Real Convergence Across the Euro Area

This paper studies the relationship between real convergence in the euro area and macroeconomic imbalances. It compares the main features of convergence within the euro area with other EU and non-EU country groups, looking at both ‘sigma’ and ‘beta’ convergence in output and total factor productivity. Expected convergence paths for euro area countries are estimated using growth regressions run on a large panel of advanced and emerging market economies and compared to actual growth. The findings support the view that EU and euro area countries display similar convergence patterns to those of other country groups, while the group of countries that adopted the euro first exhibit relatively weak convergence since before the financial crisis. Such differences could be partly linked to relatively low dispersion in per capita incomes across this country group, although lack of convergence is also largely due to persisting differences in total factor productivity performance. The findings also suggest that macroeconomic imbalances accumulated in the pre-crisis period such as high private and government debt and strong growth in the non-tradable sector have been associated with lower convergence, particularly for euro area countries.

In the run-up to the Economic and Monetary Union (EMU), the Maastricht criteria emphasised nominal convergence as a requirement for achieving a stable common currency, with the entry criteria requiring convergence in nominal variables including infl ation, interest and exchange rates, public defi cits and debts. At the same time, the academic debate was largely focused on the desirable characteris-tics of countries sharing a common currency. In line with the optimal currency area (OCA) theory (Mundell, 1961), countries ought to be suffi ciently similar and integrated to reduce the likelihood of asymmetric shocks and have fl exible product and labour markets to lower the costs of adjusting in the absence of nominal exchange rates. In this respect, the academic debate in the period preceding the EMU was focused on real rather than on nominal convergence, emphasising the structural transformations along the convergence process that would reduce differences in economic institutions, the occurrence of asymmetric shocks and adjustment costs in a monetary union.
During the fi rst decade of the EMU, nominal convergence appeared to go hand in hand with real convergence. Nominal interest rates converged on the back of fi nancial integration and a reduction in perceived risks. In anticipation of a stable currency and no redenomination risks, both the mean and the variance of ten-year government bond rates across 12 euro area (EA) countries dropped signifi cantly between 1994 and 1997 (see Figure 1). This process lasted for about a decade, but was interrupted by the European sovereign debt crisis of 2010-2012, during which this variance spiked to levels last seen only prior to the 1990s. Real convergence in per capita incomes was observed across the whole euro area but not among the EA11 (founding members including Greece but excluding Convergence in domestic demand and a reversal in the convergence process (Diaz del Hoyo, 2017).
The dispersion in external positions was mirrored in diverging unemployment trends (see Figures 3 and 4). Between 1999 and2007, the periphery was in a relatively strong cyclical position resulting in falling unemployment rates. Over the same period, cyclical positions were weaker in the core and unemployment increased between 2002 and 2005. This pattern reversed in the post-crisis period, when current account reversals were followed by surging unemployment in the periphery.    Convergence patterns in the euro area have been closely connected to dynamics in capital fl ows and current account balances. In the run-up to the EMU, capital fl ew from countries in the euro area 'core' to the 'periphery'. Current account divergences were generally seen as supportive of the convergence process as capital moved from relatively high-income countries to relatively lowincome ones (Blanchard and Giavazzi, 2002). The global fi nancial crisis, however, implied a reappraisal of risk and a sudden withdrawal of capital from the periphery. 'Sudden stops' in current accounts led to a major contraction 1 See also ECB (2015).

Convergence
These developments had implications not only for the cycle but also for the growth potential. Prior to the crisis, the fl ow of investment to the periphery was channelled primarily to the non-tradable sector. This meant that persistent real interest rate differentials were refl ected not only in the differences in cyclical positions, according to the Walters critique of the EMU, but also in divergent economic structures, notably the composition of output between tradables and non-tradables (Buti and Turrini, 2015). 2 The growth of the non-tradable sector in the euro area periphery -in some cases the counterpart of largescale housing market bubbles -was generally accompanied by cost competitiveness losses and worsened the prospects for a more durable growth engine based on exports.
The aim of this paper is to test the hypothesis that precrisis macroeconomic imbalances had implications for real convergence within the euro area. Previous work has analysed the link between business cycle synchronisation and variables related to macroeconomic imbalances. 3 The present instead focuses on the role of imbalances in explaining the pace of convergence.
In doing that, this paper goes a step further than existing companion papers in several respects. 4 First, it assesses convergence patterns across the euro area against the experience of other non-EU and non-euro area benchmark country groups. To this purpose, a large panel including advanced and emerging economies is considered. Second, it explores convergence along different dimensions, not only in terms of per capita GDP but also in terms of total factor productivity (TFP). Both 'sigma' and 'beta' convergence are analysed. Third, it relates deviations from expected convergence paths to a number of variables associated with the presence of macroeconomic imbalances, including government and private debt, current account balances, net international investment positions (NIIP), credit fl ows and growth in the non-tradable sector.

