We examine inequality persistence in a multicountry unbalanced panel using a battery of stationarity and long‐run memory tests. Inequality is measured by the Gini indices of income inequality. Results suggest that we cannot reject a unit root in inequality measures. This applies to both gross and net indices: thus while redistributive measures have reduced the level of inequality, they have not sufficiently modified its apparent unit root. A more likely conclusion is that inequality measures are exceptionally persistent if not strictly a unit root. We also introduce a new panel stationarity test useful for series subject to unknown structural breaks.