ENTROPY - BASED SEGREGATION INDICES Ricardo

Recent research (Reardon and Firebaugh, 2002, Frankel and Volij, 2009, and Mora and RuizCastillo, 2009a) has shown that two entropy-based segregation indices possess an appealing mixture of basic and subsidiary but useful properties. It would appear that the only fundamental difference between the mutual information, or M index, and the Entropy, Information or H index, is that the second is a normalized version of the first. This paper introduces another normalized index in that family, the H* index that, contrary to what is often asserted in the literature, is the normalized entropy index that captures the notion of segregation as departures from evenness. More importantly, this paper shows that applied researchers do better using the M index than using either H or H* in two circumstances: (i) if they are interested in the decomposability of segregation measures for any partition of organizational units into larger clusters and of demographic groups into supergroups, and (ii) if they are interested in the invariance properties of segregation measures to changes in the marginal distributions by demographic groups and by organizational units.