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 agents, and hence applies to analyses based on Gibrat's law and its extensions. We also discuss results that use our methods to link these two econometric factors to mobility, as measured by the expected transition times from one rank in the distribution to another. Second, we present techniques to estimate these two factors using panel data.
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