Can competing diversity indices inform us about why ethnic diversity erodes social cohesion? A test of five diversity indices in Germany.

An ever-growing number of studies investigates the relation between ethnic diversity and social cohesion, but these studies have produced mixed results. In cross-national research, some scholars have recently started to investigate more refined and informative indices of ethnic diversity than the commonly used Hirschman-Herfindahl Index. These refined indices allow to test competing theoretical explanations of why ethnic diversity is associated with declines in social cohesion. This study assesses the applicability of this approach for sub-national analyses. Generally, the results confirm a negative association between social cohesion and ethnic diversity. However, the competing indices are empirically indistinguishable and thus insufficient to test different theories against one another. Follow-up simulations suggest the general conclusion that the competing indices are meaningful operationalizations only if a sample includes: (1) contextual units with small and contextual units with large minority shares, as well as (2) contextual units with diverse and contextual units with polarized ethnic compositions. The results are thus instructive to all researchers who wish to apply different diversity indices and thereby test competing theories.