This study examines the lack of convergence among EU countries from a structural perspective. We apply the tradable-non-tradable framework (T-NT) to evaluate the heterogeneity in labour productivity before and after the great recession. We find that, across all countries, non-tradables were less relevant for aggregate productivity. The low productivity growth in peripheral EU countries was accompanied by a specific structural change pattern: there was a sharp production increase of non-tradables before the crisis relative to other EU countries. For most peripheral countries concerns about unfavourable sector structures remain, implying a continuation of unsustainable growth patterns. This has implications for the European Commission's macroeconomic imbalance procedures, since it allows identifying patterns of real divergence on a disaggregated level. Finally, we identify a link between sectoral growth asymmetries and the quality of domestic governance institutions. Especially differences in the legal system help to explain the observed productivity growth differentials.