PurposeThis article investigates the validity of the different types (conditional, unconditional, deterministic, stochastic) of ß-convergence in per capita GDP for EU-28 and EU-19 between 1990 and 2019.Design/methodology/approachThe study uses nonstationary heterogeneous panel-data methodology.FindingsThe panel data reveal that both conditional and unconditional ß-convergence are valid in EU-28 countries However, only conditional convergence exists in EU-19 countries; group-specific findings show that the income levels of 10-EU countries converge toward the EU-19 average and 11-EU countries converge to the EU-28. The convergence speed to EU average varies between 15 and 18%. The robustness of the augmented mean group (AMG) findings are checked with common correlated effects mean group (CCEMG) and are consistent. Moreover, panel unit root tests are applied to examine the stochastic and deterministic convergence of the average EU per capita income in the two groups of EU economies. The findings show no evidence of deterministic or stochastic convergence in EU countries. Besides, conditional convergence has not been experienced in countries such as Bulgaria, Croatia, Czech Republic, Hungary, Latvia, Malta, Romania, Slovakia and Slovenia, which are new members of the EU. As a remarkable aspect of the study, the evidence suggests that the Brexit is economically rational for the UK.Originality/valueThe growth and convergence processes of economies differ from each other. Convergence studies in the literature are generally based on the cross-section OLS methodology. In this context, the study is one of the rare studies to examine convergence using heterogeneous panel techniques and allows the convergence of countries to the EU average to be analyzed individually.