Physica A: Statistical Mechanics and Applications, Forthcoming
6 Pages Posted: 9 May 2014 Last revised: 1 Feb 2015
Date Written: November 11, 2014
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in domains with power law tails, especially for low values of the exponent. These estimators can vary over time and increase with the population size, as shown in this article, thus providing the illusion of structural changes in concentration. They are also inconsistent under aggregation and mixing distributions, as the weighted average of concentration measures for A and B will tend to be lower than that from A U B. In addition, it can be shown that under such fat tails, increases in the total sum need to be accompanied by increased sample size of the concentration measurement. We examine the estimation superadditivity and bias under homogeneous and mixed distributions.
Keywords: Risk, Inequality, Statistics
Suggested Citation: Suggested Citation
Taleb, Nassim Nicholas and Douady, Raphael, On the Super-Additivity and Estimation Biases of Quantile Contributions (November 11, 2014). Physica A: Statistical Mechanics and Applications, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2434363 or http://dx.doi.org/10.2139/ssrn.2434363