The Catch-Up Effect In The Case Of Non-Eurozone Countries (NEZC)

Abstract

σ Convergence, an intensely discussed topic, remains a particularly important issue for the European economy, characterized by heterogeneity. The objective of the present analysis is to find out, based on the values of GDP per capita and of the growth rate corresponding to the period 1997-2017, by means of consecrated (ß and a convergence) and alternative methods of study of convergence, the number of years necessary for the non-Eurozone European countries (NEZC) as a group and separately to catch up with the EU27 average and with the Eurozone countries (EZC) and Sweden. We start from the assumption that the economy of the European developed countries will maintain the average rhythm of growth of the last 27 years. The simulation of convergence shows a progress tendency of the NEZC group in a context of persistent development gaps. Even when 10% growth rates are registered, NEZC need over a decade to reduce development gaps. NEZC, as a group and separately, showed a trend that facilitated the reduction of economic gaps, proved by ß convergence, and partially by a convergence, but at growth rates of over 4%, in some of the cases such as Bulgaria and Romania, the process is slow; the Czech Republic and Hungary hold the best chances of convergence in a relatively short period.

Headnote

Abstract: σ Convergence, an intensely discussed topic, remains a particularly important issue for the European economy, characterized by heterogeneity. The objective of the present analysis is to find out, based on the values of GDP per capita and of the growth rate corresponding to the period 1997-2017, by means of consecrated (ß and a convergence) and alternative methods of study of convergence, the number of years necessary for the non-Eurozone European countries (NEZC) as a group and separately to catch up with the EU27 average and with the Eurozone countries (EZC) and Sweden. We start from the assumption that the economy of the European developed countries will maintain the average rhythm of growth of the last 27 years. The simulation of convergence shows a progress tendency of the NEZC group in a context of persistent development gaps. Even when 10% growth rates are registered, NEZC need over a decade to reduce development gaps. NEZC, as a group and separately, showed a trend that facilitated the reduction of economic gaps, proved by ß convergence, and partially by a convergence, but at growth rates of over 4%, in some of the cases such as Bulgaria and Romania, the process is slow; the Czech Republic and Hungary hold the best chances of convergence in a relatively short period.

Key words: economic convergence, economic growth, Eurozone Countries (EZC), Non-Eurozone Countries (NEZC), the catch-up effect

(ProQuest: ... denotes formulae omitted.)

Introduction

Convergence is a European objective even for less developed member countries. In the case of some of the recent EU members, joining the Union was perceived as a process that would standardize life conditions on the European territory. To the great disappointment of these states' populations, it turned out that a standard of life comparable to the one of the Western European economies is impossible to reach overnight. The status of member does not guarantee a standard of life similar to that of the old member states, but yet this is a wish to fulfil and an objective to meet in the future, tightly related to the process of economic growth. The latter, in its turn, depends upon the typology of factors that have a role to play in the case of each country. Only a sustainable growth supports real convergence of the economy. Where the relatively high rates of growth have fragile factors as a support, the nominal convergence will not transform into the real one. Consequently, the reduction of gaps compared to developed economies takes place slowly, not at all in some miraculous way, disappointing the population of less developed countries whose expectations are always great.

The researches concerned with the European economic convergence reached different results, as we will see in the first part of this paper. Results differ according the chosen methodology. Exact forecasts are excluded, as economic and social evolution always depends on a wide range of factors, with different results in space and time. Reality especially validated less optimistic scientific results about the convergence of EU less developed countries, though we cannot deny the progress these countries accomplished; yet, this was not enough in order to guarantee the population the standard of life they are looking for, comparable to the developed European members.

