One striking characteristic of several of these crises was how an initial country-specific shock was rapidly transmitted to markets of very different sizes and structures around the globe. This has prompted a surge of interest in ‘contagion.’ But what is contagion? Despite the fact that the term is widespread, there is little agreement on what exactly it entails. Many people assume that contagion occurred...but few agree on exactly which countries were subject to contagion. Numerous theoretical papers have described the various channels by which contagion could occur, but empirical work sharply disagrees on whether or not contagion actually occurred during recent financial crises...

– Kristin Forbes and Roberto Rigobon (Chapter 3, 2001)

1 Introduction

International financial market spillovers or contagion effects can broadly be defined as the spread of market volatility or disturbances from one regional market or economy to another. An alternative and less standard definition can entail the propagation of country-specific news to other markets—even if such news is not incorporated in the asset prices of the supposed country that is the catalyst for the contagion (Chapter 2, IMF 2016).

There are several factors that can augment the propagation of spillovers. These factors have to do with the extent to which markets or economies are interlinked with one another. The stronger the ‘channels’ or interlinkages that bind them together, the higher the probability that a shock in one afflicted market will transmit into the remaining markets.

Recent research interest in spillovers and contagion effects has ballooned in the last few years. For example, beginning in 2011, the International Monetary Fund (IMF) has published spillover reports to identify and analyze global spillovers and their effects. In their 2015 report, for instance, the IMF warned of impending spillover effects from euro area countries and cited, among other reasons, the large size of their output gaps in relation to the output gaps of other advanced economies (IMF 2015).

The European debt crisis has indeed fuelled research in this subject, particularly Greece, which is the focal point of discussion in socioeconomic and political news headlines. In relation to its European counterparts, Greece has, for better or worse, received numerous bailout packages and has implemented laborious austerity measures to avert exiting the Eurozone. Monetary authorities, such as the IMF and European Central Bank (ECB) contend that if Greece leaves the Eurozone, it may trigger an irreversible domino effect for the remaining European Union (EU) member states; specifically, it may raise borrowing costs—especially for other struggling countries such as Ireland, Italy, Portugal and Spain—as well as produce aggregate market volatility in European and international stock markets. From a political viewpoint, if Greece leaves, other struggling countries may also entertain the possibility of exiting—a move that will ensure the disintegration of the EU and the multiple layers of complex economic and legal agreements that presently bind all members.Footnote 1

The recent news headlines paint an unflattering picture of Greece’s economic state of affairs. Although Greece’s (mis-)management of its domestic affairs have done little to quell these headlines, a nontrivial proportion of these news headlines have insinuated Greece as the catalyst for negative market shocks in other financial markets (CNBC 2015a, b, c; Wall Street Journal 2015a, b, c, d; The Guardian 2016). Such headlines are not to be taken lightly because it is, by now, well established in asset pricing and behavioral finance literature that news headlines, especially negative ones, have a significant impact on investor sentiment and the behavior of asset prices (Boudoukh et al. 2013; Da et al. 2015; Sicherman et al. 2016).

Clark et al. (2004) show, using present-day and historical evidence, the extent to which finance, trading and investing has become so intimately entwined with media companies, such as Bloomberg and CNBC. As they illustrate, these media companies, with all their embellishments, impart news on viewers as being urgently needed and momentous: “Breathless excitement characterizes such commentary, being associated with ‘breaking news,’ ‘new information,’ and ‘unexpected events.’ Talk is fast and furious. Talk is also often interrupted by some sudden happening. Talk moves at a breakneck pace covering topic after topic though interrupted, of course, by commercial breaks...” (p. 299). In a similar vein, Thrift (2001) eloquently discusses how a new market culture has formed as a result of media companies and that asset price movements and trading behavior are prone to irrationality and manipulation.Footnote 2

One only has to perform a quick internet search of news headlines pertaining to Greece with references to “spillovers,” “contagion,” “domino effects,” and the like, in order to appreciate the sheer size of headlines that insinuate Greece as the catalyst for negative market shocks in other countries at large. The question is, however, are these news headlines empirically justifiable? It is one thing to claim that Greece is in domestic turmoil and another to claim that it serves as the transmission channel for problems in other countries. Greece’s dire domestic state of affairs are not a precondition for branding Greece the instigator for market shocks that transpire elsewhere. Or, are they?

