IZVIRNI ZNANSTVENI ČLANEK - ORIGINAL SCIENTIFIC PAPER CONVERGENCE OF BUSINESS CYCLES AS A CONFIRMATION OF OCA THEORY Konvergenca poslovnih ciklov kot potrditev teorije optimalnega valutnega področja Prejeto/Received: December 2011 Popravljeno/Revised: Marec 2011 Sprejeto/Accepted: April 2012 Vesna Dizdarevic Promo + d.o.o. promoplus@siol.net Robert Volčjak EIPF, Ekonomski institut d.o.o. robert.volcjak@guest.arnes.si Abstract This paper examines business cycles in EU members and compares them with the business cycles of the economic and monetary union in Europe (EMU) members assumed to satisfy the optimal currency area (OCA). Accordingly, a multi-resolution decomposition of GDP growth signals is used, and correlation coefficients are computed for decomposed signals to assess the numerical values of synchronicities of business cycles. Our results reveal indications that areas adopting the euro in many ways confirm OCA theory and that the business cycles of most of the new EU members are not synchronized with the EMU; as such, these members might experience some difficulties if joining the euro too early. Keywords: convergence, business cycles synchronization, wavelets, multi-resolution analysis Izvleček V članku so obravnavani konjunkturni cikli in še posebej njihova konvergenca v evrskem območju, kakor to predpostavlja teorija optimalnega valutnega področja (OCA). Uporabljena je bila multiresolucijska dekompozija časovnih vrst BDP, za pridobitev numeričnih vrednosti sinhronizacije konjukturnih ciklov pa so bili izračunani korelacijski koeficienti dekomponiranih časovnih vrst. Rezultati kažejo, da območje evra v marsičem potrjuje teorijo OCA, hkrati pa tudi opozarjajo, da utegnejo imeti nove članice EU težave, če se odločijo prezgodaj pridružiti evrskem območju. Ključne besede: konvergenca, konjunkturni cikli, valčki, multiresolucijska analiza 1 Introduction The topic of business cycles, especially convergence, has received a great deal of attention in recent years, mainly motivated by the economic and monetary union in Europe (EMU). In the context of a single currency and common monetary policies in the euro-adoption area, the similarity of the business cycles of the participant countries is a major concern. Nowadays, the enlargement process of the European Union has resulted in pressing questions about the preparedness of the candidate countries for integration. The literature on business cycle synchronization is related to that on optimal currency areas and, more broadly, on economic unions. If several countries delegate to some supranational institution the power to perform a common monetary (or fiscal) policy, then they lose this policy stabilization instrument. With the recent enlargement of the European Union, the interest on this topic is guaranteed for a while. The optimal currency area (OCA) theory states that countries are more suited to belonging to a monetary union when they meet certain criteria related to the real convergence of an economy— namely, a high degree of external openness, mobility of factors of production, Naše gospodarstvo / Our Economy Vol. 58, No. 3-4, 2012 pp. 3-15 DOI: 10.7549/ourecon.2012.3-4.01 UDK: 338.12:339.738(4) JEL: C10, E32 and diversification of production structures. According to this theory, if there is a clear convergence between business cycles of countries willing to join the monetary union and the business cycle within the currency area, then this tends to prove that these countries are ready to enter the currency area. A revival of the empirical testing of the OCA theory preceded the introduction of the monetary union in Europe. Usually, empirical studies tend to assess the correlation between the German (or another large EU economy) business cycle and business cycles in other potential member countries (De Bandt, Herrmann, & Parigi 2006). A relatively unexplored tool for forecasting is wavelets. Wavelet multi-resolution analysis allows one to decompose a time series into a low-frequency base scale and higher-frequency scales. Those frequency components can be analysed individually or compared across variables (Rua, 2010). As business cycles can be statistically decomposed into components with different frequencies (trend, season, noise), it is natural to use multi-resolution analysis to compare gross domestic product (GDP) with the components of well-defined frequencies that allow such comparison. The aim of this paper is to treat business cycles in the EU members and compare them with the business cycles of EMU members that are assumed to satisfy the optimal currency area. Accordingly, a multi-resolution decomposition of GDP growth signals is used, and correlation coefficients are computed for decomposed signals to assess the numerical values of the synchronicities of business cycles. This paper is organized as follows. After a brief literature review, the methodological framework is addressed, the multi-resolution decomposition is presented, and a brief description of the database and calculations is provided. The results of the convergence of business cycles are then discussed. Finally, the results are summarized in the conclusion. 