**7. Convergence Analysis**

The evolution of the coefficient of variation, presented in Table 1 and in Figure 2, provides useful information about changes of inequality in Lerner index values across countries and/or years. However, the visual inspection of these changes cannot always provide safe results regarding the existence of convergence or divergence in terms of the Lerner index across euro area countries during a given period, especially when the Lerner index has presented significant ups and downs along this period. The same situation holds in the case of the two concentration measures (HHI/CR5) and the NPL ratio.

To overcome these problems, we employ two concepts of convergence, namely β-convergence and σ-convergence (Barro and Sala-i-Martin 1991), which have been prevailing for many years in the growth literature. β-convergence applies if poor countries tend to catch up with rich ones in terms of per capita income or product levels. In the case of competition, β-convergence would apply if countries with lower levels of competition were found to tend to catch up with countries with higher levels of competition. On the other hand, σ-convergence applies if the dispersion of per capita income or product across countries declines over time. The existence of β-convergence is a necessary but not sufficient condition for σ-convergence. Regarding competition, σ-convergence would apply if the dispersion of competition levels across countries showed a tendency to decline over time.

In the case of competition, the β-convergence test is performed through the estimation of Equation (14).

$$\ln\left(\frac{\mathbb{C}\_{\text{it}}}{\mathbb{C}\_{i,t-1}}\right) = \alpha + \beta ln\mathbb{C}\_{i,t-1} + \sum \mathbb{C}\_{\text{count}}ry\_i + \varepsilon\_{it} \tag{14}$$

where *Cit* is the level of competition, as expressed by the (inverse of) the Lerner index, in country *i* in year *t*, α and β are parameters to be estimated, *Countryi* are dummy variables to control for possible country effects, and ε*it* is a random error term. There is β-convergence when the coefficient β in (14) is statistically significant and negative. A higher absolute value of the coefficient β corresponds to a greater tendency towards β-convergence.

Following Lapteacru (2018), the σ-convergence test is performed through the estimation of Equation (15):

$$D\_{\rm if} = \alpha + \sigma T + \sum \text{Country}\_{\rm i} + \varepsilon\_{\rm it} \tag{15}$$

where *Dit* is the absolute value of the difference between the competition in country *i* in year *t* and the average competition in year *t*, *T* is a time trend, α and σ are parameters to be estimated, *Countryi* are dummy variables to control for possible country effects, and ε*it* is a random error term. There is σ-convergence when the coefficient σ in (15) is statistically significant and negative. A higher absolute value of the coefficient σ corresponds to a greater tendency towards σ-convergence.

The estimation of Equations (14) and (15) is performed by applying Ordinary Least Squares (OLS) regressions. A same type convergence analysis, as that described for competition, was also performed for concentration (HHI/CR5) and NPLs. The results, which are presented in Table 7, cover the total period under study (i.e., 2005–2017), as well as two important sub-periods: (a) the period 2008–2012, which includes the years of the financial and debt crisis in the euro area, and (b) the period 2013–2017. This division was based on the evolution of financial integration in the euro area. As Berenberg-Gossler and Enderlein (2016) note, financial integration reached a minimum in July 2012. After the ECB announcement of the OMT program on 26 July, 2012, there was a gradual, but often fragile, decline of financial market fragmentation across all markets. It should also be noted that the sub-period 2005–2007 was not included in the regression analysis, due to its limited time coverage that might possibly provide biased estimations.


**Table 7.** Regression results for β-convergence and σ-convergence.

Notes: Standard errors are reported in parentheses. \*, \*\* and \*\*\* indicate statistical significance at the 10%, 5% and 1% levels respectively. Country dummies are not reported for brevity. Source: BankScope database, ECB, World Bank, own calculations.