This paper seeks to answer this question by delineating and dissecting, across various economic regimes, the dynamic interdependencies between credit default swap (CDS) spreads among twelve EU members (Belgium, Bulgaria, Croatia, France, Germany, Greece, Hungary, Italy, Portugal, Romania, Slovakia, and Spain) across various economic regimes that encompass the crash of 2008–2009 and the European debt crisis of 2011–2013. Using a multivariate vector autoregression (VAR) framework, and throughout each of the economic regimes, this paper identifies the transmission channels for credit risk and whether a single country, such as Greece, or a particular set of countries, is responsible for disproportionately spreading credit risk. If Greece is found to be the dominant transmission channel of credit risk to other countries, it is plausible evidence that it is the ‘black swan’ which causes negative shocks to other EU members. If not, then Greece has become a scapegoat, or ‘black sheep,’ that the media can facilely target for Europe’s economic problems at large.

The sovereign CDS market provides over-the-counter (OTC) credit protection contracts whereby protection sellers compensate protection buyers in the event of a predefined sovereign credit event. For this insurance protection, the protection buyers pay a fixed fee, which is the CDS spread. As has been shown in the literature, the time-series behavior of CDS spreads provide a unique window for viewing the risk-neutral probabilities of major credit events as investors see them (Pan and Singleton 2008). In terms of price discovery for credit risk, Blanco et al. (2005) find that CDS prices lead bond prices. As a result, it is not surprising that Acharya and Johnson (2007) suggest that insider trading first takes place in the CDS market—especially in the presence of negative market news. In a similar vein, Hull et al. (2004) show that CDS spreads can be used to predict rating changes.

The motivation for this paper stems from the sheer number of business news articles which brand Greece as the instigator for credit risk transmissions yet the lack of empirical evidence to support this claim. This is important to examine given that news headlines can shape aggregate beliefs and create, as Shiller (2000) describes, “self-fulfilling prophecies.” So far, there is limited work into which countries serve as the transmission channels for sovereign credit risk throughout this European debt crisis ordeal (Kenourgios 2014; Kenourgios and Dimitriou 2015). Some emerging research focuses on the transmission channels between European nations and banks (Alter and Schuler 2012; Cornett et al. 2016; Mink and Haan 2013) or the interdependencies between implied volatility in the Euro and CDS spreads (Hui and Chung 2011). In particular, Cornett et al. (2016) show that changes in Greek CDS spreads have an insignificant impact on the abnormal returns of international US banks. When attempting to measure banks’ exposures to Greece’s credit risk, they report that Greek CDS spreads provide no explanatory power for rates of return on banks beyond what the US market index provides. Mink and Haan (2013) document qualitatively analogous findings and also find that, although bank returns do not react to Greece, they do react positively to news about bank bailouts—this is even the case for banks that are not exposed to Greece or the credit risks of other indebted euro-area countries.

Thus, this paper contributes to at least three strands of literature. First, it is relevant to literature that seeks to identify the determinants of CDS spreads, second, it is related to work on identifying transmission channels by which credit risk propagates during the European debt crisis and, third, it is related to work on financial contagion at large—work that has been the primary focus for international monetary authorities and regulators in the last few years.

The remainder of this paper is structured as follows. The second section describes the data that is used to conduct tests as well as explains the various economic regimes that serve as sub-samples. The third section describes the analytical framework and methodologies for implementing empirical tests. The fourth section discusses the results. The fifth section entertains various alternative approaches used as robustness and, finally, the sixth section concludes.

