On measuring concentration in banking systems

Assuming a Pareto-type distribution of bank sizes, we investigate the effect of changes in Zipf's exponent (α) and the sample size on the behavior of different concentration indices, such as the 3-bank concentration ratio, the Herfindahl-Hirschman index and the top 5%-concentration ratio. We derive analytical relations between these concentration indices and investigate the elasticity of these indices to changes in α and in the sample size N. We show different regimes under which each index can be used most appropriately. Our results are highly relevant for policymakers who rely on such concentration measures to derive public policy recommendations in banking.