In order to estimate the convergence time of NEZC in relation to the European average, to EZC and Sweden, we analyzed first the results of other researches on similar topics and using similar methodologies. The analysis proper starts with methodological explanations, and continues with explanations of the results obtained. The results we reached are circumscribed by those that have already been obtained, considering that NEZC go through a process of convergence in the period 1997-2017. What we have highlighted is the different ability of these countries to transform the nominal convergence into a real one, as well as the period of time they are to do it. The results obtained describe a heterogenous Europe, which will continue to evolve at different speeds. The Czech Republic and Hungary have the highest chances to reduce development gaps compared to EZC and Sweden, while Romania and Bulgaria remain the economies of the NEZC group whose convergence need the longest period of time, in spite of the relatively high growth rates registered over the last years. We can notice, in the case of Romania and Bulgaria, social and economic improvement, so that an intensification of disparities as a result of a process of divergence is as possible as a reduction, as a result of convergence, the direction of these two economies being not so clear and always allowing for changes. I have structured the work as follows: literature review, the convergence framework of the European states, methods and methodology, and conclusions.

1.Literature Review

EU States' Economic Growth

In Western Europe, after World War II, the economic growth was so accelerated and it differed so much from the time's conception of reality, that it was compared to a - Belgian, German, Italian and French - miracle, even though there are no economic miracles [23]. The differences of growth between the European countries can be explained by means of those of economic structure. [1] The differences between the European regions are to be explained, according to Guisan and Fridas [15], not only by the differences of incomes and the disparities between the labour markets, but also by some circumstances affecting social wealth, such as education, health, the legal system or activities of governmental institutions. Tabellini, following an analysis of gross value added per capita in the case of 69 regions of 8 European states (France, West Germany, UK, Italy, the Netherlands, Belgium, Spain and Portugal) in the period 1970-2001, shows that there is an obvious relation between culture, literacy, institutions and growth. [30]

Rivera-Batiz and Romer showed that the economic integration of the countries with a similar level of income per capita leads to long-run growth if it technological innovation, as a result of the stimulation of research-development activities, is accelerated, but also when the trade of goods is extended. [26]

In relation to the EU membership, Baldwin and Seghezza notice that the process accelerated the growth, as a result of economic liberalization, which, in its turn, stimulated the expansion of the investments of physical capital in Europe. [2]

Esteban attributes interregional inequity to the differences in the structure of sector activities and also to the disparities in productivity. [12]

Figuet and Nenovsky remark, following their analysis of European convergence, that Romania and Bulgaria differ very much from the rest of the economies; also, Bulgaria goes faster in terms of integration, registering nominal, but not real convergence, in the context of an economy more 'elastic' to shocks than Romania's one, in whose cases one can notice positive, but insignificant signs of convergence. [13]

Gijium, Behrens, Hinterbergher, Luts and Meyer assess, in an analysis of sustainability, scenarios regarding the extraction of natural resources at a European and global level, showing in its basic scenario that, in a context in which the resource exploitation on the European territory remains the same until 2020, while internal resources decrease, than imports increase, thus creating the framework for a Europe which, in the future, will rely more and more upon products made abroad and where the pressures upon he environment will grow bigger, the economic will get polarised between winners and losers, and the sectors associated to the extraction of resources or based on intensive energy based production will be confronted with a reduction of production and of investments. [14]

Paas and Vahi consider innovations - which contribute to the growth of productivity and to a competitive advantage, the privilege of the countries that invest substantially in the research-development activity, both in the private and the public sectors - as the reason for the European regional disparities, while the persistent gaps of the GDP will remain a challenge for the EU economy. [24]

The EU28 countries went, in the period 1999-2014, through a process of real convergence, the best results being registered, in the period 1999-2014, by the countries which adopted the Euro in 2002, but also by Estonia, Latvia, Lithuania, Romania and Slovakia. [9]

A study dedicated the Central and Eastern European (CEE) countries show that the growth model based on the consumption of resources and on indebtedness proved to be ineffective and unsustainable, and the economic growth of these states (the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovenia, Slovakia, Bulgaria, Romania and Croatia) converges towards the EU one, but their results differ to a great extent. In his analysis, Disoska points out that the states with a low economic level tend to develop faster and to reduce the wealth disparities as a result of the technological transfer, of the structural changes, of the intensification of changes as a result of the elimination of commercial barriers, of the stimulation of direct investments that supported technological transfer but without noticing a significant progress towards results like those of the developed states, at least for the period 1995-2014. [8]