2 Description of sample data and economic regimes

2.1 Data and sub-sampled economic regimes

To examine interdependencies in credit risk, weekly CDS spreads are collected for Belgium (BE), Bulgaria (BG), Croatia (HR), France (FR), Germany (DE), Greece (EL), Hungary (HU), Italy (IT), Portugal (PT), Romania (RO), Slovakia (SK), and Spain (ES), respectively, from Bloomberg starting from October 1, 2004 until July 15, 2016—a sample period that encompasses the 2008–2009 financial crisis as well as the 2011–13 European debt crisis.Footnote 3 The abbreviations for each country just mentioned, which are used throughout the paper, are those used officially by the EU and are listed and referenced in Table 1.

Table 1 Glossary of country codes in the European Union
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As mentioned earlier, in the sovereign CDS market, protection buyers essentially buy insurance from protection sellers in the event of some prespecified credit event. For example, for the Greek CDS market, the Greek CDS seller compensates the Greek CDS buyer for prespecified losses on a given face value amount of Greek debt. Thus, the Greek CDS buyer is insuring themselves against Greece’s credit risk by transferring such risk onto the Greek CDS seller. The CDS spread is the price (fee) that the CDS buyer pays the seller in order to have this insurance. During periods when the probability of a Greek debt default rises there is a commensurate rise in Greek CDS spreads, and vice versa.

After checking the various CDS tenors (maturities) for all the CDS markets in each of the twelve aforementioned EU markets, this paper will focus exclusively on 5-year CDS spreads. For all twelve EU markets, the 5-year CDS tenor is the most liquid and complete in terms of data continuity—a finding that is, by now, standard in the literature.

Time-series plots of each countries’ weekly CDS spreads (in basis points) are shown in Fig. 1. The starting date for all the plots is October 1, 2004 and the end date is until July 15, 2016. The shaded regions are OECD recession periods for the Euro area and reflect the 2008–2009 financial crisis and 2011–2013 European debt crisis, respectively.Footnote 4 Consistent with these OECD recession periods, this paper forms subsamples which reflect distinct economic regimes (these are labeled as ‘regime 1,’ ‘regime 2,’ ‘regime 3,’ ‘regime 4’ and ‘regime 5,’ respectively) on each of the plots.

Fig. 1
figure 1figure 1

Time series plots of CDS spreads (in basis points)

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Fig. 2
figure 2

GDP per capita (in US$)

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Regime 1 embodies a period of normal global economic growth and tranquility. The start date for this regime is October 1, 2004 and ends February 29, 2008. Figure 2 plots the time-series of the sampled countries’ GDP per capita (in US$). As can be seen, all countries experienced growth in their GDP per capita during the regime 1 time period—even countries that are now considered “troubled,” such as Greece, Spain and Italy. These growth rates in their GDP per capita coincided with growth rates observed in France and Germany. Figure 3 plots the time-series of the countries’ debt-to-GDP (in %) and shows that, during regime 1, the debt-to-GDP for each country did not experience any unusual level of growth to suggest something was amiss—albeit Greece, Italy and Belgium (in that order) had the highest levels of debt relative to their GDP compared with the other EU members.

Regime 2 embodies the 2008–2009 financial crisis that gripped financial markets around the world. This regime is one of the two sampled OECD recession shaded periods and its starting date is March 7, 2008 and ends June 26, 2009. From Fig. 1, we can see that all countries experienced a substantive rise in their respective CDS spreads. For Greece, this rise in its CDS level (although noticeable) is exponentially dwarfed by its CDS level during the 2011–2013 European debt crisis (regime 4). Bulgaria, Croatia and Romania are the only three EU members that experienced higher CDS levels during the 2008–2009 crisis (regime 2) than during the 2011–2013 crisis (regime 4). From Fig. 2, we can see that every sampled country experienced a decline in its GDP per capita. Likewise, on aggregate, all countries experience a rise in their debt-to-GDP—albeit this rise is not uniform across all EU members; for example, Bulgaria’s debt-to-GDP remained flat in relation to the other EU countries while Greece’s debt-to-GDP rose significantly and ‘out-of-line’ with its EU counterparts.

