Persistence in ecological footprint inequality across European Union countries: evidence from unit root tests

To develop effective and equitable emission reduction policies in the European Union, it is necessary to consider not only the level of environmental inequality but also its persistence over time. Therefore, examining the stationarity properties of inequality indicators is important for determining whether such inequalities are temporary or permanent. Accordingly, this study analyzes the stationarity characteristics of ecological footprint inequality in the European Union for the period 1961–2024. Ecological footprint inequality is measured using three complementary inequality indices: the Gini coefficient, the Theil-T index, and the Atkinson index. In addition to traditional unit root tests such as ADF, PP, and KPSS, the analysis employs Fourier-based tests, structural break unit root tests, and the artificial intelligence-based ARNN-ADF test to examine the stationarity structure of the series. Furthermore, the ARFIMA model is employed as a robustness check to assess the long-memory properties of ecological footprint inequality. The findings of this study are test-dependent. Conventional unit root tests suggest level stationarity, whereas Fourier-based, structural-break and nonlinear tests provide stronger evidence of persistence. ARFIMA results further indicate a stationary long-memory process operating close to the non-stationarity boundary. These findings suggest that shocks to ecological footprint inequality are not purely transitory but tend to persist over long periods. Overall, the results highlight the need for structural and long-term policies to reduce ecological footprint inequalities across European Union countries.