Wojciech analysing the socio-economic development of EU27 in the period 2004-2013 by means of multidimensional taxonomic methods, with the help of GDP/capita, occupation rates, expenses on research as a GDP percentage, notices that Romania and Bulgaria are European states with a high degree of similarity, making up together an object divergent from the rest of the members. [33]

Presently, the European model does not function as well as in the years following the World War II, and compared to the USA, productivity is inferior and the regulations are ineffective [4]. Yet, after 2016, the economic growth of EU28 recovered, being sustained by the internal demand and the exterior trade. According to EEAG (European Economic Advisory Group), in the period 2013-2014, in the case of EU28, on average, the import exceeded the export, but in the context of a resuming growth at a global level and of the currency undervaluation, new conditions were created for a European economic growth, supporting the private consumption and investments, but also the reduction of the economic gap of the CEE EU member states. [10]

For 2020, economic growth of EU28 was forecasted to 1.2%, contrasting China - 6.1%, India - 7.3%, Japan - 0.5%, SUA - 2.3%, a moment when the average GDP per capita will reach 43,720 dollars, while in the case of China it will reach 17,060 dollars, India 6,990 dollars, Japan 39,320 dollars, and USA 59,400 dollars. [19]

A forecast of The Economist Unit prognosticates that some countries in Europe, especially Greece, Portugal and Germany, will register a decrease of the labour force of one fifth by 2050, an aspect that will influence growth, while China, India and Mexico will register increases of the nominal GDP, and USA, Japan, Germany, UK and France will register decreases and Brazil will maintain its nominal GDP value relatively consistent. [31] Southern Europe will need many years of strong economic growth in order to balance its labour market [16] according to a Golden Sachs report, and according to SEB Group, the forecasts for the Eurozone, the Baltic countries, the Western and Northern Europe remain optimistic, in the context of a rising occupation rate, of increasing private expenses, and of decreasing political instability and budget deficits. [28]

Economic Convergence of the European Countries

The convergence in the European area is an intensely debated topic, as this is the process by which the disparities between the countries decrease, and the degree of economic homogeneity increases. [5] Broadly speaking, convergence supposes a levelling out tendency of the income per capita at a regional level, and strictly speaking it represents the relatively quick development of some least developed regions compared to the develop ones, allowing for a reduction of the differences between them. [7]

Using alternative approaches for the analysis of the convergence, starting from the idea that the evolution of the distribution in the whole region is more important than the average one, notice that the manifestation of a continuous European productivity while this is not accompanied by one of the standard of life measured by GDP per capita, and that the place and physical geography are important without limiting the possibility of the peripheral areas to reduce the gaps. [21]

The examination of the real and nominal convergence in the case of Czech Republic, Cyprus, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, Slovakia and Slovenia indicates a slow and consistent evolution of the real convergence per capita towards the European standards, as well as the convergence of the strong inflation and of the interest rate, these countries being considered to need a few decades from the moment the analysis was made in order to finish the convergence process. [20]

The hypothesis of the real convergence was studies by Cuñado and Perez de Garcia in the case of some CEE states, including compared to Germany and USA, for the period 1950-2003, no real manifestation of the process being remarked. Poland, Czech Republic and Hungary reduced their disparities compared to Germany, but only Poland managed to reduce them compared to the USA. [6]

Vojinović and Próchniak studied the o and ß convergence GDP per capita for ten European countries, reaching the conclusion that in the second half of the 1990s and in the 2000s, the existence of both types of convergence was confirmed, at a rate of 2.87% in the period 1995-2006 and of 3.23% in the period 1996-2006, while the differences of incomes are still high. [32]

Mikulić et al analysed the regional convergence in the period 2001-2008, by the method of ß convergence, taking into consideration the demographic variables, the conditions of the labour market, the industrial structure, the institutional factors and the economic policy for the new member states and Croatia, reaching the conclusion that the process of convergence at a regional level is slower than the one at a national level, the highest disparities being registered in Romania, and the lowest in Slovenia and Croatia; in Bulgaria and Romania again, the inequalities increased, unlike Poland, where they decreased, and Croatia, where a relatively consistent trend of the convergence was maintained. [22]

