درباره اندازه گیری تمرکز در سیستم بانکداری

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.

Deregulation, liberalization, and consolidation in the banking industry, reflected by increasing cross-border mergers and growing M&A activity within national boundaries, have increasingly prompted concerns about greater market power enjoyed by banks and the subsequent impact upon financial stability (Mishkin, 1999 and De Nicoló et al., 2004). It is therefore critical to assess the implications of these developments on bank market structure to draw appropriate policy inferences. Moreover, commonly used concentration measures such as the k-bank concentration ratio 1 and the Herfindahl–Hirschman index (HHI) are extensively used as a proxy for competition in models explaining banking sector performance as a function of market structure ( De Nicoló et al., 2004, Barth et al., 2004 and Beck et al., 2006). In some countries, such as in the U.S., these concentration measures play a pertinent role in the enforcement of anti-trust laws ( Bikker, 2004). In sum, precise measures of concentration are crucial for welfare-related public policy making in the banking industry. This letter compares and contrasts alternative measures of concentration, Zipf's α, and the top 5% concentration ratio (k5%k5%) with the more widely used 3-bank concentration ratio (k3k3) and the Herfindahl–Hirschman index (HHI). We also discuss the regimes in which the application of these indices is appropriate in order to draw better inferences for public policy in banking. To this end, we evaluate the sensitivity of our measures to different sample sizes and different bank size distributions, since the number of banks varies considerably across banking systems. Finally, we present an empirical illustration of the proposed measures using bank data obtained for 15 countries.

We present an analysis of the sensitivity of different measures of concentration to different distribution specifications and sample sizes for the banking industry. Under the assumptions of a Pareto-type distribution of bank sizes, we compare the sensitivity of k3k3, k5%k5% and HHI measures of concentration under different regimes. Our results indicate that the relative concentration index (k5%k5%) is more adequate for comparing concentration of samples with α<1α<1 and large sample sizes (N>50N>50). However, for small sample sizes, N<50N<50, the k5%k5% index is inadequate and the HHI or k3k3 measures are preferable. Of these two, the k3k3 bank concentration ratio is least sensitive to both changes in α and N. The analyzes highlight that policymakers in banking should take such parameters into account when comparing concentration measures across different banking markets. We illustrate our findings with an empirical example by analyzing the distribution of bank sizes in a cross-country setting. For our sample, with values of 0.25<α<1.10.25<α<1.1 and sample sizes ranging from N=60N=60 to N=1478N=1478 per country, we conclude that the most robust concentration index is k5%k5%. However for other types of distributions and sample sizes, this may not be the case. Clearly, for these cases, adequate measures of concentration should be selected. Therefore, the choice of the concentration index and the purpose for which it is used should be carefully investigated before using these indices to draw inferences about the relation between concentration and other economic factors such as the degree of competition in banking.