Fig. 3
figure 3

Debt-to-GDP (%)

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Regime 3, starting from July 3, 2009 until June 24, 2011, can be thought of as an artificial ‘calm before the storm’ period. The reason why it may have been artificial is because monetary authorities went to great and unprecedented lengths to quell the mayhem that rocked financial markets during regime 2. Between October and December of 2009, Greece’s credit rating was downgraded by all three of the ‘Big Three’ credit rating agencies. Between February and December of 2010, Greece formally requests bailout packages from the ECB and IMF while instituting a series of austerity measures. In addition, laws are passed raising the retirement age, cutting pensions, raising taxes on certain goods and cutting certain government employee’s salaries—all this while Greece is plagued with violent riots and protests.

Although regime 3 is not recognized as a recessionary period by the OECD or even the National Bureau of Economic Research (NBER), it is a time when systemic risks were building up in our financial system. While the respective CDS spreads of Bulgaria, Germany, Croatia, Hungary, Romania and Slovakia oscillated at relatively lower levels during regime 3 than they did during regime 2, Belgium, Greece, Spain, France, Italy and Portugal experienced relatively higher CDS levels during regime 3.

Regime 4, the second sampled OECD recession period which starts from July 1, 2011 until February 22, 2013, will go down in history, as did the 2008–2009 crisis, as a destructive period for our global financial system. Table 2, which provides summary statistics for the full sample in panel A (October 1, 2004 until July 15, 2016) as well as for each of the five regimes (panels B through F), illustrates the severity of Greece’s credit risk during the 2011–2013 European debt crisis. For regime 4 (in panel E), we can see that Greece’s CDS spreads had deviated exponentially from the CDS spread levels of its EU peers. The average CDS level was 8992 basis points for Greece during regime 4. Portugal had the second highest average (869 basis points) while Germany had the lowest (72 basis points). Throughout regime 4, Greece’s CDS spread reached an inconceivable 26,089 basis points—an amount many times larger than its EU peers. The standard deviation of its CDS spread was also highest and reflects the violent changes in market perception each time Greece, the ECB and the IMF announce a supposed ‘positive’ or ‘negative’ piece of news.

Table 2 Summary statistics of CDS spreads (in basis points)
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Regime 5, which starts from March 1, 2013 until July 15, 2016, reflects our present-day state of affairs. From Fig. 1, we see that the CDS spreads of all sampled EU members are lower than they were relative to regime 4. Greece experienced a sharp spike in its CDS level between late June and early July. This was most likely associated with its missed payment to the IMF, which happened on June 30, 2015. From panel F of Table 2, we can see that Greece had the highest average CDS level for regime 5, followed by Croatia, Portugal, Hungary, Romania, Italy, Belgium, Spain, Slovakia, Belgium, France and Germany, in that order.

2.2 Correlations and stationarity tests

Table 3 reports contemporaneous correlations of the logarithmic first differences in CDS spreads among the twelve sampled EU members; whereas panel A reports correlations for the full sample, panels B, C, D, E and F report correlations for regimes 1, 2, 3, 4 and 5, respectively.

Table 3 Correlation matrix between log changes in CDS spreads
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Computing logarithmic first differences of CDS spreads provides us with a time-series of changes in the CDS spreads for each country. From panels B through F we can obtain a preliminary sense of the degree to which interdependencies exist between the countries’ CDS markets before and after recessionary economic periods (regimes 2 and 4, respectively). As discussed, regime 1 (panel B) reflects a period of normal economic growth. We can see that inter-market correlations are lower relative to what is reported in panel A. The average pairwise correlation (not tabulated) is 0.2161 in regime 1 whereas it is 0.4261 (not tabulated) for the full sample (panel A).

In regime 2, we see a significant rise in pairwise correlations—an insinuation that inter-market interdependencies augmented as aggregate investor fear rose across all markets. The average pairwise correlation for regime 2 (not tabulated) is 0.6308—an approximately 48% increase when compared to the average from regime 1.

Despite regime 3 (panel D) not being recognized as a recessionary period by monetary authorities and policymakers, we see that inter-market correlations remain elevated; the average pairwise correlation (not tabulated) is 0.6646 and analogous to the correlations in regime 2. This suggests that market participants feared that European markets, on aggregate, experienced a rise in credit risks following the 2008–2009 financial crisis.

