# An Empirical Analysis of Income Convergence in the European Union

**ABSTRACT** In this paper, we investigate the convergence process within the European Union (27 countries). More particularly, we study the convergence process of the new entrants from Central and Eastern Europe and of the 15 Western countries between 1990 and 2007. Applying a panel approach to the convergence equation derived by Mankiw et al. (1992) from the Solow model, we highlight the existence of heterogeneity in the European Union and show that new entrants and former members of the European Union can be seen as belonging to significantly differ ent groups of convergence. The existence of heterogeneity in the European Union or the Eurozone might affect their stability as the recent Greece’s sovereign debt crisis illustrates it.

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**ABSTRACT:**This paper explores empirically the issue of income convergence for the Balkans over the period 1994–2011 and the investigation relies on income differentials from both the averages of the European Union’s-15 (EU-15) and the European Union’s-24 (EU-24) as well as within the Balkan group. The adopted methodology deploys the non stationary panel unit root framework to cope with the problem of limited sample providing more reliable insight and, in particular, the analysis uses the univariate and panel minimum Lagrange Multiplier (LM) unit root tests, suggested by Lee and Strazicich (2003, 2004) and Im et al. (2005), that accounts for one and two endogenously determined structural breaks. The overall evidence is in favor of catching up with the EU benchmark cases as well as in favor of convergence within the Balkan area. However, disparities for some countries are confirmed.Empirica 03/2013;

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Centre de Recherche en Economie Publique et de la Population

CREPP Working PaPer Series

CREPP WP No 2010/01

An Empirical Analysis of Income Convergence in the European

Union

Laurent Cavenaille

David Dubois

April 2010

CREPP - Centre de recherche en Economie Publique et de la Population

Boulevard du Rectorat 7 (B31)

4000 Liège Belgium

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An Empirical Analysis of Income Convergence

in the European Union∗

Laurent Cavenaile†

David Dubois‡

April 21, 2010

Abstract

In this paper, we investigate the convergence process within the European Union

(27 countries). More particularly, we study the convergence process of the new

entrants from Central and Eastern Europe and of the 15 Western countries be-

tween 1990 and 2007. Applying a panel approach to the convergence equation

derived by Mankiw et al. (1992) from the Solow model, we highlight the existence

of heterogeneity in the European Union and show that new entrants and former

members of the European Union can be seen as belonging to significantly differ-

ent groups of convergence. The existence of heterogeneity in the European Union

or the Eurozone might affect their stability as the recent Greece’s sovereign debt

crisis illustrates it.

JEL Classification: O47, O52

Keywords: Economic Growth, Convergence, European Union, Panel Approach

∗We are grateful to Lionel Artige, Denis de Crombrugghe and all the participants at

the 15th May HEC-ULg Seminar for their helpful comments.

†HEC-Universit´ e de Li` ege, Belgium. Address: HEC-ULg, Rue Louvrex 14, Bldg N1,

B-4000 Li` ege, Belgium. Tel. (+32)42327432. E-mail: Laurent.Cavenaile@ulg.ac.be

‡HEC-Universit´ e de Li` ege, Belgium. Address: HEC-ULg, Bld du Rectorat 7, Bldg B31,

B-4000 Li` ege, Belgium. Tel. (+32) 43663125 E-mail: David.Dubois@ulg.ac.be

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1 Introduction

The idea of integrating Central and Eastern Europe countries in the Euro-

pean Union dates back to the early 1990’s. On the first of May 2004, ten

new countries1joined the European Union. Among these ten countries, eight

belong to Central and Eastern Europe. Less than three years later, on the

first of January 2007, two other countries from Eastern Europe, Bulgaria and

Romania, entered the European Union which is now composed of 27 coun-

tries. For the first time in its history2, EU opened its doors to countries from

the former Eastern bloc.

Less than fifteen years after the collapse of the Soviet bloc in 1990 and the

resulting shift from a planned economy to a market economy system, some

Central and Eastern Europe countries were allowed to join the European

Union which was until then exclusively composed of Western countries.