2 Literature Review The term economic convergence refers to a diminishing of the differences in living standards (in the opposite case, we use the term divergence), economic levels, and the manufacturing performance of particular countries or their regions (Nachtigal et al., 2002). A widely used device for measuring the symmetry or asymmetry of shocks is a measure of the synchronicity of business cycles (Artis, Mar-cellino, & Proietti, 2004). Various authors have attempted to assess and explain business cycle convergence and synchronization. Artis and Zhang (1997) addressed the question of whether the exchange rate mechanism (ERM) has implied an increasing conformity among the business cycles of the participant countries. Angeloni and Dedola (1999) compared business cycle fluctuations of output, industrial production, stock indices, and prices across countries in various sub-samples. Wynne and Koo (2000) documented differences and similarities between business cycles in the European Union and business cycles in the Federal Reserve districts in the United States. The literature on business cycle synchronization is related to the literature on optimal currency areas and, more broadly, economic unions. The topic of business cycles— especially their convergence—has received a great deal of attention in recent years, mainly motivated by the economic and monetary union in Europe. The optimal currency area theory (OCA) is one theory that helps make decisions on whether or not certain countries enter the monetary union. According to OCA theory, developed roughly five decades ago, two countries or regions will benefit from a monetary union if they share similar business cycles, trade intensively, and rely on efficient adjustment mechanisms to smooth out asymmetric shocks. OCA theory was developed in the Bretton Woods system by Mundell (1961), McKinnon (1963) and Kenen (1969). After the breakdown of the Bretton Woods system, the OCA theory was regularly used to assess the desirability of having a fixed exchange rate in different countries. Although papers on this topic apply various methods (see Table 1) to reach different results, most find that the business cycles in several new member states are about as synchronized with the euro area as several of the peripheral members of the euro area. Many approaches have been used by various authors to assess the numerical values of the European economic activity convergence. Some papers examine the correlations of a detrended indicator of aggregated output. Business cycle coordination is analyzed mainly from the perspective of the international transmission of business cycles. Several authors apply various filters (e.g., Hodrick-Prescott [HP] or Band-Pass filters) or use time-series models. In addition, value at risk models (VaR), particularly structural VaR, are used to recover underlying shocks with properties derived from the economic theory. Economic time series contain important information about economic activity, from long-run movements in productivity to business cycle fluctuations. They also contain high frequency noise, whose sources range from transitory shocks to measurement error. Linear filtering is a useful tool for extracting the component of interest (e.g., the business cycles component of real gross national product [GNP]) from the economic time series. Prominent examples in the economics literature include the Hodrick and Prescott (1980) filter and the approximate Band Pass filter (Baxter & King, 1999). Multi-resolution wavelet analysis is an alternative linear filter-based method; it is a natural way to decompose an economic time series into the long-run trend, the business cycle component, and high frequency noise (Yogo, 2008). 