{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T06:49:21Z","timestamp":1759042161685},"reference-count":33,"publisher":"Wiley","issue":"7","license":[{"start":{"date-parts":[[2017,5,15]],"date-time":"2017-05-15T00:00:00Z","timestamp":1494806400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J of Applied Econometrics"],"published-print":{"date-parts":[[2017,11]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>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\u2010sectional 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\u2010ranked processes must on average grow more slowly than lower\u2010ranked 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\u2010based out\u2010of\u2010sample forecasts of future commodity prices outperform random\u2010walk forecasts at a 1\u2010month horizon.<\/jats:p>","DOI":"10.1002\/jae.2573","type":"journal-article","created":{"date-parts":[[2017,5,15]],"date-time":"2017-05-15T09:06:43Z","timestamp":1494839203000},"page":"1244-1260","source":"Crossref","is-referenced-by-count":7,"title":["Nonparametric methods and local\u2010time\u2010based estimation for dynamic power law distributions"],"prefix":"10.1002","volume":"32","author":[{"given":"Ricardo T.","family":"Fernholz","sequence":"first","affiliation":[{"name":"Robert Day School of Economics and Finance Claremont McKenna College Claremont, CA USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2017,5,15]]},"reference":[{"key":"e_1_2_7_2_1","doi-asserted-by":"crossref","unstructured":"Alquist R. &Coibion O.(2014).Commodity\u2010price comovement and global economic activity. 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