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The U.S. banking sector has become substantially more concentrated since the 1990s, raising questions about both the causes and implications of this consolidation. We address these questions using nonparametric empirical methods that characterize dynamic power law distributions in terms of two shaping factors -the reversion rates (a measure of crosssectional mean reversion) and idiosyncratic volatilities of assets for different size-ranked banks. Using quarterly data for subsidiary commercial banks and thrifts and their parent bank-holding companies, we show that the greater concentration of U.S. bank-holding company assets is a result of lower mean reversion, a result consistent with policy changes such as interstate branching deregulation and the repeal of Glass-Steagall. In contrast, the greater concentration of both U.S. commercial bank and thrift assets is a result of higher idiosyncratic volatility, yet, idiosyncratic volatility of parent bank-holding company assets fell. This contrast suggests that diversification through non-banking activities has reduced the idiosyncratic asset volatilities of the largest bank-holding companies and affected systemic risk.

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Summary This paper introduces nonparametric econometric methods that characterize general power law distributions under basic stability conditions. These methods extend the literature on power laws in the social sciences in several directions. First, we show that any stationary distribution in a random growth setting is shaped entirely by two factors: the idiosyncratic volatilities and reversion rates (a measure of cross‐sectional mean reversion) for different ranks in the distribution. This result is valid regardless of how growth rates and volatilities vary across different economic agents, and hence applies to Gibrat's law and its extensions. Second, we present techniques to estimate these two factors using panel data. Third, we describe how our results imply predictability as higher‐ranked processes must on average grow more slowly than lower‐ranked processes. We employ our empirical methods using data on commodity prices and show that our techniques accurately describe the empirical distribution of relative commodity prices. We also show that rank‐based out‐of‐sample forecasts of future commodity prices outperform random‐walk forecasts at a 1‐month horizon.