Simionescu, following the analysis of o convergence for the period 2000-2012, notices that within the EU territory, convergence is not confirmed, but only an improvement of the situation. [29]

2.Methods and Methodology

The convergence is studied by different methods. The best known convergence hypotheses are the absolute (unconditioned) convergence, the conditioned convergence and the club convergence. [22]

The unconditioned convergence involved the fact that the incomes per capita of the countries or regions converge in the long run towards the same unique and stable equilibrium, regardless of the initial conditions; the classical instrument to test it is the a and ß convergence, these two indicators being mutually correlated and verified. Sala-i-Martin uses the concepts of a and ß convergence to measure the degree of convergence and the process speed. [27] ß convergence is defined as a negative relation between the level of the initial income and the rate of economic growth. The theoretical framework of the hypothesis derives from the traditional neoclassic theory, whose premise is the fact that at the basis of the economic growth there are three production factors, the population, the accumulation of capital and technology. The higher the capital accumulations, the more temperate the marginal revenues and the economic growth in the developed countries. ß convergence is tested by means of the equation proposed by Baumol (1) and its derivatives. [3] The hypothesis of absolute or unconditioned convergence is confirmed if the estimated ß coefficient is statistically significant and negative.

... (1)

where T is the time, YT is the value of the variable at the end of the period of time, t0 is the initial time period, Yto is the real value of the variable at the beginning of the period, ß is the slope, and St represents the error.

For instance, Ertur, Gallo and Baumont demonstrated that spatial dependency and heterogeneity count in the estimation of the process of ß convergence for 138 European regions for the period 1980-1995, showing that the average rate of growth of the GDP per capita is positively influences by the average rate of growth of the neighbouring regions, starting from the equation (2) [11].

... (2)

where gt represents the average rate of growth of GDP per capita, t being the period, Yor the initial level of the GDP per capita, S the vector of unity, and s the error.

The conditioned convergence involves the fact that the incomes per capita of the economies in the long run converge only if the countries or regions in question have similar characteristics, usually in terms of technological level, socio-demographic features (education, population rise), institutional environments. The conditioned convergence occurs when there is a negative relation between the incomes per capita and the rates of growth. According to Ertur, Gallo and Baumont the conditioned convergence is tested with equation (3) and is verified if the estimated value of ß is significantly negative. [11]

... (3)

where g represents the average rate of growth of the GDP per capita, X is the matrix of the constant explanatory variables in equilibrium.

Club convergence is defined as being the process by which a country or a region belonging to the same club moves from ones equilibrium position to the equilibrium position of the club so that in conditions of stability the rate of economic growth would be similar for all economies of the club, an aspect supposing the necessity of homogeneity and the existence of similar initial conditions. [22]

Quah introduces another type of convergence, the a convergence, by means of which he shows that the negative relation between the economic growth and the real development level does not offer a unique answer in convergence terms, the relation tending to become negative if the income differences do not decrease. [25]

Iancu proposes the following calculation formula for a convergence [17]:

... (4)

where N represents the number of regions or countries.

We will not insist upon the methodology of convergence. We will use the ß and a methods of convergence and we will analyse the GDP per capita in order to obtain information about the process of European convergence.

The objective of the paper is to calculate the period of time necessary for the NEZC, as a group and separately, to converge towards the European average, towards the EZC states and Sweden, is the reduction of economic gaps is proved to be possible.

The indicators we used are the ones we consider relevant for economic growth, the GDP per capita and the rate of growth of the GDP per capita. The GDP per capita reflects the value of the production of a country in relation to the number of inhabitants, viewed as the best method to make comparisons that reflect the standard of life of the population. The rate of growth of the GDP per capita is the one that illustrates the rhythmicity of economy, in its dynamics. Except for their limitations, especially in the case of the GDP per capita (it does not take into consideration the environment costs, the size of the black economy or that of domestic economy), they remain significant for the study of economic convergence.

