Assumption-light and computationally cheap inference on inequality measures by sample splitting: the Student-t approach

Inference on inequality indices remains challenging, even in large samples. Heavy
right tails in income and wealth distributions hinder the quality and threaten the
validity of asymptotic approximations to finite sample distributions. Attempts to
improve on asymptotic approximations by bootstrap techniques or permutation
tests are only partial successes. We evaluate a different approach to robust inference, relying on Student t statistics obtained from split samples. This relatively
simple ‘t-based’ approach requires no consistent variance estimators, no random
sampling of populations, and only mild distributional assumptions. We compare
its performance with that of refined bootstrap and permutation techniques. We
find that the more complex bootstrap methods still have the edge in one-sample
tests, where the t-approach suffers from a negative skew. In two-sample comparisons though, the t-approach offers advantages: it is undersized while bootstrap tests and permutation tests are often oversized. In certain circumstances it is less powerful than permutation tests and bootstrap tests, but for large samples, this difference dissipates. It is also more generally applicable than permutation tests
and easily generates confidence intervals. These differences are illustrated with an
empirical application using two different sources of household data from the Russian Federation.