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

Midões C. de Crombrugghe D.
December 2023 Springer

Journal of Economic Inequality
2023 #21 Issue 4 899 - 924 pp.

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.

Bootstrap inference , Difference-in-inequality testing , Inference on inequality measures , Permutation tests , Sample splitting

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Institute of Environmental Science and Technology of the Universitat Autònoma de Barcelona (ICTA-UAB), Barcelona, Spain
Ca’ Foscari University of Venice, Venice, Italy
Nazarbayev University, Astana, Kazakhstan
Maastricht University, Maastricht, Netherlands

Institute of Environmental Science and Technology of the Universitat Autònoma de Barcelona (ICTA-UAB)
Ca’ Foscari University of Venice
Nazarbayev University
Maastricht University

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