3 Methodological Framework Fourier analysis is a mathematical tool for studying the cyclical nature of a time series in the frequency domain. However, under the Fourier transformation, the time information of a time series is completely lost. Meanwhile, the wavelet transformation breaks down a time series into shifted and scaled versions of a mother wavelet function that has a limited spectral band and limited time duration. Table 1: Various Methods Used for Correlation of Business Cycles Author(s) Methodology and Economies Results Boone and Maurel (1998) Assessed whether it would be optimal for the Central and Eastern European Countries to form a monetary union with either Germany or the EU using the Hodrick Prescott filter method. The percentage of the Central and Eastern European Countries business cycle fluctuations explained by a German shock is very high; furthermore, the impulse responses are positively correlated. Fidrmuc and Korhonen (2001, 2003) Assessed the correlation of supply and demand shocks between the countries of the euro area and the accession countries in the 1990s. Some accession countries have a quite high correlation of the underlying shocks with the euro area. Many EU countries seem to have a much higher correlation with the core euro area countries than in the previous decades. Continuing integration within the EU also seems to have aligned the business cycles of these countries. Fidrmuc (2001, 2004) Computed the potential correlation of the business cycle in Germany and in the Central and Eastern European Countries using Frankel and Rose's (1998) relation between the degree of trade integration and the convergence of the business cycles of trading partners. The discussion focused on five associated countries (Czech Republic, Hungary, Poland, Slovenia, and Slovakia) and confirmed previous findings, such as that the Central and Eastern European Countries have rapidly converged to the EU countries in terms of business cycles and trade integration. In particular, business cycles in several Central and Eastern European Countries (Hungary, Slovenia and, to a lesser extent, Poland) have been strongly correlated with the business cycle in Germany since 1993. Korhonen (2001, 2003) Examined the correlation of short-term business cycles in the euro area and the EU accession countries with the help of vector autoresression models. Clear differences emerged in the degree of correlation among accession countries. Generally, for smaller countries, the relative influence of the euro area business cycle is larger. Also, the most advanced accession countries are at least as integrated with the euro area business cycle as are some small current member countries of the Economic and Monetary Union. Artis et al. (2004) Analyzed the evolution of the business cycle in the accession countries after a careful examination of the seasonal properties of the available series and the required modification of the cycle-dating procedures. The analysis was based on the industrial production index (total industry) series using the Hodrick Prescott filter method. The degree of concordance within the group of accession countries is not, in general, as large as that between the existing EU countries (the Baltic countries constitute an exception). Between them and the euro area, the indications of synchronization are generally rather low, with the exception of Poland and Hungary, and lower relative to the position obtained for countries taking part in previous enlargements (again with the exceptions of Poland, Hungary, and this time Slovenia). 4 Wavelet Multi-resolution Decomposition As a coherent mathematical body, wavelet theory was developed in the mid-1980s (Goupillaud & Morlet, 1984; Grossmann & Morlet, 1984). The literature rapidly expanded, and wavelet analysis is now extensively used in physics, statistics, econometrics, and applied economics. In this respect wavelet tools have also been generalized to accommodate the analysis of time-frequency dependencies between two time series, e.g. the cross-wavelet power spectrum, the cross-wavelet coherency, and the phase-difference (Aguiar-Conraria & Soares, 2009) Computational tools known as wavelets, particularly multi-resolution (MR) analysis, allow for the decomposing of a signal (e.g., a time series of gross domestic product [GDP], industrial production, inflation, stock returns) into high and low frequency components (Chui, 1992; Percival & Walden, 2000). High frequency (irregular) components describe the short-run dynamics whereas low-frequency components represent the long-term behaviour of a signal. Identification of the business cycle involves retaining the intermediate frequency components of a time series— namely, we disregard