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Title: Robust inference on income inequality: t-statistic based approaches Authors:  Rustam Ibragimov - Imperial College London and St. Petersburg State University (United Kingdom) [presenting]
Paul Kattuman - University of Cambridge (United Kingdom)
Anton Skrobotov - Russian Presidential Academy of National Economy and Public Administration and SPBU (Russia)
Abstract: Empirical analyses on income and wealth inequality often face the difficulty that the data are heterogeneous, heavy-tailed or correlated in some unknown fashion. The focus is on applications of the recently developed robust $t$-statistic methods in the analysis of inequality measures and their comparisons under the above problems. In particular, a robust large sample test on equality of two parameters of interest (e.g., a test of equality of inequality measures in two regions or countries) is conducted as follows: The data in the two samples dealt with is partitioned into fixed numbers $q_1$, $q_2>1$ (e.g., $q1 = q2 = 2, 4, 8$) of groups, the parameters (inequality measures) are estimated for each group, and inference is based on a standard two-sample $t$-test with the resulting $q_1$, $q_2$ group estimators. This results in valid inference under general conditions that group estimators of parameters (e.g., inequality measures) considered weakly converge, at an arbitrary rate, to independent mixed normal random variates. The conditions are typically satisfied in empirical applications even under pronounced heavy-tailedness and heterogeneity and possible dependence in observations. The methods complement and compare favorably with other inference approaches available in the literature. The use of robust inference approaches is illustrated by an empirical analysis of income inequality measures and their comparisons across different regions in Russia.