Zipf ’s Law and Its Correlation to the GDP of Nations

Abstract

This study looks at power laws, specifically Zipf ’s law and Pareto distributions, previously used to describe city size distribution, income distribution within firms, and word distribution within languages and documents among other things, and Gibrat’s law describing growth rate. This study seeks to discover if Zipf’s law can also be used to model the distribution of GDP’s worldwide using Gibrat’s law as a justification. The simplest method to determine Zipf's law’s applicability, and the one used in this study, was to create a log log plot, plotting rank versus size of the GDPs. Using that plot, Zipf ’s law was verified through two criteria. First the plot must appear linear and second it must have a slope of -1. For the purpose of this study, the data looked at was for all countries and then countries split into categories of emerging economies and advanced economies for the years 2005, 2006, 2007, and 2008. The results of this study showed that all countries and countries with emerging economies did not appear linear on the log log plot while advanced economies appeared linear with a slope roughly -.70, suggesting that GDP distribution of advanced economies instead follow a Pareto distribution. Advanced economies also showed a significantly smaller variation in growth rates over the four years as implied by Gibrat’s law. This was used as a possible explanation for the distribution discovered.