very high- and low-frequency components. For instance, it is customary to associate a business cycle with cyclical components between 6 and 32 quarters (Burda & Wyplosz, 2005). Wavelets were specifically designed for isolating shortlived phenomena from long-term trends in a signal (Baqaee, 2009). Wavelet methods have been popular due to their computational efficiency, flexibility, and overall superiority to established techniques of analyzing and transforming data. One of the greatest strengths of wavelets over conventional frequency-domain techniques is their ability to deal with non-stationary data (Crowley, 2007). Wavelet analysis performs the estimation of the spectral characteristics of a time series as a function of time, revealing how the different periodic components of the time series change over time. Although the Fourier transformation breaks down a time series into constituent sinusoids of different frequencies and infinite duration in time, the wavelet transform expands the time series into shifted and scaled versions of a function that has limited spectral band and limited duration in time. Wavelets can be a particularly useful tool when the signal shows a different behaviour in different time periods or when the signal is localized in time as well as frequency. As it enables a more flexible approach in time-series analysis, wavelet analysis is seen as a refinement of Fourier analysis (Rua, 2010). We can also describe this in a more formal manner (Wolfram Research, 1996). Let us mark the resolution level with an integerj (i.e., jeN0), and let the scale associated with the level j=0 have a value of one while at the level j have a value of 1/2j. Let f(t) be a function, wheref(t)eL2(R), where L2(R) is the space of measurable functionsf defined on the real line R, that satisfy Ji/ (t )|2 dt < Mark with fj(t) the approximation function f(t) on resolution level j. On the next level of resolution, j+1, we add fluctuation or details and mark them with dj(t); the approximation function f(t) on the new resolution level is then f+i(t)= fj(t)+ j). We obtain the original functionf(t) when we let the resolution go to infinity: f (t ) = fj (t ) + É dk (t ). k=j The concept of multi-resolution marks the simultaneous presence of different resolutions. However, the previous equation presents only one possibility of the development or decomposition function f(t) to its smooth part and details. We can suppose analogously that £2(R) is the space of square-integrable functions as composed of a sequence of subspaces {Wk} and Vj. With Vj we denote the subspace of functions that contain signal information down to scale 2-j. The multi-resolution analysis involves a decomposition of the function space into a sequence of subspaces Vj, such that subspace Vj is contained in all the higher subspaces. If we denote the approximation to f(t) at level j by fj(t), then fj(t)eVj. Since information at resolution level j is necessarily included in the information at a higher resolution, Vj must be contained in Vj+1 for all j. The difference betweenfj+1(t) andfj(t) is the additional information about details at scale 2-(j+1), which is denoted by dj(t)= f+i(t) - j). Thus, we get f+i(t) = j) + dj(t) and can further decompose our subspaces accordingly, writing V+1 = Vj ® Wj, where Wj is called the detail space at resolution level j and is orthogonal to Vj. We can continue the decomposition of the space V and obtain V+1 = Wj ® Vj = Wj ® Wj-1 ® V-1 = »=Wj ® Wj-1 ® Wj-2 ® » ® Wjj ® j Thus, we can conclude that the approximation space at resolution j (i.e., Vj) can be written as a sum of subspaces. Similarly, the approximation of the function f(t) at resolu-tionj (i.e.,f(t)) is contained in subspaces Vj, and details dk(t) in Wk. The function that we are using for this purpose is called a "wavelet". We can introduce wavelets in many possible ways (Chui, 1992; Valens, 1999), including considering the space £2(R). The local average value of every function in ¿2(R) must "decay" to zero at ±®. It follows that the base function must be oscillatory (wavelike). Therefore, we look for "waves" generating L2(R) that, for all practical purposes, decay sufficiently fast. We can say we look for small waves or "wavelets" to generate the space L2(R) and we prefer to have a single function, say y, to generate all of L2(R). Because the wavelet y has very fast decay, an obvious way to cover the entire real line R is to shift the wavelet function y along the real line. Shifting a wavelet simply means considering all the integral shifts