Regime 4 (panel E) corresponds with the 2011–2013 European debt crisis. Average pairwise correlations (not tabulated) remain relatively high at 0.5742. Closer inspection of the inter-market correlations reveal that some countries experienced noticeable shifts in their pairwise correlations with other markets. For example, during the 2008–2009 financial crisis (regime 2) and the ‘calm before the storm’ period (regime 3), Greece’s average pairwise correlations with the other respective countries were 0.6663 and 0.6285, respectively (not tabulated). Now however, in regime 4, Greece’s average pairwise correlation with the other respective countries is 0.1822 (not tabulated). This is a marked difference and may be attributable to the fact that international banks and governments reduced their holdings of Greek debt before the 2011–2013 European debt crisis (Cornett et al. 2016; Wall Street Journal 2015e). On July 26, 2012 (during the middle of regime 4), Mario Draghi, the current president of the ECB, stated publicly that the ECB will do “whatever it takes” to save the euro (Wall Street Journal 2015e). His stance on ‘saving’ the euro and preventing Greece from exiting the Eurozone may be another reason for the low pairwise correlation between Greece’s CDS changes with those of its peers.

Now in our present-day state of affairs (regime 5 in panel F), Greece’s average pairwise correlation with the other sampled countries is 0.2412 (not tabulated)—an analogous finding compared with that of regime 4. This suggests other CDS markets have reduced their degree of comovement with that of Greece. Despite this, however, it is curious why the media, as referenced earlier and as is discussed more rigorously in the upcoming sections, insinuates that Greece’s debt problems will spillover into other markets.

Although the correlation matrix in Table 3 is not a formal statistical method for discriminating between transmission channels or even determining causal relations and their directionality, it does suggest some heterogeneity in the interdependence structure between the CDS markets across the regimes—something that is empirically tested in the next section and discussed in Sect. 4.

Table 4 Unit root tests
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Stationarity tests are performed and reported in Table 4 for the full sample (panel A) and each of the regimes (panels B through F). Each of the panels estimates unit root statistics for the logarithmic levels (log-levels) in CDS spreads as well as logarithmic first differences (log-changes) in CDS spreads. Justification for expressing CDS time-series data in log-levels prior to performing regression-type modelling is provided by Alter and Schuler (2012) and Forte and Pena (2009). Additional justification for log-levels is self-evident when visually inspecting CDS spread levels in basis points (Fig. 1); specifically, we can see prolonged periods where CDS spread levels are relatively low and other periods when they are multiplicatively higher (Greece being an immoderate example).

For each of the panels (full sample and each economic regime) and for log-levels and log-changes, the augmented Dickey-Fuller (ADF) test (Dickey and Fuller 1981), the Phillips–Perron (PP) test (Phillips and Perron 1988), and the Elliot, Rothenberg and Stock point optimal (ERS) test (Elliott et al. 1996) are performed to decipher whether or not the respective series contain a unit root in their univariate time-series representations. The purpose of estimating all three tests is to provide confirmatory, rather than competing, evidence that log-levels contain a unit root (i.e. are non-stationary) whereas log-changes do not contain a unit root (i.e. are stationary).

Assuming that the \(y_t \) time-series (in our case, log-levels or log-changes) follows an AR(k) process, the ADF test is specified as follows:

$$\begin{aligned} \Delta y_t =\mu +\gamma t+\alpha y_{t-1} +\sum \nolimits _{j=1}^{k-1} \beta _j \Delta y_{t-j} +u_t \end{aligned}$$
(1)

whereby \(\Delta \) is the difference operator and \(u_t \) is a white-noise innovation series. This test checks the negativity of the parameter \(\alpha \) using its regression t ratio. The asymptotic distribution of the statistic is derived in Dickey and Fuller (1979) while Hall (1994) shows that the asymptotic distribution is insensitive to parameter selection based on standard information criteria.

