Bank mergers as scale-free coagulation

Abstract

The asset size distribution of US banks is viewed as the result of a scale-free coagulation process. When two banks merge, the assets of the combined institution equals the sum of the assets of the constituent banks. Analysis of the Smoluchowski coagulation equation suggests the emergence of a steady state, power-law distribution with an exponent that only depends on the degree of homogeneity of the coagulation rate. Bank merger data satisfies such power-law scaling. We develop an underlying theoretical framework for bank mergers quite different from prevailing ideas based on game theory on the one hand, and recent econophysical models on the other. As a corollary we show that in order to avoid the emergence of a mega-bank, the rate of return should decrease with the bank size. Finally, we suggest that stochastic coagulation may provide a unifying description of fast integration processes characteristic of globalization.