Abstract
In this study, we investigate the sensitivity of different concentration measures, such as classical index concentration and spatial index concentration, to varying regimes for Zipf's exponent (Ɓ) for the Pareto-type distribution of bank sizes. We establish relationships between each concentration measure and Zipf's exponent by introducing the Riemann zeta function and calculating the elasticity for each index. We prove that the spatial concentration index is the most robust for varying regimes. Therefore, the choice of an appropriate concentration index must be carefully considered before drawing inferences about the relationship between concentration and banking fragility.
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