The PP test is based on the standard OLS regression estimate, \(\hat{a}\), from an AR(1) specification:

$$\begin{aligned} y_t =ay_{t-1} +u_t \end{aligned}$$
(2)

Using the OLS regression estimate \(\hat{a}\), the PP unit root statistics are estimated as follows:Footnote 5

$$\begin{aligned} Z_a= & {} T\left( {\hat{a}-1} \right) -\frac{1}{2}\left( {\hat{\lambda }^{2}-s^{2}} \right) \left( {\frac{1}{T^{2}}\sum \nolimits _{t=1}^T y_{t-1}^2 } \right) ^{-1} \end{aligned}$$
(3)
$$\begin{aligned} Z_t= & {} \frac{s}{\hat{\lambda }}t_{\hat{a}=1} -\frac{1}{2}\left( {\hat{\lambda }^{2}-s^{2}} \right) \left( {\frac{\hat{\lambda }^{2}}{T^{2}} \sum \nolimits _{t=1}^T y_{t-1}^2 } \right) ^{-1/2} \end{aligned}$$
(4)

whereby \(t_{\hat{a}=1} =s^{-1}\left( {\hat{a}-1} \right) \left( {\mathop \sum \limits _{t=1}^T y_{t-1}^2 } \right) ^{1/2}\) and \(s^{2}=T^{-1}\mathop \sum \limits _{t=1}^T \hat{u} _t^2 \) and \(\hat{\lambda }^{2}\) are the estimators for the short—and long-run variances of \(\left\{ {u_t } \right\} \).

For the full sample (panel A) and for each of the regimes (panels B through F) the test statistics unanimously support the notion that log-levels contain a unit root (i.e. are non-stationary) while log-changes do not contain a unit root (i.e. are stationary). For the ADF test, the appropriate lag structure is atheoretical and more of an empirical question. Various lag structures are entertained (not tabulated) in order to check the robustness of the ADF test. In general, the test statistics at various lags consistently fail to reject the null hypothesis of a unit root for log-levels while rejecting this null for log-changes. For all ADF test statistics tabulated in Table 4, the Akaike information criterion (AIC) is used to select the optimal lag structure. The PP test also yields qualitatively analogous findings for the full sample (panel A) as well as each of the regimes (panels B through F) for log-levels and log-changes.Footnote 6

Whereas the critical values for the ADF and PP tests become larger (in absolute terms) when you move from a 10% to a 1% level of significance in rejecting the null, the ERS critical values become smaller. The ERS test seeks to modify the ADF test by de-trending the time-series so that explanatory variables are removed from the data prior to performing the test regression. De-trending the data is performed by quasi-differencing the time-series in question, \(y_t \).

The quasi-difference of \(y_t \) that depends on the value of a, which represents the particular point alternative against which we test the null:

$$\begin{aligned} d\left( {y_t \hbox {|}a} \right) =\left\{ {{\begin{array}{l} {y_t } \\ {y_t -ay_{t-1} } \\ \end{array} }} \right. {\begin{array}{l} {if\quad t=1} \\ {if\quad t>1} \\ \end{array} } \end{aligned}$$
(5)

The value for a is needed in order to obtain an ERS test statistic. This value can be obtained by an OLS regression with the quasi-differenced time-series \(d(y_t |a)\) on the quasi-differenced \(d(x_t |a)\):

$$\begin{aligned} d\left( {y_t \hbox {|}a} \right) =d\left( {x_t |a} \right) ^{{\prime }}\delta \left( a \right) +\eta _t \end{aligned}$$
(6)

whereby \(x_t \) contains either a constant or both a constant and trend, and where \(\delta \left( a \right) \) is an OLS from this regression. The residuals, \(\eta _t \left( a \right) \), can be defined as \(\hat{\eta }_t \left( a \right) =d\left( {y_t \hbox {|}a} \right) -d\left( {x_t \hbox {|}a} \right) ^{\prime }\delta \left( a \right) \) while the sum of squared (SSR) residuals function, \(SSR\left( a \right) \), can be defined as \(SSR\left( a \right) =\sum \hat{\eta }_t^2 \left( a \right) \). The ERS point optimal tests statistic, \(P_T \), tests the null (that \(y_t \) contains a unit root), \(a=1\), against the alternative \(a=\bar{a}\). The test statistic is computed using SSR and the value for a from (6):

$$\begin{aligned} P_T =\left[ {SSR\left( {\bar{a}} \right) -\bar{a}SSR\left( 1 \right) } \right] /f_0 \end{aligned}$$
(7)

whereby \(f_0 \) is the estimator for the residual spectrum at frequency zero.