Obviously, candidates to the European Union membership have to meet some

political and economic requirements. In particular, applicants must possess

stable institutions that ensure the respect of democracy and human rights,

a viable market economy system and the capacity to cope with competitive

pressures.3If these constraints have forced the new entrants from Central

and Eastern Europe to achieve some kind of structural and institutional con-

vergence toward Western standards, there still remains a long way to cover

before they can catch up their backwardness in terms of income per capita.

While the membership to European Union might be expected to speed up the

process of convergence to the Western Europe countries in terms of per capita

income levels, we can wonder if the income level convergence must be a con-

sequence of membership or a necessary prerequisite. Indeed, the European

Union does not impose any conditions on the process of income convergence

before joining the Eurozone. A central question is then to verify if new en-

trants already exhibit income convergence with the existing members of the

European Union or if we can identify the existence of two heterogeneous

groups in terms of convergence process within the European Union. Too

large heterogeneities within the European Union or the Eurozone might be

problematic as the recent troubles surrounding the Greece’s sovereign debt

have underlined it. As a consequence, testing the absence of heterogeneity,

among others, in terms of income convergence might be of prime importance

before a country is allowed to join the Eurozone.

1These ten countries are the Czech Republic, Estonia, Hungary, Latvia, Lithuania,

Poland, Slovenia and Slovakia plus Cyprus and Malta.

2If we except the somewhat particular case of East Germany.

3See Article 49 of the Treaty on European Union (Treaty of Maastricht, 1992) and the

criteria set by the European council in Copenhagen (1993).

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In this context, this paper focuses on the process of convergence in terms of

per capita income levels in the European Union. We will make use of regres-

sion models which have been developed in the growth convergence literature

to check whether the countries in the European Union in 2010 are already

converging . More particularly, we examine the convergence process of two

distinct groups i.e. the 15 Western countries and the new entrants coming

from the former Eastern Bloc.

Our paper is structured as follows. We first introduce the theoretical Solow

model, a short review of the literature on growth convergence, estimation

procedures and convergence within the European Union. The last sections

of our paper are dedicated to the description of our methodology, our empir-

ical results and to their analysis.

2 Literature Review

The debate on convergence between neoclassical and new growth theory pro-

ponents has led to a large number of definitions of the term convergence and

to a very well developed literature on the topic (for a thorough review of the

literature, see Islam (2003)). For our analysis, we consider the Neoclassical

Growth Solow model (1956).

The production function considers two factors of production, namely labour

L and capital K. This function has two important properties. First, it ex-

hibits constant returns to scale and, second, it assumes diminishing returns

to each factor. This second assumption is crucial for the model and especially

in the study of convergence. We include a technology variable A which is

labour-augmenting.

Y (t) = K(t)α(A(t)L(t))1−α

If we express the variables in intensive form (i.e. per effective worker) the

production function is then y(t) = k(t)αand the evolution of the capital can

be written as:

˙k(t) = sy(t) − (n + g + δ)k(t)

= sk(t)α− (n + g + δ)k(t)

where s is the constant saving rate, n the growth rate of the population, g

the rate of technological progress and δ the rate capital depreciation. Note

that s, n, g and δ are exogenous and thus determined outside the model.

We can derive that k converges to the following steady state value:

k∗= [s/(n + g + δ)]

1

1−α

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and then plugging k∗into the production function, taking the logs and di-

viding by labour we find the steady state income per capita:

ln(Y (t)

L(t))∗= lnA(0) + gt +

α

1 − αln(s) −

α

1 − αln(n + g + δ)

Thus, at the steady state, the income per capita depends positively on the

saving rate and negatively on the population growth rate.

Moreover if we consider that the share α of capital is around one third while

the share of labour is two third, then the elasticity of income with respect to

s is around 0.5 and the elasticity with respect to (n + g + δ) is around -0.5.

Rearranging, we end up with the following form:

ln(y(t)) − ln(y(0)) = (1 − e−λt)

α

1 − αln(s) − (1 − e−λt)

α

1 − αln(n + g + δ)

− (1 − e−λt)ln(y(0))

where λ is the rate of convergence.