of y—namely, y(t-k), &eZ, where Z denotes the set of integers. Next, to properly represent f(t), we must also consider waves with different frequencies—in particular, waves with frequencies partitioned into consecutive "octaves" or frequency bands or scales. For computational efficiency the integral powers of 2 are used for frequency partitioning. So we can now consider wavelets of the form y(2jt-k), y,keZ. The family y(2jt-k) is thus obtained from a single wavelet function y(t) or mother wavelet by a binary dilation (by 2j) and a dyadic translation (or shift of k/2j). The definition of wavelets along with y(t) also requires a scaling function ^(t). The wavelet function is in effect a band-pass filter; scaling it for each level halves its bandwidth. As a result, in order to cover the entire spectrum, an infinite number of levels is required. The scaling function filters the lowest level of the transformation and ensures that the entire spectrum is covered (Valens, 1999). For example, the simplest possible wavelet is the Haar wavelet, defined as V(t ) = 1, 0 < t < 1/2 -1, 1/2 < t < 1 0, otherwise Its scaling function 9 can be described as (p(t ) |1, 0 < t < 1 0, otherwise We can note that any continuous real function can be approximated by linear combinations of the constant function y(t),y(2t),y(4t),... ,y(2jt),... and their shifted functions. The technical disadvantage of the Haar wavelet is that it is not continuous, and therefore not differentiable, yet this property can be an advantage for the analysis of time series with sudden jumps. Wavelets have many characteristics. Here we mention just a few important ones. According to Sheng (1996), functions y(t)eL2(R) satisfying the admissibility condition expressed as | I2 ' I \| d\ = 0, where ¥(©) stands for the Fourier transformation of y(t), can be used to first analyze and then reconstruct a time series without the loss of information. Moreover, the admissibility condition implies that the Fourier transformation of y(t) vanishes at the zero frequency: I Y(ffl) |2 = 0. A zero at the zero frequency also means that the average value of the wavelet in the time domain must be zero: J" y/(t)dt ■ 0. This implies, as previously mentioned, that the wavelet function y(t) must be oscillatory—in other words, a wave. Finally, we can state some sort of admissibility condition for the scaling function ^(t) as well J" (p(t)dt = 1, which implies that the zero moment of the scaling function cannot vanish. As previously mentioned, the shift and scaling of the wavelet function y can be written as 1 WbaO (t) =~rV sja t - b a In the original time series, it can look like an approximation of level 0, A0. Of course, it is valid as this: Aj = Aj+i + Dj+i At a given j, the detail level Dj of MR analysis of time series can now be written as function D j(t ) = X CM^,k (t ) keZ and finally, we make the entire time series as f (t )=X D j jeZ If we define approximation level J, AJ , as Aj =s d, j >J , we can express time of series f as sum of approximation Aj and details of level Dj f = Aj +X Dj j^J . Concerning the choice of the wavelet function for the multi-resolution decomposition, we chose the Meyer family wavelets for those members that are infinitely continuous differentiate; this allowed for smooth functions at every level of details. The Meyer wavelet y and its scaling function 9 are in the frequency domains defined as follows (Misiti, Oppenheim, & Poggi, 2005) where a is the scale factor, b is the translation factor, and a"1'2 stands for energy normalization across the different scales. To express the time series ft) based on function y, we define wavelet transformation as (Wf )(b , a)=Jf (t )7ä w t - b a dt, y(m) = /'-).—\-1/2 im/2 (2n) e sin V 2n' M-1 // /'-).—\-1/2 im/2 (2n) e cos n —v 2 V v 4n -m -1 // 2n . ,4n — < \\ < — 3 1 1 3 4n . I^ 8n — - 4n where v(a) = a4 (35 - 84a + 70a2 -20a3), a e [0,1]. Both functions are shown in Figure 1. 5 Database and Calculations In this paper, quarterly data are analyzed. The multi-resolution scales are such that scale (or detail) 1 (D1) is associated with 1- to 2-quarter dynamics, scale 2 (D2) with 2- to 4-quarter dynamics, scale 3 (D3) with 4- to 8-quarter or 1- J \=0 3 0 3 Figure 1: Meyer wavelet family (author's calculations). 