Abstract
We use wavelet analysis to study the impact of the Euro adoption on the oil price macroeconomy relation in the Euroland. We uncover evidence that the oil-macroeconomy relation changed in the past decades. We show that after the Euro adoption some countries became more similar with respect to how their macroeconomies react to oil shocks. However, we also conclude that the adoption of the common currency did not contribute to a higher degree of synchronization between Portugal, Ireland and Belgium and the rest of the countries in the Euroland. On the contrary, in these countries the macroeconomic reaction to an oil shock became more asymmetric after adopting the Euro.
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Notes
- 1.
The phase-angle ϕ x (τ, s) of the complex number W x (τ, s) can be obtained from the formula: \(\tan (\phi _{x}(\tau,s)) = \frac{\mathfrak{I}(W_{x}(\tau,s))} {\mathfrak{R}(W_{x}(\tau,s))},\) using the information on the signs of ℜ(W x ) and ℑ(W x ) to determine to which quadrant the angle belongs to.
- 2.
The precise requirements are that \(\vert \psi (t)\vert < C(1 + \vert t\vert )^{-(1+\epsilon )}\) and \(\vert \hat{\psi }(f)\vert < C(1 + \vert f\vert )^{-(1+\epsilon )}\), for C < ∞, ε > 0.
- 3.
Actually, it is also common to call it the Gabor wavelet. Authors who do this, usually reserve the name Morlet to the real part of Eq. (2).
- 4.
In the above formula and in what follows, we will omit the arguments (τ, s).
- 5.
Some authors prefer a slightly different definition, Arctan \(\left (\frac{\mathfrak{I}\left (W_{\mathit{xy}}\right )} {\mathfrak{R}\left (W_{\mathit{xy}}\right )}\right ).\) In this case, one would have \(\phi _{\mathit{xy}} =\phi _{x} -\phi _{y},\) hence the name phase-difference.
- 6.
The grey contour designates the 5 % significance level, obtained by 1,000 Monte Carlo simulations based on two independent ARMA(1,1) processes as the null. Coherency ranges from white/light grey (low coherency) to black/dark grey (high coherency). The cone of influence, which is the region subject to border distortions is shown with a thick line.
- 7.
Basically, we reduce each of the distance matrices to a two-column matrix, called the configuration matrix, which contains the position of each country in two orthogonal axes.
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Acknowledgements
We offer this paper as a token of our intellectual respect for James Ramsey, who, in a series of papers, some of them co-authored with Camille Lampart, got us interested on wavelet applications to Economics. We thank an anonymous referee for his comments. The usual disclaimer applies. Financial support from Fundação para a Ciência e a Tecnologia, research grants PTDC/EGE-ECO/100825/2008 and PEst-C/EGE/UI3182/2013, through Programa Operacional Temático Factores de Competitividade (COMPETE) is gratefully acknowledged.
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Aguiar-Conraria, L., Rodrigues, T.M., Soares, M.J. (2014). Oil Shocks and the Euro as an Optimum Currency Area. In: Gallegati, M., Semmler, W. (eds) Wavelet Applications in Economics and Finance. Dynamic Modeling and Econometrics in Economics and Finance, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-07061-2_7
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