Empirical Methods for Dynamic Power Law Distributions in the Social Sciences

TL;DR

This paper develops nonparametric econometric methods to analyze power law distributions in social sciences, revealing how growth and reversion rates shape stationary distributions and explaining size effects in commodity prices.

Contribution

Introduces novel nonparametric methods to estimate growth and reversion factors in power law distributions, extending the understanding of size effects in social science data.

Findings

Methods accurately describe empirical commodity price distributions

Existence of a generalized size effect in commodities

Stationary distributions shaped by volatility and reversion rates

Abstract

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 show how our results offer a structural explanation for a generalized size effect in which higher-ranked processes grow more slowly than lower-ranked processes on average. Finally, we employ our empirical methods using panel data on commodity prices and show that our techniques accurately describe the empirical distribution of relative commodity prices. We also show the existence of a generalized "size" effect for commodities, as predicted by our econometric theory.