Real convergence in the euro area
The dataset used in this analysis is a large panel of advanced and emerging economies, obtained mostly from the Summers-Heston Penn World Tables (PWT) version 9.1. 5 These contain comparable information on variables expressed in purchasing power parity for many countries and years.
Before turning to evidence on real convergence across the euro area, the notions of beta convergence and sigma convergence are recalled.
Unconditional beta convergence is observed when the growth rate of real per capita GDP is negatively related to the starting level of real per capita GDP.
Conditional beta convergence is observed when the growth rate of real per capita GDP is negatively related to the initial level of real GDP per capita, taking into account the impact of other variables that may affect growth. Formally, where, the average growth rate of country i over a time period t is approximated by the log difference of GDP per capita,  logY it , and is put in relation with the level of GDP per capita at the start of the period Y it-1 , a set of Z it conditioning variables, and a random disturbance u it .
Beta convergence implies that poorer economies eventually catch up with richer countries by growing faster, hence parameter β in equation (1) is expected to be negative. Moreover, conditional beta convergence implies that countries converge to steady-state growth rates that may differ depending on country characteristics.
The concept of sigma convergence relates to the crosssectional dispersion of income. There is sigma convergence if income dispersion across a specifi c group of countries declines over time. Abstracting from the set of conditioning variables Z, equation (1) can be rewritten as follows (see Barro Sala-i-Martin, 2004).
If λ > 0, equation (2) implies that poor countries grow faster than rich ones (i.e. there is beta convergence). Defi ning the variance of logY it as σ t 2 , equation (2) also implies where σ t

Convergence
Moreover, the fall in dispersion is stronger the higher the existing degree of dispersion σ t-1 2 ..

Sigma convergence
To assess sigma convergence, Figures 5 and 6 show the standard deviation of log GDP per capita for the euro area, the EU, the EA11 and a broader group of high-income countries. Figure 5 displays data from 1995 to avoid missing data for former transition countries, while Figure 6 has a longer horizon by excluding transition countries from the country groups. The dynamics of income dispersion indicate that sigma convergence has been faster in the EU and the euro area than among other high-income countries. This confi rms previous studies that regard the EU as a 'convergence club'. 6 However, the group of EA11 countries displays convergence mostly up to the mid-1970s (when the longer horizon is considered) and divergence after the global fi nancial crisis, particularly when countries that underwent macroeconomic adjustment programmes in the aftermath of the global fi nancial crisis are included.
In the neoclassical growth model (Solow, 1956;Swan, 1956), output convergence is driven by convergence in the capital stock. Incentives to invest are higher in countries with a relatively low capital stock and higher marginal productivity of capital. Figure 7 looks at convergence patterns in the capital stock per capita to check whether the neoclassical model prediction matches the data. The graph compares the EA11 group and the larger group of advanced non-transition economies since 1960 and the euro area countries since 1995 (due to missing data). It 6 See Böwer and Turrini (2010).
appears that convergence is much more visible when looking at capital per capita rather than GDP per capita, including for the EA11 group. This confi rms the standard mechanism of convergence from neoclassical growth theory.
Dynamics in GDP per capita may differ from those in capital per capita because of the impact of TFP. 7 In modern growth theory, where TFP growth is the result of a process of innovation and gradual adoption of new vintage technologies, income convergence can also be driven by TFP convergence (Aghion and Howitt, 2006). Countries further away from the frontier have more room to grow by adopting better technologies that already exist. Figure 8 shows the standard deviation of TFP in the EA11. Some limited convergence seems to have played a role up until the 1990s. However, TFP dispersion fl uctuated afterwards. There is more evidence of steady convergence for the broader set of advanced economies as well as for the euro area, despite the short time series available for the latter.
A comparison of sigma convergence for GDP per capita with that of GDP per employee is provided in Figure 9 for the EA11 group. The graph shows quite clearly that while the dispersion in the two variables co-moved quite closely over the whole period starting from the 1960s, an upward spike occured in GDP per capita after the crisis, whereas evidence of divergence is much more limited for the GDP per employee. This fi nding permits a better interpretation of the divergence process in the post-crisis period as a 7 Using a standard Cobb-Douglas production function, y = Ak α , where y and k stand, respectively, for output and capital per worker and A is TFP.  Convergence phenomenon that was not caused by strong divergence in capital per employee or TFP, but rather by a very large divergence in employment rates.
Overall, there is evidence of sigma convergence in the euro area occurring at rates similar to those observed across other country groups. For the EA11, sigma convergence appears to have occurred slowly up until the mid-1970s. The relatively slow rate of convergence in GDP per capita is partly due to the EA11 group being highly homogeneous in terms of income conditions. An additional factor that underpins the stall in income convergence is the lack of TFP convergence in recent decades. The divergence in income per capita in the postcrisis period is mainly linked to divergent employment rates. This phenomenon is likely transitory and concentrated in the few countries most affected by post-crisis recessions, induced by the unwinding of macroeconomic imbalances and debt crises.
The absence of sigma convergence does not imply absence of beta convergence. In other words, it does not exclude that in general countries with relatively low income per capita have witnessed faster growth, as the occurrence of certain types of shocks can produce dispersion.