According to the regression results of Table 7, the Lerner index of market power presented β-convergence in all country groups across all the three periods examined. These results are generally in accordance with the results of β-convergence tests, performed by Weill (2013), which sugges<sup>t</sup> that during the period 2002–2010 the least competitive banking systems in the EU-27 experienced a greater improvement in competition than the most competitive banking systems. Regarding σ-convergence, the related regression coefficient for the period 2008–2012 for both the EA-19 and the EA-Co groups is positive and statistically significant, thus indicating a diverging trend. This coefficient remains positive for the period 2013–2017, however having lost its statistical significance. Regarding the EA-Pe group, its related regression coefficient for the period 2008–2012 was found to be positive, but not statistically significant. In the period 2013–2017, it became negative, but still not statistically significant. According to the regression results for the total period 2005–2017, both the EA-19 and the EA-Co

groups experienced a diverging trend of market power, while the regression coe fficient for the EA-Pe group is positive, but not statistically significant.

The adverse evolution of the σ-convergence of market power during the period under examination may be attributed to the 2008 crisis, which led to distortions in competition created by the state aid granted to banks, while mergers were allowed without taking into account their e ffects on market power (Maudos and Vives 2019).

The σ-convergence related regression coe fficient of the HHI concentration measure for both the EA-19 and the EA-Co groups in the period 2008–2012 is negative and statistically significant; thus, indicating a converging trend. The corresponding regression coe fficient for the EA-Pe group is also negative, but not statistically significant. Its sign turned to positive in the period 2013–2017, with the coe fficient remaining not statistically significant. In addition, the HHI concentration measure did not present β-convergence in the case of both the EA-19 and the EA-Co groups during this period. Finally, the EA-Co group was the only one that experienced σ-convergence during the total period 2005–2017. From 2008 to 2012, both the EA-19 and the EA-Co groups experienced σ-convergence of the CR5 concentration measure, in contrast to the EA-Pe group, the regression coe fficient of which was found to be negative, but not statistically significant. The CR5 concentration measure did not present β-convergence during the period 2013–2017 in any of the three country groups under examination. The regression results also show that none of the three groups experienced σ-convergence during the total period 2005–2017, with the situation being worse in the case of EA-Pe group.

The observed diverging trends in concentration, measured by the HHI and CR5 concentration indices, were caused by the global financial crisis of 2008, which accelerated the pace of bank concentration in the countries that had been hit most severely by the crisis and whose banking systems had been subject to restructuring (Maudos and Vives 2019). Concentration in Cyprus and Greece, which were already characterized by highly concentrated banking systems, increased further during the crisis period, widening the gap with Italy, which has the lowest bank concentration in the EA-Pe group, including strong cooperative and savings banking sectors (ECB 2016). Regarding the EA-Co group, which was a ffected less than the EA-Pe group by the global financial crisis, the observed diverging trends in concentration during the period 2013–2017 may be attributed to the fact that in countries, such as Austria, France, and Luxembourg, which were already characterized by very low bank concentration, concentration decreased further, widening the gap with other more concentrated banking systems in the EA-Co group.

During the period 2008–2012, both the EA-19 and the EA-Pe groups experienced lack of σ-convergence with respect to the NPL ratio, while the related regression coe fficient for the EA-Co group was found to be positive, but not statistically significant. The situation for the EA-Co group changed in the period 2013–2017, since the related regression coe fficient not only changed to negative but also became statistically significant; thus, suggesting a clear convergence. In the case of the EA-19 group, the related regression coe fficient remained positive. Finally, the NPL ratio did not present β-convergence in the case of the EA-Pe group during the period 2013–2017. Regarding the total period 2005–2017, both the EA-19 and the EA-Pe groups experienced a clear divergence, in contrast to the EA-Co group, the regression coe fficient of which was found to be negative, albeit not statistically significant.

The convergence of the NPL ratio in the EA-Co group during the period 2013–2017 may be attributed to the fact that the countries of this group are characterized by low or relatively low levels of NPLs. Although the NPL levels increased enormously in Latvia and Lithuania at the outburst of the crisis, they entered into a very sharp decreasing path afterwards. On the contrary, the divergence of the NPL ratio in the EA-Pe countries may be attributed to the fact that these countries experienced higher levels of NPLs than the EA-Co countries during the crisis, which remain very high in the case of Cyprus and Greece.
