http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WJ3-45FCBSK-23&_user=984616&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000049824&_version=1&_urlVersion=0&_userid=984616&md5=5bd07d5825126723d2a79f17691c76bb
http://dx.doi.org/10.1006%2Fjeth.1999.2565

This paper explores a natural decomposition requirement for inequality measures, motivated by Shorrocks and Anand, which we call path independent decomposability. Given a collection of population subgroups, overall inequality is to be decomposed into between-group and within-group terms based on a notion of a representative income of a population (such as the mean income). Between-group inequality is the measure applied to the smoothed distribution, which replaces each income in a subgroup with its representative income. Within-group inequality is the measure applied to the standardized distribution which re-scales subgroup distributions to a common representative income level. Path independence then requires overall inequality to be the sum of the within and between-group terms.