The growth rate depends positively on the saving rate and negatively on the

growth rate of the population and on the initial income (i.e. the lower the

initial income the higher the growth rate).

One important distinction is undoubtedly the difference between absolute (or

unconditional) and conditional convergence. The first approach assumes that

countries are homogeneous so that they share the same steady state even if

they do not share the same income per capita at a certain moment. Conse-

quently, countries with lower initial level of GDP should experience higher

growth rates than initially richer countries. On the other hand, conditional

convergence makes no assumption about shared steady states so that other

parameters might explain differences in steady state levels of per capita in-

come. As a consequence, countries may converge to their own steady state

which is a function of some other variables. In this framework, a richer coun-

try could be characterized by a higher growth rate than a poorer country if

the former is farther from its steady state than the latter (this means in this

case that the steady state of the rich country would be much higher than

that of the poor country).

Baumol (1986) introduces in its pioneering paper a third kind of convergence

that is club convergence (see Galor (1996) for a more formal analysis of club

convergence). Club convergence implies that there may exist many per capita

income equilibria to which groups of countries converge. As opposed to the

unconditional convergence, this approach allows more than one unique equi-

librium while it does not suppose that each country has its own equilibrium

as in the conditional definition of convergence. The search for determinants

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of the belonging to one club or another has also led to an abundant literature

(see among others Durlauf and Johnson (1995), Desdoigts (1999)).

Early papers trying to empirically investigate the convergence of different

countries mainly focus on what is called β-convergence. This measure of

convergence takes its name from the fact that it is based on the value (and as

importantly on the sign) of the beta estimates from a regression of the growth

rate of the per capita GDP on the initial level of per capita income . More

recently, another type of convergence has been put forward (see for instance

Quah (1993)) which is based on the evolution of dispersion of per capita in-

come across countries. This kind of convergence is called sigma-convergence.

Besides the many definitions that have been assigned to convergence, the

empirical literature has also given rise to different econometric approaches

to the estimation of convergence. Seminal papers such as Baumol (1986)

or Mankiw et al. (1992) use cross-sections to estimate β-convergence using

two different models. Mankiw et al. (1992) take the theoretical Solow model

as a starting point for testing convergence in terms of per capita income

levels. Consequently, they introduce in their regression the determinants of

the steady state under the Solow framework. Under the assumptions of the

Solow model, we can write the steady state of per capita income y∗as:

y∗= A(0)egt[s/(n + g + δ)]

α

1−α

where A(0) is the initial level of total factor productivity, g is the growth

rate of A, s is the saving rate, δ is the depreciation rate and α is the income

share of the capital in the Cobb-Douglas production function. Mankiw et al.

(1992) then derive the equation which allows them to test convergence from

the Solow model.

lny(t2) − lny(t1) = (1 − e−λt)(lny∗(t1) − lny(t1))

where y is the per capita income.

Substituting the value of y∗from the steady state equation, they get the

growth-initial level equation:

lny(t2) − lny(t1) = (1 − e−λt)

α

1 − αln(st1) − (1 − e−λt)

α

1 − αln(nt1+ g + δ)

− (1 − e−λt)lny(t1)

The parameter λ which can be estimated from the value of the estimated β4

is interpreted as the speed of convergence5. In addition, from a theoretical

4We refer to the term β to denote the coefficient related to the initial level of income.

This is in line with the definition of β-convergence.

5λ is easily calculated as: λ = −ln(1 + β)/t

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point of view, we can notice that the coefficients related to the saving rate

and to the combination of the population growth rate, the depreciation rate

and the growth of total factor productivity sum to zero.

In order to estimate their regression, Mankiw et al. (1992) allow the saving

rates and the population growth rates to differ from one country to another.

However, they fix the sum of the depreciation rate and of the growth rate of

total factor productivity to be equal to 0.05 for all countries.

A few years later, Islam (1995) develops a panel data approach to β-convergence

built on the same regression and data as Mankiw et al. (1992). As Islam

(1995) argues, the advantage of the panel approach is that it allows to ac-

count for the initial level of total factor productivity (A(0)) which should be

included in the individual effect. To apply methods for panel data to the

dataset6, Islam divides the period into five subperiods of five years7each.