As in the ADF and PP tests, the optimal lag structure test statistics tabulated in Table 4 for the ERS test are based on the AIC. Various lag structures entertained for the ERS test (not tabulated) generally support the notion that log-levels are non-stationary while log-changes are stationary. Taken altogether, the ADF, PP and ERS test statistics are consistent with one another for the full sample (panel A) as well as each of the sub-sampled economic regimes (panels B through F).

2.3 Cointegration tests

The natural empirical question that follows, having established that CDS spreads are stationary in their logarithmic first differences (log-changes), is whether or not they share a common stochastic trend. In other words, are they cointegrated with one another? If they are, any empirical specification which seeks to delineate credit risk transmission channels ought to consider the long-run equilibrium relation that exists among all the sampled CDS spreads.

A priori, we have no way of knowing whether or not a long-run equilibrium relation exists. The appearance of comovement among all the CDS markets (inferred by their pairwise correlations or the fact that they exhibit similar behaviors in their graphical representations) is not a condition for cointegration. If it is the case that all the twelve sampled CDS markets are cointegrated, a linear combination of any set of CDS spreads ought to be stationary.

Given that there are twelve sampled CDS markets, the multivariate cointegration framework of Johansen (1991, 1995) is implemented to find out how many of the CDS series, if any, are cointegrated with one another. If all of the CDS series are cointegrated, it means we will have a total of eleven cointegrating equations at any given point in time (since there are twelve sampled series).

The Johansen (1991, 1995) multivariate cointegration methodology begins with a vector autoregression (VAR) of order p:

$$\begin{aligned} y_t =A_1 y_{t-1} +\ldots +A_p y_{t-p} +Bx_t +\varepsilon _t \end{aligned}$$
(8)

whereby \(y_t \) is a k-vector of non-stationary variables, \(x_t \) denotes a d-vector of deterministic variables, and \(\varepsilon _t \) is an \(n\times 1\) vector of innovations. In a more compact form, this VAR can be expressed as:

$$\begin{aligned} \Delta y_t =\varPi y_{t-1} +\sum \nolimits _{i=1}^{p-1} \varGamma _i \Delta y_{t-i} +Bx_t +\varepsilon _t \end{aligned}$$
(9)

whereby:

$$\begin{aligned} \varPi =\sum \nolimits _{i=1}^p A_i -I\hbox { and }\varGamma _i =-\sum \nolimits _{j=i+1}^p A_j \end{aligned}$$
(10)

For the coefficient matrix \(\varPi \) in (9) and (10) to have reduced rank \(r<k\), there must exist \(k\times r\) matrices a and \(\beta \) with respective rank r, such that \(\varPi =\alpha \beta ^{\prime }\) and \(\beta ^{\prime }y_t \) are stationary series (Engle and Granger 1987). In this case, r denotes the number of cointegrating relationships (i.e. the cointegrating rank) while the elements of a are the adjustment parameters. Each respective column of \(\beta \) represents a cointegrating vector. Johansen (1995) shows that for a given cointegrating rank, r, the maximum likelihood estimator for a cointegrating vector, \(\beta \), describes an arrangement of \(y_{t-1} \) that generates the r largest canonical correlations between \(\Delta y_t \) with \(y_{t-1} \), following corrections for lagged differences and when deterministic variables, \(x_t \), are present (Hjalmarsson and Osterholm 2010). The Johansen methodology, (8)–(10), entails estimating the \(\varPi \) matrix using an unrestricted VAR and subsequently testing whether restrictions implied by the reduced rank of \(\varPi \) can be rejected.