1.5 Meyer wavelet 0.5 1.2 1 Meyer scaling function -6 -4 -2 0 2 4 6 8 to 2-year dynamics, scale 4 (D4) with 8- to 16-quarter or 2-to 4-year dynamics, and scale 5 (D5) with 16- to 32-quarter or 4- to 8-year dynamics. Quarterly data for the GDP of EU countries, Austria (at), Belgium (be), Bulgaria (bg), Czech Republic (cz), Germany (de), Denmark (dk), Estonia (ee), Spain (es), EU 15 (eu15), EU 25 (eu25), Euro Area 12 (ez12), Finland (fi), France (fr), Hungary (hu), Ireland (ie), Italy (it), Latvia (lt), Lithuania (lv), the Netherlands (nl), Poland (pl), Romania (ro), Sweden (se), Slovenia (si), Slovakia (sk), and the United Kingdom (uk), measured in millions of euros at constant 1995 prices and exchange rates, were obtained from Eurostat. Most data range from 1996Q1 to 2008Q2, except for Romania (2000Q1-2008Q2) and Ireland (1998Q1-2008Q2). From these, due to potential seasonal-ity in the data, the business cycle time series for a country i was computed as GDPit/GDPit-4. Descriptive statistics for the obtained real GDP growth series are presented in the Appendix (Table A1). The GDP growth time series was then fed into the MATLAB software with the wavelets toolbox, through which every GDP growth series was decomposed into smooth level and five detail levels (D1-D5) using, due to their indefinitely differentiability, the Meyer family of wavelet functions. To ensure better convergence illustration or synchronization of cycles at the different scales of detail, for selected analyses we show countries together with components at all scales (D1-D5) as well as the original signals in the Appendix (Figure A1). At first glance, one can assess the different synchronizations of business cycles on individual scales of details, which also confirms the numerical calculation of correlation coefficients in the Appendix (Table A2). 6 Results Numerically, different levels of synchronicity of the GDP growth time series can be represented by correlation coefficients. All correlation coefficients for different EU member countries are computed with respect to the euro area and the results are shown in the Appendix (Table A2). For each country, the overall correlation coefficient was computed between that country's GDP growth series and the euro area's GDP growth series (second column), together with correlation coefficients among the five MR components of the country's GDP growth series and the five MR components of the euro area's GDP growth series. The diagonal cells with the same frequency are shaded grey; for convenience, the correlation coefficients with the absolute value above 0.5 are printed in bold. From the overall correlation coefficients, four main different levels of synchronicity of business cycles can be seen. Large, old EU members have a high synchronicity to the euro area and correlation coefficients values above 0.8 (e.g., Germany 0.91, Italy 0.90, France 0.89) The same high level of synchronicity can also be seen at almost all different same-frequency levels of GDP MR components. The second group includes the smaller euro area economies, with correlation coefficients above 0.5 (e.g., the Netherlands 0.78, Belgium 0.75, Finland 0.65). Also in this group are the old EU members not in the euro area, with Sweden being the most synchronous with the euro area (correlation co-efficient=0.71). The third group is composed primarily of new members of the EU (in 2004), with 0.13.0.C0;2-7 6. Baqaee, D. (2009). Using wavelets to measure core inflation: The case of New Zealand (Discussion Paper Series DP 2009/05). Reserve Bank of New Zealand. 7. Baxter, M., & King, R. G. (1999). Measuring business cycles: Approximate band-pass filters for economic time series. 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Economic Letters, 100(2), 208-212. http://dx.doi.org/10.1016/j.econlet.2008.01.008 APPENDIX Table 1: Descriptive statistics for the real GDP growth series Average Standard deviation Maximum Minimum Asymmetry Skewness Austria 2.4 1.3 5.0 -0.5 -0.27 -0.59 Belgium 2.3 1.2 5.2 -0.6 0.13 -0.27 Bulgaria 3.3 6.6 18.3 -21.5 -2.27 6.96 Czech Republic 3.5 2.7 7.9 -2.1 -0.37 -0.68 Denmark 2.1 1.6 4.5 -1.3 -0.43 -1.04 Estonia 6.9 3.6 12.0 -1.1 -0.92 0.09 EU 15 2.3 1.0 5.1 0.3 0.40 0.42 EU 25 2.4 1.0 5.1 0.4 0.34 0.33 Euro area 12 2.2 1.0 5.0 0.0 0.38 0.37 Finland 3.8 1.6 7.1 -1.3 -0.35 0.68 France 2.2 1.1 5.2 0.4 0.44 0.15 Irland 6.5 3.2 14.4 -1.3 0.02 0.64 Italy 1.4 1.2 4.2 -0.6 0.50 -0.49 Latvia 7.3 3.2 12.9 0.1 -0.31 -0.52 Lithuania 6.6 3.3 11.6 -4.3 -1.36 2.56 Hungary 3.8 1.5 6.6 0.6 -0.84 0.12 Germany 1.6 1.3 4.4 -1.1 0.27 -0.16 Netherland 2.8 1.5 5.8 -0.2 -0.47 -0.48 Poland 4.7 2.4 11.8 -0.3 0.27 0.38 Romania 5.5 3.3 9.8 -5.7 -2.06 5.85 Slovakia 5.2 3.2 14.3 -2.7 -0.21 0.84 Slovenia 4.5 1.3 7.4 2.4 0.37 -0.78 Spain 3.6 1.0 7.3 1.6 0.84 2.42 Sweden 3.0 1.6 6.2 -1.5 -0.50 0.10 United Kingdom 2.9 0.9 5.7 0.4 0.19 1.58 Source: Eurostat, own calculations. Figure 1: MR components of GDP growth at different scales of details 96 97 98 99 00 01 02 03 04 05 06 07 08 -EZ12 D5 ■■■■ ........ SI D5 — -— CZ D5 -DE D5 ..... ...... UK D5 -----NL D5 — -EE D5 16 12 96 97 98 99 00 01 02 03 04 05 06 07 08 EZ12 DE NL ■■■■ SI ■■■ UK EE CZ EZ12 .............SI -CZ DE ----------UK NL -EE EZ12_D4 DE_D4 NL D4 SI_D4 -CZ_D4 UK_D4 EE D4 EZ12_D2 DE_D2 NL D2 SI_D2 -CZ_D2 UK_D2 EE D2 - EZ12_D1 DE_D1 -----NL D1 SI_D1 -CZ_D1 UK_D1 EE_D1 Source: Eurostat, own calculations. Table 2: Correlation coefficients of GDP growth between EA and EU members countries Euro area 12 Country Correlation L d1 D2 d3 d4 d5 EU25 0.9770 dl 0.953752 0.004493 -0.003975 -0.003641 -0.003703 d2 -0.006145 0.934317 0.009582 -0.016525 -0.013868 d3 -0.007213 0.018677 0.990372 0.037329 0.042178 d4 -0.004723 -0.027715 0.042398 0.998219 0.135373 d5 -0.005428 -0.003962 0.046966 0.240061 0.992227 Euro area 12 Country Correlation L d1 D2 d3 d4 d5 EU15 0.9814 d1 0.959111 0.004415 -0.003289 -0.003347 -0.003403 d2 -0.003350 0.945447 0.014130 -0.017631 -0.015363 d3 -0.006978 0.022870 0.992213 0.039622 0.042446 d4 -0.004628 -0.027397 0.044016 0.997837 0.130394 d5 -0.005373 -0.005861 0.047946 0.165739 0.999982 Austria 0.7267 d1 0.221615 -0.013512 0.004412 0.008193 0.005469 d2 0.008791 0.551204 0.035231 -0.028576 -0.012460 d3 -0.007923 -0.130513 0.745668 -0.003088 0.038970 d4 6.98E-05 0.031206 -0.006458 0.602028 0.592158 d5 -0.003051 -0.032062 0.023135 0.771726 -0.288128 Belgium 0.7511 d1 0.244746 -0.026349 0.003470 0.018998 0.004229 d2 0.002427 0.463686 -0.001840 0.007603 -0.017793 d3 -0.011423 0.022295 0.855342 0.068431 0.047890 d4 0.004843 0.065799 -0.028445 0.237741 0.457648 d5 -0.002934 -0.030143 0.024163 0.766913 -0.255445 Germany 0.9143 d1 0.916335 -0.008807 0.002924 0.007536 0.001821 d2 -0.011282 0.845426 0.005632 -0.006739 -0.006604 d3 -0.011483 -0.017649 0.960187 0.077957 0.065914 d4 -0.003143 -0.004493 -0.000544 0.822916 0.522826 d5 -0.001068 -0.005782 0.024373 0.610699 0.433593 Spain 0.7389 d1 0.232214 -0.023824 0.009215 0.015346 0.007185 d2 -0.022159 0.195177 -0.000497 0.028376 0.019600 d3 -0.011107 0.083164 0.485736 0.076802 0.056102 d4 0.006014 0.068939 -0.040926 0.121846 0.486614 d5 -0.002816 -0.041915 0.042982 0.702226 0.147526 Finland 0.6582 d1 0.404893 -0.007645 0.003548 0.007027 -0.000159 d2 -0.004789 0.183430 0.020013 0.025999 0.010029 d3 -0.009720 -0.071808 0.867501 0.007402 -0.036164 d4 -0.003807 0.046464 -0.082226 0.162488 0.733442 d5 0.003885 -0.000589 -0.011487 0.468575 -0.210425 France 0.8865 d1 0.788831 0.009152 -0.006027 -0.006696 -0.005213 d2 0.003949 0.931527 0.012191 -0.028121 -0.020396 d3 -0.012532 -0.011675 0.806189 0.090417 0.050699 d4 0.003856 0.045745 -0.051823 0.570423 -0.004155 d5 -0.004820 -0.034371 0.054166 0.620719 0.672344 Ireland 0.6219 d1 0.034247 -0.003750 -0.005454 -0.002731 -0.000559 d2 0.011503 0.466659 0.024766 -0.000583 0.000205 d3 0.006187 0.029541 0.638025 0.003253 0.016160 d4 -0.044933 0.015634 0.188287 -0.006750 0.516102 d5 0.043476 -0.002117 -0.091410 0.839392 0.347320 Italy 0.9045 d1 0.797997 -0.001365 -0.001164 0.001281 -0.002544 d2 0.008453 0.839144 0.027627 -0.035797 -0.014922 d3 -0.008898 0.065115 0.907917 0.081863 0.057536 d4 0.001522 0.044549 -0.048528 0.296512 0.720939 d5 -0.002909 -0.042378 0.045228 0.689488 0.189953 Netherland 0.7762 d1 0.610808 -0.016453 -0.006174 0.009572 -6.17E-05 d2 -0.003976 0.717838 -0.033273 -0.015649 -0.027906 d3 -0.008811 -0.023475 0.736669 0.032510 -0.002305 d4 -0.000787 0.026985 0.017112 0.370969 0.718304 d5 -0.001327 -0.013659 0.000779 0.793836 -0.128897 Slovenia 0.4383 d1 0.463952 0.040292 -0.023124 -0.031356 -0.017091 d2 -0.036525 0.273216 -0.038937 0.017112 0.002676 d3 -0.015467 -0.187438 0.339077 -0.008406 -0.002994 d4 0.000994 0.044913 0.041432 0.264106 0.666294 d5 0.000545 -0.007411 -0.006576 0.640032 -0.379520 Euro area 12 Country Correlation L d1 d2 d3 d4 d5 United Kingdom 0.5582 d1 0.440933 -0.013967 0.004817 0.009926 0.005741 d2 0.012807 0.246886 -0.008436 -0.007249 -0.004945 d3 -0.010388 -0.171022 0.764814 -0.040809 -0.013740 d4 -0.004015 0.037436 -0.065790 0.087530 0.656455 d5 0.004993 0.006707 -0.025100 0.418329 -0.356038 Sweden 0.7119 d1 0.750696 -0.016912 0.007216 0.012551 0.005373 d2 0.000834 0.426320 -0.014615 -0.016828 -0.033004 d3 -0.007498 0.056066 0.652777 0.066009 0.063388 d4 0.000829 0.044120 0.005872 0.485278 0.397688 d5 0.002194 -0.003840 -0.010581 0.603667 -0.250228 Denmark 0.5516 d1 0.744414 -0.015639 0.003707 