康不平等研究的影响。
