Empirical analyses of income and wealth inequality often face the difficulty that the observations are heterogeneous, heavy-tailed or correlated in some unknown fashion. This paper focuses
on applications of the recently developed computationally simple approach t-statistic based robust inference approach in the analysis of inequality. Two regions can be compared in terms of
inequality as follows: the data in the samples relating to the two regions are partitioned into
small numbers of groups, and the chosen inequality index/measure is estimated for each group.
Inference is then based on standard t-tests with the resulting group estimators. The t-statistic
based approach results in valid inference, as long as the group estimators of the inequality index
are asymptotically independent, unbiased, and Gaussian, possibly with different variances. These
conditions are typically satisfied in empirical applications. The presented method complements
and compare favorably with other approaches to inference on inequality. We apply this approach
to examine income inequality across Russian regions. Our analysis reveals that income distribution in Russia is notably heavy-tailed, with most regions exhibiting higher levels of inequality
compared to Moscow. Robust comparisons of this type offer a good foundation for evaluating
and shaping regional policies aimed at addressing income disparities.