The values of GDP per capita and the rates of growth were taken from the base of statistic data of the World Bank, being verifiable. The period we had in view was 1990-2017, as it offers a solid basis for an exhaustive analysis of convergence and for the simulation of the necessary time to reduce disparities.

The convergence of NEZC is analysed in relation to the 19 countries of the Eurozone (EZC) and to Sweden, which we consider separately, as this is a state in the category the developed countries (the GDP/capita value in 1990 was 20107 dollars, and in 2017 - 50208.16 dollars, that is almost twice as big as the European average), but is not part of the group using euro as its currency.

The analysis of the convergence was made for the EU27, the states in the Eurozone - EZC (Austria, Belgium, Cyprus, Denmark, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Portugal, Slovakia, Slovenia, Spain), Sweden and the countries outside the Eurozone - NEZC (Bulgaria, Croatia, Czech Republic, Hungary, Poland and Romania).

To start with, we determined the average GDP per capita (table no. 1), based on the data in annexed tables 1a, b, c.

We can notice the differences between the values of GDP per capita and the rates of growth (graphs 1 and 2). A high rate of economic growth of the states in the NEZC group does not translate to the highest level of the GDP per capital. The states in the group, having started their process of economic growth later than those in the EZC group, have a higher progress potentiality, thus justifying the superior rate of growth of the GDP per capita. It is likely for the NEZC to maintain or even rise the annual rate of growth of the GDP per capita, but not of the value of the GDP per capita. With a view to economic convergence or homogenisation of the European states, the countries in the NEZC group should reach, in a period of time as short as possible, the economic results of the EZC group and of Sweden, considering that the average value of the GDP per capita is much under that of the EU27.

Before calculating the convergence time, we will focus on the ß convergence to see whether in the analysed framework the process of disparities reduction between the countries occurs. The ß convergence is studied according to the following model:

... (5)

where a is constant. ß is the slope, s is the error, T is the analysed period of time (1995-20017).

We will calculate the convergence time of NEZC, as a group and separately, based on the method proposed by Aurel Iancu who, following the analysis of Romania's convergence using as a calculation basis the value of the GDP per capita for the period 1980-2003, 1990-2004, reached the conclusion that this country is and will remain a peripheral one, and the convergence of the Romanian economy is an illusion [18], a remark that has not yet been disconfirmed.

We will therefore calculate the necessary time for convergence of NEZC compared to the European average according to the formula (6), deduced from the equality YtNEZC = YtEU (6):

...

Y0EU = value of GDP per capita for EU27

Y0NEZC = value of GDP per capita for NEZC

r0EU = average rhythm of growth of EU27

r0NEZC = average rhythm of growth of NEZC

The convergence will take place in a reasonable period of time if the NEZC will register annual average rhythms of convergence higher than those of EU27, i.e. roNEZC roEU. Convergence occurs when YtNEZC = YtEU (6), where

...(8)

... (9)

This algorithm will be also used to calculate the convergence time for the NEZC group and for each country separately, in relation to the EU27 average, to EZC and to Sweden.

Therefore, we can formulate the following hypotheses of the research:

H1: NEZC converge to EZC and Sweden.

H2: NEZC reduce, as a group and separately, the time of convergence to EU27, EZC and Sweden.

H3: a convergence is confirmed for NEZC

The number of years necessary to convergence will be determined starting from the presumption that in the future there will be rates of growth within the interval (4%-10%). The rates of growth lower than 4% counterbalance the process of convergence and will not modify favourably the present state of the analysed economies. In order to surprise the positive effects of the rise of GDP per capita in its dynamics, our option was to relate to positive rates of growth high enough to determine an ascendant movement of the economy.

3.Results and Discussions

The hypotheses of the research are validated in the proposed order, starting from the demonstration, by the method of ß convergence, of the fact that NEZC reduce the development gaps. The time period necessary to the convergence decreases as the rate of economic growth increases, so that the a convergence is confirmed.

1.ß convergence of the NEZC states (validation of the H1 hypothesis: NEZC converge towards the EZC and Sweden)

The determination of ß convergence of the NEZC group was made based on formula (5).

...