Beta convergence
Beta convergence takes place when countries with a lower income per capita grow faster over a medium-to long-term period. Figure 2 shows prima facie evidence of beta convergence in the euro area. A more rigorous analysis also needs to take into account that growth rates across countries not only vary because of different initial income conditions, but also because of other factors that explain long-term growth performance. In this respect, growth regressions are estimated to take these variables into account as well. Evidence on convergence obtained from growth regressions are interpreted as a test for 'conditional' convergence. In addition to initial income per capita, growth rates are put in relation to other possible explanatory variables by means of a panel regression that exploits both cross-sectional and time-series variation. More specifi cally, the regression estimated is as follows: where the dependent variable Y it is either output per capita (in PPP) or TFP and Z it is a vector of control variables. The subscript i refers to countries, and t is the time period over which growth rates are computed. Following standard practice in the estimation of growth regressions

Figure 9
Sigma convergence: GDP per capita vs GDP per employee -standard deviations, EA11 Sources: Penn World Tables 9.1.

Convergence
with panel data, annual observations are converted into averages over fi ve-year, non-overlapping sub-periods, in order to avoid short-term disturbances (see Barro Sala-i-Martin, 2004).
The control variables capture factors that affect steadystate growth in the neoclassical growth model. Population growth accounts for the dilution of capital stock per capita and is associated with an expected negative coeffi cient. The share of investment in GDP serves as a proxy for the savings rate, which should be associated with faster capital accumulation (positive coeffi cient expected). A measure of human capital accumulation (the PWT 9.1 index of human capital based on years of schooling and return to education) is also included to account for investment in skills yielding improvements in labour input (a positive coeffi cient is expected). 8 Two additional variables aim to control for factors that may affect TFP growth: openness to trade (imports plus exports as a share of GDP) accounts for the fact that open economies can import technology and know-how (Edwards 1996;Frenkel and Romer, 1999); quality of institutions, as measured by the Fraser index of economic freedom, takes into account the fact that good institutions are associated with stronger incentives to innovate and take risks (Glaeser et al., 2004). The terms γ and δ are region and time effects, 8 See Mankiw et al. (1992).
respectively. The inclusion of fi xed effects capturing main world regions permits the control of unobserved factors specifi c to geographical areas without the loss of crosssection variation implied by a full set of country fi xed effects (Temple, 1999).
The estimation results are shown in Table 1. Results are displayed for the full sample of 66 advanced and emerging economies and for country sub-samples and sub-periods. 9 The control variables generally have the expected signs, even though some coeffi cients are not signifi cant for all regions and periods. A well-known diffi culty when estimating growth regressions is the possible endogeneity of investment, as this variable not only affects growth, but is also driven by expected growth rates. The issue does not seem to be relevant in these estimates, however, as the coeffi cient of the investment variable is qualitatively  unchanged when using instrumental variables estimation, using the price of investment goods as an instrument for investment, as is customary in related literature. 10 For the whole sample of countries, there is evidence of beta convergence as the coeffi cient on the logarithm of the initial GDP per capita is negative and statistically signifi cant, providing therefore support to the catchingup hypothesis. This is also the case for the EU (column 3) and for the euro area (column 4), but not for the EA11 (column 5). Looking only at the period after euro adoption (columns 6-8), the same results still hold for the euro area, the EU and the EA11. However, looking at the period after 2007, which includes mostly the global fi nancial crisis and the European sovereign debt crisis, evidence of convergence for the euro area and the EU becomes weaker (columns 9 and 10). In the case of the EA11, after 2007 the evidence points to divergence rather than convergence, as the coeffi cient for initial per capita income becomes positive, although insignifi cant in column 11. 11 10 Exogeneity tests also indicate that investment can be treated as exogenous. Tests for exogeneity and validity of instruments are reported in Table 1. 11 The estimation results for the shorter sample starting after 2007 are only indicative as the number of observations is small. In particular, inference for this sample should be viewed with caution throughout the analysis.
Growth regressions have also been run to test for convergence in TFP growth. Table 2 shows the estimation results. Initial TFP, human capital, investment, institutions (Fraser index) and openness have all been considered as possible control variables. Initial TFP is expected to be negatively associated with TFP growth as laggard countries have more room to grow by adopting existing technologies. Human capital controls for the fact that countries with a more educated population tend to innovate more. The variable that measures institutional quality accounts for different incentives for innovation and entrepreneurship. Openness controls for the degree of impediments to technology absorption. Apart from initial TFP levels and institutions, other control variables appear to be statistically insignifi cant in explaining TFP growth (column 1). Once restricting the specifi cation to signifi cant variables in column 2, the coeffi cient for initial TFP levels are barely affected. Columns 3-9 therefore use this restricted specifi cation, controlling only for initial TFP and institutions captured by the Fraser index.
Results provide evidence that TFP convergence exists among the whole sample of countries (columns 1 and 2), as well as for the EU and the euro area (columns 3 and 4). There is instead no evidence of convergence for the EA11, and TFP appears to diverge over the period following the fi nancial crisis (columns 5, 8 and 9). Conversely, there is evidence of convergence across the EU as a