0.011546 0.003823 d2 -0.016402 0.306012 -0.021566 -0.005414 -0.018197 d3 -0.014390 -0.273655 0.328073 0.081528 -0.051045 d4 -0.002282 0.006732 0.052323 0.535333 0.668383 d5 0.003865 0.018804 -0.043349 0.410551 -0.554542 Czech Republic -0.2224 d1 -0.183917 -0.003059 -0.000600 0.003314 0.000539 d2 -0.032550 -0.450248 -0.129607 0.031627 -0.011535 d3 0.008479 0.041839 -0.356920 -0.005123 0.098226 d4 0.007126 0.016343 0.027367 -0.043548 0.174019 d5 0.001969 0.012885 -0.031348 0.318478 -0.686259 Poland 0.4673 d1 0.018754 -0.006183 0.000475 0.004349 0.000865 d2 0.012605 0.838604 0.058924 -0.040491 -0.009589 d3 -0.001679 0.099140 0.811693 0.012552 0.086035 d4 -0.001478 -0.038569 0.041335 0.867092 -0.083008 d5 0.002920 0.017318 -0.031815 0.429657 -0.499836 Hungary 0.4016 d1 0.086229 0.006322 0.011257 0.000373 0.004616 d2 -0.003471 0.503662 -0.010206 -0.012392 -0.021968 d3 -0.007421 -0.028442 0.597110 0.062781 -0.068015 d4 -0.006103 -0.022644 0.040922 0.584100 -0.202258 d5 -0.003996 -0.017526 0.041996 -0.274862 0.727780 Slovakia -0.2317 d1 0.282341 0.000638 0.011722 0.006080 0.006834 d2 -0.023639 0.048875 -0.009270 0.019093 -0.010061 d3 -0.009638 0.041192 0.413700 0.071956 0.099270 d4 -0.006244 -0.011548 0.047270 -0.260726 0.820830 d5 0.008413 0.031452 -0.059975 0.094142 -0.659212 Estonia 0.2371 d1 0.336771 0.006878 -0.001689 -0.004143 -0.001565 d2 0.008066 0.838602 0.054474 -0.027623 -0.009407 d3 -0.005963 -0.002362 0.651685 0.061304 -0.054919 d4 0.001835 0.041663 -0.036439 -0.466674 0.501049 d5 0.002269 0.015875 -0.033917 0.352139 -0.629330 Latvia 0.1174 d1 0.515277 0.004087 0.004177 -0.001845 0.000862 d2 0.001597 0.731896 0.044161 -0.017963 0.000237 d3 -0.007105 -0.032310 0.472825 0.060387 -0.074309 d4 -0.005583 0.028042 -0.035941 -0.003753 0.687280 d5 0.001031 0.013536 -0.024616 0.432807 -0.511381 Lithuania -0.2773 d1 0.591051 0.004955 -0.003121 -0.005275 -0.002548 d2 -0.000269 0.150302 -0.000887 0.001715 0.016680 d3 -0.001932 -0.008769 0.300380 0.022602 -0.078080 d4 -0.001439 0.015498 -0.057654 -0.777292 -0.131135 d5 0.004703 0.013651 -0.045760 0.178073 -0.844302 Bulgaria 0.3525 d1 0.322482 -0.016906 0.005630 0.011514 0.005716 d2 0.013024 0.651294 0.032749 -0.058798 -0.014800 d3 -0.004951 0.116993 0.280922 0.075319 0.055107 d4 0.004641 0.057039 -0.019272 0.481563 0.152503 d5 -0.008909 -0.041416 0.077538 0.297245 0.896321 Euro area 12 Country Correlation L d1 d2 d3 d4 d5 Romania 0.0186 dl 0.310376 -0.011776 0.003404 -0.009169 -0.010616 d2 0.050558 0.533389 -0.154589 0.029973 -0.010387 d3 0.011205 0.117284 0.545343 -0.054872 -0.009940 d4 -0.010032 -0.030445 -0.214020 -0.935397 -0.313396 d5 -0.017401 -0.026685 -0.138098 0.475455 -0.713575 Source: Eurostat, own calculations. \ In 2011, Vesna Dizdarevic graduated from the University of Maribor, Faculty of Economics and Business, with a doctorate in international economics. Her research focuses on macroeconomics, economic analysis, and politics. She is currently employed at the Promo + d.o.o. Ljubljana. Vesna Dizdarevic je leta 2011 doktorirala na Ekonomsko-poslovni fakulteti Univerze v Mariboru z doktorsko disertacijo s področja mednarodne ekonomije. Osredotoča se na raziskovanje na področjih makroekonomije, ekonomske analize in politike. Zaposlena je v podjetju Promo + d.o.o. v Ljubljani kot direktorica projektov. __X In 2000, Robert Volčjak earned his Ph.D. in information administration sciences at the University of Ljubljana, Faculty of Economics. He was associated with the Economic Institute EIPF, the leading Slovenian institution in econometric research, in 1996 as a junior researcher; since 2003, he has worked as research associate. His research focuses on macroeconomic modelling, operations research, and mathematical economics, and he has developed more 60 scientific and professional papers in these areas that have been published in prominent national and international journals and presented at conferences in Slovenia and abroad. Robert Volčjak je leta 2000 doktoriral na Ekonomski fakulteti Univerze v ^ /V Ljubljani. Kot znanstveni sodelavec je zaposlen na Ekonomskem inštitutu EIPF ■v v Ljubljani. Glavna področja njegovega raziskovalnega dela so makroekonomija, ekonomske analize in politika, ekonomsko modeliranje, statistična in ekonome-trična analiza, matematična ekonomija ter operacijske raziskave in upravljavske znanosti. Z omenjenih raziskovalnih področij je do danes nastalo več kot 60 znanstvenih in strokovnih del, ki so bila objavljena v priznanih domačih in tujih revijah ter predstavljena na konferencah v Sloveniji in v tujini.