In addition to cross-section and panel data methodologies, convergence study

has also recently been evaluated using time-series techniques (see among oth-

ers Evans and Karras (1996)).

Regarding the European Union, several papers have investigated income

growth convergence. Recently, Mora (2005), Fischer and Stirbock (2006) and

Battisti and Vaio (2008) have studied optimal regional convergence clubs in

the European Union. Their primary goal is to define clubs of regions within

the European Union sharing the same characteristics in terms of income

growth convergence without assuming any a priori restriction on the com-

position of these potential clubs. Another part of the literature has focused

on the convergence process of new entrants from Eastern Europe. Using a

cross-sectional approach, Matkowski and Prochniak (2007) find a clear (ab-

solute) β-convergence within the group of new member countries while their

convergence process toward members seems slower. Kocenda et al. (2006)

and Ingianni and Zd´ arek (2009) also show evidence of β-convergence among

new entrants countries as well as toward former members although they high-

light significant disparities among new member states with regard to their

convergence toward former members using a time-series approach. In this

context, the contribution of this paper is threefold. Firstly, we use the latest

update of the Penn World Tables which covers the period from 1990 to 2007.

Secondly, we apply the Islam (1995) panel data procedure which allows us to

account for potential individual effects. Lastly and more importantly, we ex-

plicitly derive a test for the existence of heterogeneity in income convergence

speed between Western and Central and Eastern European countries.

6Islam (1995) uses the same database as Mankiw et al. (1992)

7He considers five year periods to be less influenced by business cycle and less likely to

be serially correlated than one year periods.

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3 Data and Methodology

The data that we use to test convergence in terms of per capital income level

are taken from the latest version of the Heston, Summer and Aten’s Penn

World Tables.8

In particular, our regressions are based on the GDP per

capita in constant prices, the population and the investment share of Gross

Domestic Product for the 27 countries of the European Union from 1990 to

2007. Some of these variables need some more explanation. First, as any

income variable in the Penn World Tables, GDP per capita is expressed in

terms of purchasing power parity. On the other hand, we choose to work with

the investment rate rather than with saving rates. Indeed, if the theoretical

Solow model uses the saving rate, it also assumes a closed economy in which

case the saving rate coincides with the investment rate. Since we work with

open economies, the role of foreign investments on the evolution of the stock

of capital and hence the steady state is not negligible. That is why we prefer

to use investment rates rather than saving rates.9In addition, we also follow

the hypothesis from Mankiw et al. (1992) on the values of the growth rate of

technology and the depreciation rate whose sum is assumed to be common

to all countries in the sample and to be equal to 0.05.

The aim of this paper is to test whether the new members of the European

Union from Central and Eastern Europe converge to the 15 Western Euro-

pean countries. In addition to testing convergence in the enlarged European

Union (27 countries), we also check whether the 10 members from Central

and Eastern Europe and the 15 Western European Union countries belong

to two different groups in terms of convergence. We base our methodology

on the club convergence literature (Durlauf and Johnson (1995) and Fischer

and Stirbock (2006)) to test for two different groups in the European Union.

More particularly, our tests are based on the comparison of convergence rates

for the different groups of countries. However, as opposed to the traditional

literature on club convergence, we do not need to make use of any statistical

procedure to group countries. Since we want to specifically test the conver-

gence behaviour of the 10 countries of the Eastern bloc, the groups that we

consider are imposed by the goal of our paper itself.

8Alan Heston, Robert Summers and Bettina Aten, Penn World Table Version 6.3,

Center for International Comparisons of Production, Income and Prices at the University

of Pennsylvania, August 2009.

9However, in order to remain consistent with the notation from the theoretical Solow

model, we use s for the investment rate.

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4 Results

The main improvement of the panel approach with respect to the cross-

sectional method is that it allows for the presence of individual (country)

effects. From this point of view, Islam (1995) notably mentions the unob-

servable initial level of technology, A(0). As a consequence, we first divide

the full time period into six shorter time periods of three years in order to

obtain a panel. We proceed in three steps. First, we test income convergence

for the 27 countries in the European Union and then we apply the same

analysis to the two groups of 10 and 15 countries as previously described.

