
Introduction
In 2004, eight Central and Eastern European (CEE) countries became the European Union members; in 2007 the EU was further enlarged to include Bulgaria and Romania, and in 2013Croatia followed suit. Today, more than a decade since the largest enlargement ever of the European Union it is worth attempting to assess the impact of European integration on economic growth of new EU member states from the CEE region and on the process of equalization of income levels within the enlarged European Union. Such an assessment seems particularly desirable in view of the fact that according to theoretical and empirical literature, the phenomenon of real economic convergence (or catching up) does not occur automatically. For example, in the traditional theory of international trade (Viner, 1950) economic integration leads to real convergence in income levels between countries, while some more recent theories (Krugman, 1991) claim that integration may also be conducive to increasing differences in the levels of economic development. Similar conclusions stem from the new models of endogenous growth (Romer, 1986, 1990; Lucas, 1988) where income convergence between countries has not been confirmed. Empirical studies show that the tendency toward equalization of income levels usually occurs within homogeneous groups of countries, while more diversified groups tend to exhibit divergence trends. In turn, some most recent empirical studies on the prospects of income convergence in the EU suggest that due to unfavourable future demographic trends and the aging population the next decades may witness a permanent reversal of the hitherto growth trajectories; as a derivative, a new trend, i.e. the process of income divergence between the new and old EU members may unfold (Matkowski, Prochniak, Rapacki, 2013, 2014). As can be inferred from the above, the discussion on real convergence and growth effects of integration is far from being conclusive, and many questions remain still open. This leaves a considerable room for further analyses of main drivers of convergence or divergence in income levels and for empirical research embracing various groups of countries and covering ever longer time series.
This article aims to answer the question of whether a membership in the European Union contributed to an accelerated economic growth of the CEE countries, including their real convergence to the economic development level of Western Europe (EU15). Our analysis consists of two steps. First, the hypothesis of income level equalization between the CEE countries and the EU15 is verified based on the [beta] and [sigma] convergence concepts. Second, the impact of selected macroeconomic variables related with the EU enlargement on economic growth of the CEE countries is examined with the use of econometric modelling. The analysis covers the 19952015 period. This article is a follow up and extension of the earlier studies in this field (Rapacki and Prochniak, 2009, 2010, 2014). There was examined the effect of the EU enlargement on economic growth and real convergence of Central and Eastern Europe focusing mostly on the preaccession period and using a slightly different research method relying on a different set of explanatory variables. This study involves a completely new econometric methodology that is better fit for the analysis of panel data time series. Namely, the Blundell and Bond's GMM system estimator is applied which is the most appropriate tool to estimate dynamic panel regression models.
In the economic literature, studies on the effects of enlargement of the European Union including the income convergence between the EU countries and regions abound. Obviously, it is not feasible to list here all of them. (1) Among the recent empirical studies devoted to real convergence in the EU particularly worthwhile mentioning are the following: Batog (2010); Halmai and Vasary (2010); Szeles and Marinescu (2010); Czasonis and Quinn (2012); Kulhanek (2012); Stanisic (2012); Tatomir and Alexe (2012); Dobrinsky and Havlik (2014). Most of these studies corroborate the trend towards equalization of income levels in the countries examined.
In the aftermath of the recent global financial crunch and the crisis in the euro zone, studies pointing to the emergence of income divergence trends in Europe have become more frequent. Some of these studies confirm the income divergence at the regional level (Herbst and Wojcik, 2012); other suggest divergence tendencies based on the hypothesis of club convergence or occurring within subgroups of countries (Monfort, Cuestas, Ordonez, 2013; Borsi and Metiu, 2015); while still otheras already mentionedpoint to the possibility of real divergence in the future as a consequence of unfolding unfavourable demographic changes.
The article consists of four sections. In section 2 below we verify the hypothesis of [beta] and [sigma] convergence of the CEE countries visavis the EU15. In section 3 we embark on the econometric modelling of the impact of key variables related with the EU membership on economic growth of the CEE countries. Section 4 concludes.