Convergence
whole even for the post-crisis sub-sample (columns 6 and 7).

Deviations from convergence paths: A role for macroeconomic imbalances?
What factors could have been responsible for the lack of convergence across the euro area? Did macroeconomic imbalances play a role? To answer these questions, a fi rst necessary step is to construct a measure of the 'convergence gaps', namely quantify the gap between actual growth and the growth paths to steady-state growth rates expected on the basis of the relevant characteristics of countries, i.e. the initial level of output per capita and all other conditioning factors. These paths are obtained using the prediction from the regression estimated on the largest panel of countries and sample period (column 1, Table 1 for GDP and column 2, Table 2 for TFP). The predictions are based on the full sample to obtain more robust and less distorted estimates. As an illustration, Figure 10 plots actual GDP growth with the predicted growth paths for GDP for euro area countries over fi ve-year periods.
The second step is to relate deviations of per capita GDP (or TFP) from these predicted convergence paths to variables refl ecting the presence of macroeconomic imbalances. Figures 11 and 12 indicate some correlation between deviations and stocks of private debt and current accounts, respectively. To simultaneously take into account the role of different sources of macroeconomic imbalances, a multivariate regression analysis is carried out. To formally test for the role that imbalances have played in the convergence process, regression (5) is estimated using OLS: where ε it measures the convergence gap from GDP per capita or TFP regressions (i.e. the residuals obtained from the regressions estimated on the full sample, see Table 1 and Table 2), while IMB stands for a set of variables associated with macroeconomic imbalances. Six variables refl ecting possible macro-economic imbalances are considered: (i) the initial private debt-to-GDP ratio; (ii) the initial government debt-to-GDP ratio; (iii) the initial net international investment position (NIIP) in percent of GDP; (iv) credit to the private sector as a share Prediction from growth regression variable and the construction share are both demeaned by the country long-term average to allow for different economic structures. The current account gap is estimated as the difference between the actual current account balance as a share of GDP and the one that can be explained by the fundamentals of the economy (current account norm), following the methodology proposed in Figure 11 Convergence gaps and private debt stocks Source: Eurostat and authors' estimations.

