**8. Conclusions**

In this study, we examined the evolution of competition (through market power and concentration) and credit risk (through non-performing loans) across euro area core (EA-Co), periphery (EA-Pe) and all 19 countries (EA-19) in the period 2005–2017, as well as in two sub-periods, 2008–2012 and 2013–2017. Furthermore, we tested two hypotheses with respect to competition, concentration and credit risk: (a) the existence of fragmentation in the euro area as a whole (EA-19), as well as in core countries (EA-Co) and periphery countries (EA-Pe), and (b) the presence of β-convergence and σ-convergence among the country-members of each of the three groups.

Our analysis extends beyond the period of financial crisis, thereby taking into account the non-standard measures adopted by the ECB to support further integration. By using data from all the 19 euro area countries, which have a common currency and a single bank supervisory mechanism, a possible bias that might stem from the use of either heterogeneous data or data coming from only a subset of euro area countries was eliminated, allowing for robust testing of fragmentation and converging or diverging trends. In addition to uncovering the evolution of bank competition and risk, providing substantiated clues to policy makers about the progress of integration was a major aim of our research.

Competition (as expressed by the inverse of the Lerner index of market power) reached a minimum in 2015 and increased afterwards in all three country groups under examination (EA-19, EA-Co and EA-Pe), in line with a gradual but fragile post-crisis reintegration trend. This is supported by the Theil inequality index for market power, which reveals a decrease of the between-country inequality from 2011 onwards in each of the three groups. This evolution was also confirmed by means of β-convergence and σ-convergence tests, which showed a decrease in divergence of competition. Another finding is that the global financial crisis reversed the advances in competitive pressure that had been observed during the preceding few years.

With respect to concentration, as measured by the HHI and CR5 concentration indices, the average concentration in EA-19 and EA-Co started decreasing in 2015 and 2012, respectively, in contrast to EA-Pe, where concentration has followed a continuously increasing path since 2007. The progress that had been made during the period 2008–2012 with the achievement of β-convergence and σ-convergence in the whole euro area and the core countries was reversed in the period 2013–2017. Periphery countries did not experience convergence of concentration in either of the two periods 2008–2012 and 2013–2017.

Regarding credit risk, NPL ratios have always been higher in EA-Pe. Moreover, while the weighted average of the NPL ratio in EA-Co peaked in 2013 at 3.38%, in EA-Pe the peak of 15.56% was in 2014. The decrease thereafter has not been proportional between the two groups, in line with the β-convergence and σ-convergence tests, which indicate that the EA-Co group experienced β-convergence and σ-convergence in the period 2013–2017, while the EA-Pe group has been characterized by divergence. The Theil inequality index confirms the divergence between the two groups, indicating that the inequality between the EA-Co and the EA-Pe groups has been continuously increasing since 2008. This evolution suggests that the presence of persistent large stocks of NPLs remains a pressing challenge, which contributes to fragmentation between euro area countries. Hence, more e ffective measures, such as the creation of asset managemen<sup>t</sup> companies, NPL transaction platforms, securitization, or state guarantees schemes, should be introduced in order not only to reduce the existing NPL volumes, but also to prevent their increase in the future.

All in all, the persistence of fragmentation, in spite of some partial reintegration trends, suggests that policy measures accelerating convergence of our variables would not only strengthen financial integration, but also help in establishing a real euro area banking union.

**Author Contributions:** Conceptualization, M.K. and H.L.; methodology, M.K. and H.L.; software, M.K.; validation, M.K.; formal analysis, M.K.; investigation, M.K.; resources, M.K.; data curation, M.K.; writing—original draft preparation, M.K.; writing—review and editing, M.K. and H.L.; visualization, M.K. and H.L.; supervision, H.L.; project administration, H.L.; funding acquisition, H.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** Financial assistance from the Research Centre of the Athens University of Economics and Business.

**Acknowledgments:** The authors would like to thank participants at the ASSET Conference (Athens 2019), FEBS Conferences (Athens 2019; Prague 2019), JIMF Conference (Marrakech 2019), and EBES Conference (Kuala Lumpur 2020), for discussing and commenting on many of the research questions and approaches of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