One of the concerns of Islam (1995) in the construction of the panel was that

shorter period might be influenced among others by business cycles. As a

result, the choice of the best length of subperiods involves a trade-off be-

tween not being too influenced by business cycles and having enough data

on the time dimension. To somewhat reduce the impact of business cycles on

our results, we introduce time dummies within our regression. Indeed, these

dummies are supposed to capture (at least the part which is common to all

the countries) the impact of economic cycles on growth data.

We only report the results from constrained regressions.10This constraint is

actually rejected in none of the regressions and does not significantly affect

the coefficient estimates .

The regression using all the European countries brings some interesting re-

sults. First of all, the coefficient on the initial Gross Domestic Product is

significantly negative which would be in favor of the hypothesis of conver-

gence in the European Union. However, as suggested by Bernard and Durlauf

(1996), it is not implausible to reject the null hypothesis of no convergence

within a group of countries although it is actually composed of several groups

with different convergence processes.

Besides, individual effects are positively correlated with the explanatory vari-

ables and the hypothesis of no significant individual effect is rejected by its

related F-test. This would speak in favor of the use of a panel rather than

a cross section approach and of the fixed effect methodology rather than the

random effect approach.

Focusing on the 15 Western countries members of the European Union be-

fore 2004 and on the new entrants separately, we find evidence of significant

β-convergence within both groups.

The main question of our paper is to check whether there exists some het-

erogeneity in terms of convergence in the European Union between Western

10As described in the literature review, the equality (in absolute value) of the coefficients

on the saving rate and the combination of population growth, technological growth and

depreciation rates is derived from the theoretical Solow model.

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Table 1: Regression Results by Group: 1990-2007

EU 27

lny(t) − lny(t − 1)

Western Countries

lny(t) − lny(t − 1)

Eastern Countries

lny(t) − lny(t − 1) VARIABLES

lny(t − 1)-0.285***

(0.062)

-0.110**

(0.055)

-0.380***

(0.114)

ln(s) − ln(nt1+ g + δ) 0.174***

(0.036)

0.039

(0.063)

0.088*

(0.049)

D95

0.103***

(0.016)

0.056***

(0.012)

0.170***

(0.033)

D98

0.120***

(0.016)

0.077***

(0.013)

0.206***

(0.023)

D01

0.136***

(0.018)

0.069***

(0.016)

0.254***

(0.030)

D04

0.159***

(0.022)

0.057***

(0.019)

0.322***

(0.036)

D07

0.201***

(0.027)

0.087***

(0.022)

0.405***

(0.050)

Constant2.446***

(0.591)

1.050*

(0.545)

3.188***

(1.028)

R2

Number of countries

0.485

27

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

0.409

15

0.774

10

countries and new entrants from Central and Eastern Europe. This can be

done in a regression where we allow for different initial income coefficients

and different time dummies for both groups. The difference between the two

betas coefficients of interest for the two groups is captured in our last regres-

sion by the coefficient on the product of the dummy for Eastern Countries

and the logarithm of the initial GDP (lny(t1)EAST). The results indicate the

coexistence of significantly (at the 5% level) different rates of convergence

within the European Union and particularly between Western and Eastern

countries. While we find evidence of convergence within the European Union

(27 countries) for the period between 1990 and 2007, we also show that the

rates of convergence from the two groups of countries that we analyze are

significantly different using the panel approach with time dummies. This

supports the existence of heterogeneous groups of countries within the Eu-

ropean Union in terms of convergence rates.

