Empirical Methods for Dynamic Power Law Distributions in the Social Sciences

31 Pages Posted: 22 Feb 2016 Last revised: 17 Apr 2016

See all articles by Ricardo T. Fernholz

Ricardo T. Fernholz

Claremont McKenna College - Robert Day School of Economics and Finance

Date Written: April 12, 2016

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.

Keywords: power laws, Pareto distribution, Gibrat's law, nonparametric methods

JEL Classification: C10, C14

Suggested Citation

Fernholz, Ricardo T., Empirical Methods for Dynamic Power Law Distributions in the Social Sciences (April 12, 2016). Available at SSRN: https://ssrn.com/abstract=2735847 or http://dx.doi.org/10.2139/ssrn.2735847

Ricardo T. Fernholz (Contact Author)

Claremont McKenna College - Robert Day School of Economics and Finance ( email )

500 E. Ninth St.
Claremont, CA 91711-6420
United States

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