A statistical evidence of power law distribution in the upper tail of world billionaires’ data 2010–20

Abstract

There are real life phenomena in which the underlying process forces the majority of the objects to be small and very few to be large, e.g., wealth, city sizes, firm sizes and many alike. Such behaviors are said to follow heavy tailed distribution. To give a statistical understanding of the wealth disparity, this study investigates the tail behavior of world billionaires’ data 2010–20 taken from Forbes magazine. For this purpose, initially, the tails of underlying data sets are identified by estimating the minimum thresholds using KS test. Then three well known models namely, Power Law, Lognormal and Exponential are tested to model the tail behavior through different model adequacy criteria e.g., KS, AIC, BIC, LRT and Bayes factor. Based on numerical results using KS test, AIC, BIC and Bayes factor, we observed that upper tail of wealth data for each year follows a well-known PL distribution with exponent ranging from 1.306 to 1.571 while LRT results depict that both PL and Lognormal distribution are equally adequate for the upper tail of wealth data. Moreover, the estimate of PL exponent is significantly higher than unity which implies that the distribution of wealth among billionaires is more evenly distributed than as suggested by Zipf’s Law. Results obtained using rolling sampling indicate that the PL exponent is inversely related to the sample size. However, no such pattern is witnessed in the bootstrap simulation results while estimating the PL exponent.