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Nonparametric methods and local†time†based estimation for dynamic power law distributions

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  • Ricardo T. Fernholz

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 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.

Suggested Citation

  • Ricardo T. Fernholz, 2017. "Nonparametric methods and local†time†based estimation for dynamic power law distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(7), pages 1244-1260, November.
  • Handle: RePEc:wly:japmet:v:32:y:2017:i:7:p:1244-1260
    DOI: 10.1002/jae.2573
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    Cited by:

    1. Fernholz, Ricardo & Kramer, Rory, 2021. "Racing to Zipf's Law: Race and Metro Population Size 1910-2010," SocArXiv p5tuh, Center for Open Science.
    2. Ricardo T. Fernholz & Robert Fernholz, 2022. "Permutation-weighted portfolios and the efficiency of commodity futures markets," Annals of Finance, Springer, vol. 18(1), pages 81-108, March.
    3. Ricardo T. Fernholz & Robert Fernholz, 2017. "Zipf's Law for Atlas Models," Papers 1707.04285, arXiv.org, revised Jun 2020.
    4. Ricardo T. Fernholz & Christoffer Koch, 2018. "The Rank Effect," Papers 1812.06000, arXiv.org.
    5. Fernholz, Ricardo T. & Koch, Christoffer, 2021. "The rise of big U.S. banks and the fall of big European banks: A statistical decomposition," European Economic Review, Elsevier, vol. 135(C).
    6. Fernholz, Ricardo T. & Hagler, Kara, 2023. "Rising inequality and declining mobility in the Forbes 400," Economics Letters, Elsevier, vol. 230(C).
    7. Ricardo T. Fernholz & Caleb Stroup, 2018. "Asset Price Distributions and Efficient Markets," Papers 1810.12840, arXiv.org.
    8. Ricardo T. Fernholz & Robert Fernholz, 2020. "Permutation-Weighted Portfolios and the Efficiency of Commodity Futures Markets," Papers 2001.06914, arXiv.org, revised Dec 2020.

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