Abstract
In recent times, a large number of studies has investigated the empirical properties of financial cycles within countries, mainly based on band-pass filter techniques. The contribution of this paper to the literature is twofold. First, in contrast to most existing studies in the financial cycle literature, we perform a multivariate parametric frequency domain analysis which takes the complete (cross-) spectrum into account and not only certain frequencies. Second, we provide evidence on the cross-country interaction of financial cycles. We focus on the USA and UK and use frequency-wise Granger causality analysis as well as structural break tests to obtain three main results. The relation between cycles has recently intensified. There is a significant Granger causality from the US financial cycle to the UK financial cycle, but not the other way around. This relationship is most pronounced for cycles between 8 and 30 years.
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Note: The US (solid line, right axis) and UK (dashed line, left axis) financial cycle indices are obtained as the first principal component of national credit (source: Datastream) and house price index series (source: OECD.Stat). The gray bar denotes the beginning of the financial liberalization phase, 1985Q1, and indicates the sample split
Note: The Monte Carlo based 95%-confidence intervals are represented by dotted gray lines. The maximum period of 80 quarters equals 20 years
Note: Contributions of US innovations are represented by solid lines, contributions of UK innovations by dashed lines. The maximum period of 80 quarters equals 20 years
Note: Dashed lines show estimates from 1970Q1 until 1984Q4, solid lines those from 1985Q1 until 2013Q4. For quarterly data, the frequencies \(\pi /64\) and \(\pi /16\) in the shaded area correspond to long cycles between 32 and 8 years. Frequency \(\pi /4\) corresponds to a cycle of length 2 years
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Notes
The variable credit represents the outstanding volume of credit, measured in national currency, to the private non-financial sector from all sectors. The data are provided by Datastream with identifiers USBLCAPAA and UKBLCAPAA. The variable housing represents a national house price index. These data are collected by OECD.Stat and made available for each country under the general identifier House Prices.
The empirical results are very similar when considering credit or house prices separately.
For the USA, the first principal component explains 91% (95%) of the total variation in the pre-1985 (post-1985) period. In the case of UK, it explains 79% (98%). US indicators are constructed as \(0.94\cdot \text{ credit }+0.34\cdot \text{ housing }\) and \(0.95\cdot \text{ credit }+0.31\cdot \text{ housing }\) in the first and second sample period, respectively. For the UK, the indicators are \(0.82\cdot \text{ credit }+0.57\cdot \text{ housing }\) and \(0.78\cdot \text{ credit }+0.62\cdot \text{ housing }\).
Johansen (1995) cointegration test results can be found in Table 3 in “Appendix A”. It should be noted that even though Ordinary Least Squares delivers consistent estimates of the VAR parameters regardless of the existence of cointegration, imposing a cointegration restriction in the VAR would lead to some efficiency gain if the restriction was correct (as suggested by the Johansen test results).
Another piece of evidence which maybe interpreted in favor of our Cholesky ordering is the weak exogeneity property of the US index. We find that only the UK adjusts to deviations from the long-run relation. With a test statistic of \(\chi ^2(1)=1.33\) and a p value of 0.25 weak exogeneity cannot be rejected for the second sample period. However, theoretically this result does not imply any Cholesky ordering and should therefore be interpreted with caution. But intuitively, the non-adjustment of the USA at time t to deviations from the equilibrium at \(t-1\) makes it more plausible that the US does not react contemporaneously to UK innovations than the other way around.
As an anonymous referee pointed out, the existence of Granger causality in at least one direction is already implied by the existence of a cointegration relation, see Table 3 in “Appendix A”.
According to Eq. (11) \(M_{x\rightarrow y}(\lambda )\) is a logarithmic measure which describes the strength of the Granger causality of x on y at a given frequency \(\lambda \). The higher the value of \(M_{x\rightarrow y}(\lambda )\), the stronger the causality from x to y. In particular, if \(M_{x\rightarrow y}(\lambda )=0\), x does not Granger cause y at the frequency \(\lambda \).
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Acknowledgements
We are grateful for comments and suggestions received from Helmut Lütkepohl, Dieter Nautz, Christian Merkl, Lars Winkelmann, Sven Schreiber, and various participants at seminars at the Swiss National Bank and the IAB Nürnberg, as well as at the 2015 IAAE and the 2016 CFE conferences. Financial support from the Deutsche Forschungsgemeinschaft (DFG) through CRC 649 “Economic Risk” and by the Macroeconomic Policy Institute (IMK) in the Hans-Böckler Foundation is gratefully acknowledged.
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Jürgen Wolters: Deceased.
Appendices
A Cointegration test results
Table 3 presents the cointegration test results according to Johansen (1995). The evidence suggests that there is a cointegration relation in both sample periods.
The deterministic terms in the VECM differ from the ones included in the unrestricted VAR. The reason is that when estimating a VAR the nature of the trending (stochastic or deterministic) is unclear. Even in the presence of cointegration, a deterministic trend may be necessary to capture different drifts of the times series. Fortunately, OLS estimates of a VAR are consistent in any case. When estimating a VECM, cointegration can be tested and it can also be seen whether a deterministic time trend needs to be included in the cointegration relation. It the current case, it turned out that the series have different drifts in the first subsample but the same drift in second subsample.
B Impulse indicator saturation results
As outlined during Sect. 3 on data and model selection, we want to analyze possible changes in the characteristics of the financial cycle. Thereby, we follow the literature (Claessens et al. 2011, 2012; Drehmann et al. 2012), which specifies the break at 1985Q1, seen as the starting point of the financial liberalization. 1985Q1 is also in accordance with a Chow test, see Sect. 3.
To provide additional statistical support without a priori specifying a break date, we conducted an impulse indicator saturation analysis, see Fig. 5. Following Hendry (2011) and Ericsson (2013) (see also the references therein), we use the split-half approach. That is, we include impulse dummies for all data points of the first half of the sample and estimate the model over the full sample. The upper right graph of Fig. 5 shows the dummies being significant at the 10%-level. Then, we do the same for the second half of the sample, see middle right graph of Fig. 5. Finally, we estimate the model including all remaining significant dummies. A considerable amount of dummies (38 ones) remains significant in the first half, but only very few Breitung and Candelon (2006) in the second half, see lower right graph of Fig. 5. The three dummies in the second half clearly indicate the Lehman bankruptcy. Therefore, the results strongly point to a sample split somewhere around mid to late 1980’s.
Note: The figure shows the two blocks of impulse dummies which were included in the first half (upper left figure) and the second half (middle left figure) of the sample. The significant dummies in the first and second period are shown in the upper right and middle right figure, respectively. The combined block of dummies is shown in the bottom left figure. The significant dummies remaining in the very final model are shown in the bottom right figure
Results of impulse indicator saturation.
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Strohsal, T., Proaño, C.R. & Wolters, J. Assessing the cross-country interaction of financial cycles: evidence from a multivariate spectral analysis of the USA and the UK. Empir Econ 57, 385–398 (2019). https://doi.org/10.1007/s00181-018-1471-2
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DOI: https://doi.org/10.1007/s00181-018-1471-2