De-composing diversity: In-group size and out-group entropy and their relationship to neighbourhood cohesion

Ethnic diversity is typically measured by the well-known Hirschman-Herfindahl Index. This paper discusses the merits of an alternative approach, which is in our view better suited to tease out why and how ethnic diversity matters. The approach consists of two elements. First, all existing diversity indices are non-relational. From the viewpoint of theoretical accounts that attribute negative diversity effects to ingroup favouritism and out-group threat, it should however matter whether, given a certain level of overall diversity, an individual belongs to a minority group or to the dominant majority. We therefore decompose diversity by distinguishing the in-group share from the diversity of ethnic out-groups. Second, we show how generalized entropy measures can be used to test which of diversity's two basic dimensions matters most: the variety of groups, or the unequal distribution (balance) of the population over groups. These measures allow us to test different theoretical explanations against each other, because they imply different expectations regarding the effects of in-group size, out-group variety, and balance. We apply these ideas in an analysis of various social cohesion measures across 55 German localities and show that in-group size matters more for natives, and out-group diversity more for immigrants. In both groups, the variety component of diversity seems to be decisive. These findings provide little support for group threat as an important mechanism behind negative diversity effects, and are most in line with the predictions of theories that emphasize coordination problems, asymmetric preferences, and network closure, which are maximized where there are many small groups.