On Robust Measurement of Risk, Inequality and Concentration

Many risk, inequality, poverty and concentration measures are extremely sensitive to outliers, dependence, heterogeneity and heavy tails. In this paper we focus on robust measurement of risk, inequality, poverty and concentration under heterogeneity, dependence and heavy-tailedness of largely unknown form using the recent results on t−statistic based heterogeneity and correlation robust inference in Ibragimov & Müller (2007). The robust large sample inference on risk, inequality, poverty and concentration measures is conducted as follows: partition the observations into q ≥ 2 groups, calculate the empirical measures for each group and conduct a standard t−test with the resulting q estimators of the population measures. Numerical results confirm the appealing properties of t−statistic based robust inference method in this context, and its applicability to many widely used risk, inequality, poverty and concentration measures, including Sharpe ratio; value at risk and expected shortfall; Gini coefficient; Theil index, mean logarithmic deviation and generalized entropy measures; Atkinson measures; coefficient of variation and Herfindahl-Hirschman index; head count, poverty gap and squared poverty gap indices and other Foster-Greer-Thorbecke measures of poverty, among others. The results discussed in the paper further indicate a strong link between the t−statistic based robust inference methods and stochastic analogues of the majorization conditions that are usually imposed on risk, inequality, poverty and concentration measures related to self-normalized sums or their transforms, as in the case of Sharpe ratio, coefficient of variation and Herfindahl-Hirschman index. JEL Classification: C1; C12; C13; D31; D63; L11