The values for the calculation of natural logarithms are presented in the table below:

As one can notice, the dispersion diagram has a decreasing tendency, illustrating thus the manifestation of a relation of linearity, correlation being relatively intense. The linear equation of the form y = a + bx becomes y = 0.2348 - 0.0201x, and R2 = 0.912, so ß takes the value of -0.0201, and a takes the value of 0.2348, in which case the model will be written under the form of:

...

The negative value of the ß parameter shows that NEZC passed through a process of convergence in the period 1995-2017. The value of the coefficient of correlation (Pearson) of - 0.955 indicates a very good association between the values of the GDP per capita, meaning that the evolution of the indicator influences the degree of economic convergence, and the relation between the variables is intense. The significance for the values of the coefficient of determination, i.e. 0.912, is that 91.2% of the variation of the GDP per capita is explained by the linear relation with the initial value of the indicator. The negative coefficient of covariance demonstrates also the reversed relationships between the variables.

The study of the ß convergence validates the H1 hypothesis, the NEZC reduce their gaps compared to EZC and Sweden, and the period the process needs will be determined once the H2 hypothesis is validated.

2.Simulation of the convergence time (H2: NEZC reduce their time of convergence compared to EU27, EZC and Sweden)

The simulation of the necessary time for the economic convergence of NEZC was made considering the point of reference the average GDP per capita and the average rates of economic growth for the period 1997-2017. We assume that the NEZC register rates of growth between 4% and 10%, and EZC maintain the average rate of growth in the period 1990-2017, i.e. 2.38%, and Sweden that of 1.53%.

The simulation of the convergence of the NEZC to EU27, EZC and Sweden show a decreasing tendency of the time in which the analysed group of countries reduces the gaps compared to EZC and Sweden. The higher rates of economic growth of the NEZC, the shorter the convergence time. Therefore, the H2 hypothesis, according to which the NEZC reduce the time of convergence compared to EU27, EZC and Sweden, is verified.

A 4% economic growth allows for the NEZC to align to the EU27 average in about 82 years, to the EZC in about 148 years, and to Sweden in over 116 years. The acceleration of the rhythm of growth of the GDP per capita reduces the time of convergence. Assuming that the economy of the NEZC group increases with an average rhythm of about 10%, they will still need over 38 years to cover the gaps compared to the European average, over 49 years compared to the EZC group and about 54 years compared to Sweden (graph 3, tables 1, 2, 3 of the Annexes).

Bulgaria is one of the NEZC members whose gaps are and will remain high, even in a context of a rhythm of growth of 10%. Bulgaria will reduce the time of convergence to EU27, EZC and Sweden at a slow rhythm. The difference between a rate of economic growth of 4% and one of 10% means for Bulgaria a reduction of over 40 years of the gap compared to the EU27 average, of over 85 years compared to the EZC group and of about 55 years compared to Sweden. The time for the decrease of the disparities of growth confirms that Bulgaria remains a peripheral European country (graph 4 and tables 1, 2, 4 of the Annexes).

The economy of Croatia has, in its turn, gaps of growth to cover, as over 72 years separate it from the average EU27, over 131 years from the EZC group and about 107 years from Sweden, at a rate of growth of 4%. The disparities decrease, in the case of this state as well, as the rhythm of growth increases. A rate of growth of 10% maintain temporary differences of about 34 years compared to the European average, of over 43 years compared to the EZC and of over 49 years compared to Sweden (graph 5 and tables 1, 2, 5 of the Annexes).

The Czech Republic registers a smaller gap compared to the reference economies. The necessary time for Czech Republic to catch up with EU27, EZC and Sweden is 31 years, over 58 years and about 65 years respectively, if the rate of economic growth is 4%, and of over 14, 19 and 39 years if the rhythm of growth is a two-digit number (10%) (graph 6 and tables 1, 2, 6 of the Annexes).

Hungary reduces the time of convergence compared to EU27, EZC and Sweden because the rates of over 4% support economic growth and allow for a decrease of the gaps compared to the European average, EZC and Sweden in a period of time of 69 years, 126 years and 104 years. A rate of growth of 10% allows for Hungary to reduce the time of convergence to about 32 years compared to the European average, 42 years compared to the EZC group and 48 years compared to Sweden (graph 7 and tables 1, 2, 7 of the Annexes).