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Table 2: Global Regression: 1990-2007

VARIABLESlny(t) − lny(t − 1)Standard Errors

lny(t − 1)

lny(t − 1)EAST

ln(s) − ln(nt1+ g + δ)

ln(s)EAST− ln(nt1+ g + δ)EAST

D95,EAST

D98,EAST

D01,EAST

D04,EAST

D07,EAST

D95,WEST

D98,WEST

D01,WEST

D04,WEST

D07,WEST

Constant

-0.110

-0.270**

0.039

0.049

0.170***

0.206***

0.254***

0.322***

0.405***

0.056***

0.077***

0.069***

0.057**

0.087***

1.888***

0.076

0.114

0.087

0.094

0.024

0.022

0.022

0.027

0.037

0.017

0.018

0.023

0.026

0.030

0.549

R2

Number of countries

0.717

25

*** p<0.01, ** p<0.05, * p<0.1

5 Robustness Check: 1996-2007

As a robustness check of our results, we repeat the same methodology to the

period from 1996 to 2007 using a panel of 4 periods of 3 years. Indeed, the first

years of our original panel coincide with the period directly following the shift

from a planned to a market economy for the countries from the former Soviet

bloc. This transformation obviously required institution changes which might

have impacted the process of economic growth in these countries. As a result,

by eliminating these early years of our panel, we explicitly try to obtain

results free from any bias arising from the transition process.

While the convergence rates in the European Union and within both

groups are slightly different from those obtained using the entire panel, the

conclusions in terms of heterogeneity of income convergence within the Eu-

ropean Union remain unchanged. In addition, the R2of the regression for

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Table 3: Regression Results by Group: 1996-2007

EU 27

lny(t) − lny(t − 1)

Western Countries

lny(t) − lny(t − 1)

Eastern Countries

lny(t) − lny(t − 1) VARIABLES

lny(t − 1) -0.170***

(0.054)

-0.198***

(0.047)

-0.416***

(0.090)

ln(s) − ln(nt1+ g + δ) 0.136***

(0.031)

0.138***

(0.046)

0.109***

(0.039)

D01

0.006

(0.010)

-0.003

(0.008)

0.049***

(0.016)

D04

0.018

(0.013)

-0.005

(0.010)

0.121***

(0.025)

D07

0.050***

(0.017)

0.025*

(0.013)

0.208***

(0.038)

Constant1.503***

(0.502)

1.849***

(0.468)

3.688***

(0.800)

R2

Number of countries

0.293

27

Standard errors in parentheses

*** p<0.01, ** p<0.05, * p<0.1

0.626

15

0.641

10

the 27 countries is lower those of the regression by groups which may also

be seen as evidence for the coexistence of two significantly different groups

of convergence within the European Union.

6Conclusions

This paper aims at testing whether the new European Union members from

Eastern Europe were already exhibiting a convergence process toward mem-

bers. In particular, we test for the existence of two heterogeneous groups

of countries with different convergence rates. The presence of heterogene-

ity within the European Union could have implications on the efficiency of

functioning of the European Union and the Eurozone as the recent Greece’s

sovereign debt crisis has highlighted. We find a significant rate of conver-

gence for the 27 countries composing European Union. More importantly,

our global regression based on the Islam’s framework including dummies for

time shows that Western European countries and newcomers from Eastern

and Central Europe display significantly different rates of convergence hence

supporting the idea of heterogeneity in the European Union. These results

are robust to changes in the period of analysis. However, whether the joining

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Table 4: Global Regression: 1996-2007

VARIABLESlny(t) − lny(t − 1)Standard Errors

lny(t − 1)

lny(t − 1)EAST

ln(s) − ln(nt1+ g + δ)

ln(s)EAST− ln(nt1+ g + δ)EAST

D01,EAST

D04,EAST

D07,EAST

D01,WEST

D04,WEST

D07,WEST

Constant

-0.198***

-0.218**

0.138**

-0.028

0.049***

0.121***

0.208***

-0.003

-0.005

0.025

2.585***

0.068

0.095

0.067

0.073

0.012

0.018

0.028

0.012

0.015

0.019

0.469

R2

Number of countries

0.637

25

*** p<0.01, ** p<0.05, * p<0.1

of these Eastern Countries will reduce this heterogeneity is still a question to

be answered in future research. In addition, it might be of prime importance

to verify the disappearance of this significant heterogeneity before all the

newcomers are allowed to join the Eurozone.

12

Page 14

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