On Measuring Concentration in Banking Systems

Abstract

By assuming a Pareto-type distribution of bank sizes within banking systems, we investigate the effect of changes to Zipf's slope parameter (a) and the sample size to the behaviour of different concentration indexes, such as the 3-bank concentration ratio, the Herfindahl-Hirschman index and the 5%-concentration ratio. Analytical relations between these concentration indices are derived and the elasticity of these indexes to changes in a and the sample size N is also investigated. We show different regimes under which each index can be used most appropriately. Our results are relevant to researchers and policymakers who extensively employ these summary measures of concentration.

Keywords: Zipf's law, concentration indices, banking

JEL Classification: G21, L16, C49, D31