Poland registers significant time gaps in relation to the EU27 average, EZC and Sweden. At a rate of growth of 4%, the period to cover the gaps compared to the European average is about 67 years, to the EZC group of about 104 years and to Sweden of 94 years. A rate of 10% reduces the convergence time period to 39 years in relation to EU27, to 51 in relation to EZC and to 55 in relation to Sweden (graph 8 and tables 1, 2, 8 of the Annexes).

Romania has also a decreased convergence time compared to EU27, EZC and Sweden. Romania, in the case of a rate of growth of 4%, needs over 122 years to get aligned to the European average, 220 years for the EZC group and over 157 years for Sweden. Provided that the rate of economic growth is 10%, Romania reduces its time of convergence, but before speaking about full convergence, the temporary perspectives remain remote, of over 57 years compared to the EU27 average, of about 73 years compared to the EZC group and Sweden (graph 9 and tables 1, 2 and 9 of the Annexes).

Summarising the results obtained, we notice the convergence time of the Czech Republic and of Hungary, much shorter than the rest of the NEZC group. Poland and Croatia manage to achieve convergence in a period of time shorter than Romania's and Bulgaria's ones, who are slow countries, with slow economic dynamics, which will remain at the periphery of EU27 (graph 9 of the Annexes). The convergence time depends upon the level of the rate of growth, but also, to a great extent, on that of the GDP per capita. The higher the value of the GDP per capita, the higher the chances that, under the influence of a big rate of growth, the time of convergence diminish. Presently, Czech Republic and Hungary have the highest value of the GDP per capita, while Romania and Bulgaria have the lowest values of this indicator (table 1a,b,c of the Annexes). This demonstrates, once again, that the initial conditions are extremely important for the future economic evolution.

The analysis of the convergence time is not a static one, but one starting from the presumption that the economy of the states of the Eurozone and that of Sweden will evolve at the average rhythm of the period 1990-2017; this can reflect reality only accidentally, as the rate of growth can fluctuate significantly under the impact of the factors of influence (political, economic, social or factors of different other natures). The same thing is true for the countries outside the Eurozone, whose average rate of growth in the period 1990-2017, was 2.56%. The time of convergence of NEZC dilates in a context in which their rate of growth remains under 4%, and that of the economies of reference goes up above the average values taken into consideration. What we simulated represents a positive scenario in which the members of the Eurozone and Sweden keep the average rhythm of the last 27 years, while the rest advance with much higher rates of growth.

3.a convergence of NEZC states

H3 hypothesis is validated or not by the analysis of a convergence. Sigma convergence is the most frequently used coefficient of variance, as it allows for comparisons. [29] A decrease of the values indicates the accomplishment of convergence, and the series of time are used for a discrete interval of time, from t to t + T, so that the reduction of gaps is confirmed for ot+T<ot (convergence) and an increase for ot+T>ot (divergence).

In order to calculate the NEZC convergence to own point of equilibrium, we used the equation of a convergence proposed again by Iancu [17]:

... (10)

Where Yi>t represents GDP per capita at the end of the period

Ym,t represents the average GDP per capita

N represents the number of countries

In order to determine the a convergence, we divided the analysed period into five sub-periods (19901994, 1995-1999, 2000-2004, 2005-2009, 2010-2017) of five years each except for the last one, which is the equivalent of eight. For the first subperiod, 1990-1994, we do not have the values of the GDP per capita for Croatia, so that its a convergence is analysed starting with 1995. The countries converge if the dispersion of the GDP per capita decreases over time.

a convergence indicates the fact that the analysed countries went through oscillating periods of convergence and divergence. At the level of the whole NEZC group, we can notice a long process of divergence, very accentuated until 1999 and more tempered until 2004. Except for Poland, the period 2000-2009 was characterised by convergence, but subsequently, the a values show they went through a new period of divergence, motivated by the way in which these countries answered the challenges of the economic crisis. For Poland, the a values show a tendency of relative stability. The divergence process was slow for Romania and Bulgaria, and more accentuated in Hungary, Czech Republic and Croatia. The a values indicate similar trajectories for almost all the members of the NEZC group, the difference being just the amplitude of the convergence and divergence phenomena. In this situation, the H3 hypothesis is validated for the period 2000-2009 and partially after 2009, but not in the case of all countries.