Incomelevel convergence of the CEE countries toward Western Europe before and after the EU enlargement
The concept of real economic convergence is defined here as the tendency to equalize income levels or otherwise: economic development levels between countries. This section is aimed at the empirical verification of the hypothesis of real convergence between the 11 new EU members in Central and Eastern Europe (Bulgaria, Croatia, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, and Sloveniafurther on referred to as CEE or EU11) (2) and the old EU member states in Western Europe (EU15). (3)
Our approach is based on the neoclassical models of economic growth (Solow, 1956; Mankiw, Romer, Weil, 1992), which confirm the prevalence of real convergence, or more preciselythe conditional [beta] convergence. Such a convergence occurs when less developed countries exhibit a faster economic growth than more developed ones. The catchingup process is conditional because it takes place provided all economies concerned head towards the same steady state, or longrun equilibrium. A common steadystate occurs when the countries involved are homogeneous in terms of their political systems, institutional architectures, economic structures, etc. If less developed countries always recorded a faster growth rate, we would deal with the absolute convergence.
The CEE economies can be deemed relatively homogeneous. This results firstly from the fact that in the transition period, these countries have pursued quite similar systemic transformation strategies, socioeconomic policies and structural reforms, geared towards building a fullyfledged market economy, strongly influenced by Western patterns. Secondly, the prospects of and then the actual membership in the EU, and the need to adopt the acquis communautaire, combined to make these countries similar in terms of their institutional environment, economic structure, directions of trade and capital flows (so called external or integration anchor). Thirdly, all CEE countries have been offered similar windows of opportunity to use the EU aid funds. Hence, it can be assumed that all present members of the enlarged European Union face the same longrun equilibrium or steadystate. They should, therefore, tend to equalize income levels as suggestedinter aliaby neoclassical models of economic growth. The process of equalization in GDP per capita levels is further fostered by the objectives of the EU policy, intended to reduce income disparities between countries and regions of the enlarged European Union.
Another way to measure the catchingup process is the G convergence. It occurs when differences in income levels between countries tend to decrease over time. Income disparities can be measured by variance or standard deviation of GDP per capita levels between countries. In theoretical terms, the [beta] convergence is a necessary but not the sufficient condition for [sigma] convergence. Moreover, econometric methods used to capture the two types of convergence are different. These factors combined prompt the need of crossexamining both of them.
To test the hypothesis of the absolute [beta] convergence, we estimate the following equation:
1/T log GDP(T)/GDP(0) = [alpha] + [zeta] log GDP (0) + [[epsilon].sub.t]. (1)
The dependent variable is the average growth rate of real GDP per capita between the period T and 0, explanatory variable is the natural logarithm of the initial level of GDP per capita, while [[epsilon].sub.t] is a random factor. Negative and statistically significant value of the [zeta] coefficient means the occurrence of [beta] convergence. In this case, the value of the [beta] coefficient, measuring the speed of convergence, can be calculated from the formula (e.g., Barro and SalaiMartin, 2003, p. 467):
[beta] = 1/T log(1 + [zeta]T). (2)
Estimating the value of the [beta] coefficient allows quantification of the speed of convergence. For example, when [beta] = 2%, it would take 35 years for individual countries assuming that they stay at their hitherto growth trajectoriesto reduce by half the distance to their steady state. This is because the time it takes for a variable with a constant negative growth rate to reduce its value by half, is approximately 70 divided by the growth rate expressed in per cent: 70/2 = 35 years. More precisely, the halflife ([t.sup.*]) is a solution of the equation: [mathematical expression not reproducible], where [beta] is the rate of decline (Romer, 1996, p. 2223). Taking logs of the above formula yields:
[t.sup.*] =  log 0.5/[beta] [approximately equal to] 0.6931/[beta] = 0.6931/0.02 = 34.7 years (3)
To test the occurrence of [sigma] convergence, one needs to estimate the trend line for the income disparities between...
EU Membership and Economic Growth: Empirical Evidence for the CEE countries.
Author:  Rapacki, Ryszard 
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