Figure 12
Convergence gaps and current accounts Source: Eurostat and authors' estimations. Table 3 Deviations from convergence paths and macroeconomic imbalances Note: Robust t-statistics in brackets. Constant, time effects and regional effects included. ** p<0.01, * p<0.05, + p<01 Source: Eurostat and authors' estimation. Private debt/GDP in 2010, % area countries. 13 Current accounts seem instead less important for euro area countries in explaining deviations from convergence paths. A possible interpretation is that the liquidity provision by the European System of Central Banks helps mitigate the real effects of current account sudden stops (Merler and Pisani-Ferry, 2012). Finally, convergence paths among euro area countries appear to be comparatively more related to the growth in the nontradable sector. The narrowing of interest rate differentials in the euro area periphery, as a result of the monetary union, was matched by capital infl ows largely channelled into the construction sector and other non-tradable activities. The fact that resources were largely absorbed in non-tradable activities meant the euro area periphery had less room to grow out of exports when domestic demand became constrained by deleveraging needs. Moreover, as TFP growth is generally faster in the tradable sector, the growth of construction and non-tradable activities was associated with subsequent disappointing growth rates in TFP.

Conclusions
This paper reviews convergence patterns across the euro area and analyses the role of macroeconomic imbalances in providing a possible explanation for lack of convergence in the post-crisis period. The analysis shows that convergence in the euro area was similar to that observed among other country groups, while convergence within the EA11 (founding members excluding Luxembourg) has been lacking since the 1980s, in light of persistent absence of TFP convergence and partly associated with the fact that this is an already relatively homogeneous group in terms of per capita income. Post-crisis divergent employment rates reinforced this pattern.
Our analysis also shows that deviations from expected convergence paths are associated with a number of initial conditions, which summarise the presence of macroeconomic imbalances -private debt in particular. Most interestingly, convergence gaps within the euro area seem to be affected by a number of peculiar factors, notably government debt and the share of the non-tradable sector on value added, which do not play a signifi cant role in a comparison group. Convergence gaps across euro area countries also appear to have been comparatively less affected by external imbalances, possibly in light of the more limited extent of current account reversals within the euro area.
13 For evidence on the relation between government debt and credit risk on government bonds, see Bernoth et al. (2012). De Grauwe and Ji (2013) also fi nd that bond spreads are more sensitive to investor sentiment in countries of a monetary union than in stand-alone countries. Coutinho et al. (2018). The main data sources are Eurostat and AMECO. For non-EU countries, these sources were complemented with data from the World Economic Outlook and the Bank of International Settlements databases. Table 3 shows the results, displayed separately for the euro area and for a comparison group consisting of all countries in the sample except the euro area. It also shows two sample splits in time: after 1999, the year when the euro was introduced, and after 2007, i.e. after the eruption of the fi nancial crisis. Results are displayed both for convergence gaps relating to GDP per capita growth and to TFP growth.
For the sample starting in 1999, private debt, government debt, NIIP and the share of construction are signifi cant in explaining euro area GDP per capita convergence gaps. The corresponding coeffi cients have the expected signs. By looking at results for non-euro area countries, a loss in signifi cance is observed for all variables except private debt, while current accounts acquire some explanatory power. Results remain similar for the euro area when restricting the analysis to the post-crisis period. Wald tests fail to reject the null hypothesis that the estimated coeffi cients for the two sub-periods are equal at the 95% confi dence level. Conversely, for non-euro area countries, the signifi cance is lost for all variables.
Overall, this evidence indicates that high private debt is signifi cantly associated with subsequent growth below the one expected on the basis of fundamentals. This result appears robust across country groups and time.
For the euro area, high public debt and a high weight of non-tradables in output also seem important in driving growth below expected paths. As for external imbalances, the results are less robust. Deviations from TFP growth paths are confi rmed in the euro area especially the role of private debt and the tradable sector, while for non-euro area countries, a signifi cant role is found only for private debt.
The above results suggest an association between convergence gaps and macroeconomic imbalances, and that this association presents particular features in the case of euro area countries. The relatively stronger role of government debt in explaining convergence gaps of euro area countries is consistent with the fact that the probability of bond market tensions increases with the size of debt. As government debt is higher on average in euro area countries and since bond market tensions affect growth notably via reduced credit availability linked to sovereign-bank doom loops, one should expect a stronger impact of government debt on subsequent convergence paths for euro

Convergence
Overall, the analysis underscores the importance of conditions ensuring macro stability and resilience for economic convergence. Preventing the accumulation of excessive private debt is particularly important both inside and outside the euro area. In addition, there is a specifi c role for maintaining prudent levels of public debt and running prudent fi scal policies within the euro area. An important policy implication is that sustainable convergence requires addressing legacy imbalances.