The 1990s were the years of change for the economic system in Central and Eastern Europe, a fact that explains the differences between the countries and their relatively divergent evolution. In a study made in 2006, Cuñado and Perez de Garcia noticed that Czech Republic and Hungary were, at that moment, at the level of production of 1989, Poland had gone over it, while Bulgaria and Romania proved a very slow rhythm of recovery. [6]

Conclusions

The economic growth is an important objective for all the economies, especially for NEZC, the group we have focused on. It is well known that the process of growth has opposite results, as not every increase of the quantities measured by means of different indicators proves to have real outcomes in the economic and social development. An important role is played by the factors supporting the growth, but also by the way in which the measures of economic policy manage to channel the positive results towards fields of interest with effects of multiplication and acceleration.

The research is a comparison, on the topic of the European convergence, between NEZC on the one hand, and EZC and Sweden on the other. The main criteria of determination of the European states are the insertion in the Eurozone. In the EU27 area, the economic convergence allows for an equalisation of the standard of life of the population and it strengthens the economic stability. The main objective of the paper was to analyse the GDP per capita and the rate of economic growth corresponding to the period 1990-2017, in order to see to what extent, the member countries outside the Eurozone manage to reduce the gaps compared to the Eurozone, the EU27 average and Sweden.

We started the analysis from three research hypotheses (NEZC went, in the analysed period of time, a period of convergence; the time for the reduction of gaps decreases as the rate of growth increases; and NEZC remains a sensible group in terms of convergence manifestation).

The negative value of the ß parameter, the values of the coefficients of correlation and determination certify the manifestation of NEZC's convergence to the EU27 average, EZC and Sweden.

Once the ß convergence confirmed, we determined the speed for the reduction of gaps in the future, for NEZC as a group and separately, by each state, in relation to the EU27 average, to the EZC group and to Sweden. The assumption that the rates of growth of the NEZC will be between 4% and 10% can translate in reality in a completely accidental way, just like the assumption that the EZC group will grow by rates of 2.38%, while Sweden by 1.53%. A 4% rate allows a slow convergence, rather nominal than real in some of the cases, as is the case of Romania and Bulgaria. The growth of economy by rates of 10% halves the time of convergence, a situation when, in the most pessimistic scenario, the reduction of gaps will need about five decades. Considering NEZC member states, we can notice better results in some of the cases, such as Czech Republic and Hungary, and worse ones, like in Bulgaria's and Romania's case, who remain marginal states, with slow economies.

The study of a convergence confirms the idea that the group of NEZC converges relatively slowly, and in a different way by members. Within the group, the a analysis shows an alternation of the periods of convergence with periods of divergence, except for Poland, this remained on a trend of relative stability.

In conclusion, the NEZC are countries whose previous economic conditions influenced the future evolution, their convergence, as a group and separately, taking place more or less slowly, according to the results in the area of economic growth. We showed that these countries converge to the centres of European economic power, but the necessary time to reach this objective remains a problematic and difficult answer; we evaluated this according to the value of the rate of growth between over 100 years and under 40 years, the countries with the best results being probably Czech Republic and Hungary, while the countries with modes results remain Bulgaria and Romania. The global, regional and national evolution can modify the reality; the results of the research become then null and void, as we started from a favourable scenario, that of a constant economic growth in the case of the countries from the Eurozone and of Sweden, and of a high one, between 4%-10% in the case of the non-Eurozone countries. The possible crises or measures of economic policy with undesirable effects could accentuate the development disparities. An evolution above the estimations opens the perspective of an analysis of the causes having favoured it, so that each EU member state be able to catch up with the developed European economies.

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