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Growth cycle synchronization of the Visegrad Four and the European Union

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Abstract

In this paper, we map the growth cycle synchronization across the European Union, specifically focusing on the position of the Visegrad Four countries. We study the synchronization using frequency and time–frequency domain. To accommodate for dynamic relationships among the countries, we propose a wavelet cohesion measure with time-varying weights. Analyzing quarterly data from 1995 to 2017, we show an increasing co-movement of the Visegrad Four countries with the European Union after the countries have accessed the European Union. We show that participation in a currency union increases the co-movement of the country adopting the Euro. Furthermore, we find a high degree of synchronization at business cycle frequencies of the Visegrad Four and countries of the European monetary union.

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Notes

  1. The Eastern Bloc was generally formed of the countries of the Warsaw Pact (as Central and Eastern European countries) and the Soviet Union.

  2. The Visegrad Four countries also joined the North Atlantic Treaty Organization in 1999 and applied for membership in the European Union in 1995–1996.

  3. The literature focusing on the evolution and determinants of business cycle synchronization between Central and Eastern European (CEE) countries and the EU is extensive, see, e.g., Darvas and Szapáry (2008), Artis et al. (2004), Backus et al. (1992).

  4. These group consists of Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Portugal, and Spain. We analyze this group and the V4 countries.

  5. Characteristics of locally stationary time series are close to the stationary ones at each point of time or shorter periods.

  6. This also overcomes the problem of short-time Fourier transform, or windowed Fourier transform (Gabor 1946).

  7. It is possible to use methods of evolutionary spectra of non-stationary time series developed by Priestley (1965). However, to study time-varying dynamics we need to give up some frequency resolution, which is not the case when using wavelet techniques.

  8. In “Appendix” in ESM, we demonstrate the wavelet-based measure (Eq. 3) in two particular cases, as shown in Fig. A.2.

  9. Another possibility for testing the significance is area-wise test approach of Maraun et al. (2007).

  10. To obtain the confidence intervals of frequency cohesion, we follow the procedures of Franke and Hardle (1992) and Berkowitz and Diebold (1998), where instead of bootstrapping the cohesion measure we bootstrap each (cross-)spectrum. Schüler et al. (2017) used this approach in their power cohesion measure while studying financial cycles for G-7 countries.

  11. Data were obtained via OECD Database, May, 2018.

  12. The V4 countries are included in the EU-28; however, the contribution is minimal to change the EU GDP growth. For robustness check, we analyzed the co-movement of the V4 and the EA-19 GDPs, and these results are almost identical to those we report.

  13. Short periods of co-movement appear around and prior to 2000 at 1–2-year, and 2-year cycles, respectively, between Hungary and Slovakia, and Poland with the Czech Republic and Slovakia.

  14. We have additionally checked the co-movement of the V4 countries and the Euro area of 19 countries (EA-19) as a proxy of the EU. The results are almost indistinguishable.

  15. Poland’s economy share of agriculture in GDP is one of the higher.

  16. Two countries are in-phase if the phase difference belongs to \([-\pi /2, \pi /2]\); otherwise, they are in the anti-phase. Moreover, the first country leads the second, \(x_j\), if the phase is in \([0, \pi /2]\) and \([-\pi , -\pi /2]\); when in \([-\pi /2, 0]\) and \([\pi /2, \pi ]\), the second country is leading.

  17. Furthermore, the phase is more volatile when the coherence is low.

  18. We should also carefully interpret the phase difference at 3–8-year cycles because of the cone of influence, which affects influences results at 8 years from both sides of the sample.

  19. The figures of wavelet cohesion, heatmaps, display the results the same way as those of the wavelet coherence, except that the scale of the cohesion may be negative. Hence, the blue color depicts the negative relationship between economies, which may also be strong.

  20. In “Appendix Fig. A.1” in ESM, we provide complementary results showing cohesion of the EU-12 countries (a) and peripheral countries (b), where both show much lower synchronization than the EU core in Fig. 6.

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Acknowledgements

We are very thankful to the editor and referees for useful comments and suggestions. We would like to thank participants of two conferences for constructive discussions—the 2nd International Workshop on “Financial Markets and Nonlinear Dynamics” in Paris and Slovak Economic Association meeting in Košice.

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Authors and Affiliations

  1. Institute of Economic Studies, Charles University, Opletalova 26, 110 00, Prague 1, Czech Republic

    Luboš Hanus & Lukáš Vácha

  2. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi 4, 182 00, Prague 8, Czech Republic

    Lukáš Vácha

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  1. Luboš Hanus
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Correspondence to Lukáš Vácha.

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We gratefully acknowledge the financial support from the Czech Science Foundation under the GA16-14151S Project as well as the support from the Grant Agency of Charles University (GAUK), under Project No. 366015.

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Hanus, L., Vácha, L. Growth cycle synchronization of the Visegrad Four and the European Union. Empir Econ 58, 1779–1795 (2020). https://doi.org/10.1007/s00181-018-1601-x

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