There are two important statistics that are used to determine whether cointegration is present among non-stationary time-series and, if so, how many cointegrating equations there are at any given point in time: the trace test statistic and the maximum (max) eigenvalue test statistic, shown in Eqs. (11) and (12), respectively:

$$\begin{aligned} LR_{trace} \left( {r\hbox {|}k} \right)= & {} -T\sum \nolimits _{i=r+1}^k \hbox {log}\left( {1-\lambda _i } \right) \end{aligned}$$
(11)
$$\begin{aligned} LR_{\hbox {max}} \left( {r\hbox {|}r+1} \right)= & {} LR_{trace} \left( {r\hbox {|}k} \right) -LR_{trace} \left( {r+1\hbox {|}k} \right) \nonumber \\= & {} -T\hbox {log}\left( {1-\lambda _{r+1} } \right) \end{aligned}$$
(12)

For (11) and (12), r is the number of cointegrating vectors, T denotes the sample size and \(\lambda _i \) is the i-th largest eigenvalue of the \(\varPi \) matrix in (9) and (10). The purpose of the trace statistic is to test the null hypothesis of r cointegrating relationships against an alternative of k cointegrating relationships whereby k represents the number of endogenous variables for \(r=\left\{ {0,1,\ldots ,k-1} \right\} \). The purpose of the max eigenvalue statistic is to test the null of r cointegrating relationships against the alternative of \(r+1\) cointegrating relationships. If the sampled series are not cointegrated, the rank of \(\varPi \) is zero.

Table 5 Multivariate cointegration tests
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Table 5 reports results for the Johansen cointegration methodology described in (8)–(12) for the full sample under all five of the deterministic trend cases considered by Johansen (1995). Given that the purpose of the cointegration framework in (8) through (10) is to determine whether a long-run equilibrium relationship is present between the CDS spreads, the full sample (October 1, 2004 through July 15, 2016) is used to initially determine whether a vector error correction (VEC) framework with an adjustment factor is necessary or whether a VAR is sufficient in order to subsequently determine causal relationships (implemented in Sect. 3 and discussed in Sect. 4).

The five deterministic trend cases are described in Johansen (1995, pp. 80–84) and are reported in each of the respective panels in Table 5 for the full sample:

  1. 1.

    (Panel A): The log-level CDS spreads have no deterministic trends and the cointegrating equations do not have intercepts:

    $$\begin{aligned} H_2 \left( r \right) :\varPi y_{t-1} +Bx_t =\alpha \beta ^{\prime }y_{t-1} \end{aligned}$$
  2. 2.

    (Panel B): The log-level CDS spreads have no deterministic trends and the cointegrating equations have intercepts:

    $$\begin{aligned} H_1^*\left( r \right) :\varPi y_{t-1} +Bx_t =\alpha \left( {\beta ^{\prime }y_{t-1} +\rho _0 } \right) \end{aligned}$$
  3. 3.

    (Panel C): The log-level CDS spreads have linear trends but the cointegrating equations have only intercepts:

    $$\begin{aligned} H_1 \left( r \right) :\varPi y_{t-1} +Bx_t =\alpha \left( {\beta ^{\prime }y_{t-1} +\rho _0 } \right) +\alpha _\bot \gamma _0 \end{aligned}$$
  4. 4.

    (Panel D): The log-level CDS spreads and the cointegrating equations have linear trends:

    $$\begin{aligned} H^{*}\left( r \right) :\varPi y_{t-1} +Bx_t =\alpha \left( {\beta ^{\prime }y_{t-1} +\rho _0 +\rho _1 t} \right) +\alpha _\bot \gamma _0 \end{aligned}$$
  5. 5.

    (Panel E): The log-level CDS spreads have quadratic trends and the cointegrating equations have linear trends:

    $$\begin{aligned} H\left( r \right) :\varPi y_{t-1} +Bx_t =\alpha \left( {\beta ^{\prime }y_{t-1} +\rho _0 +\rho _1 t} \right) +\alpha _\bot (\gamma _0 +\gamma _1 t) \end{aligned}$$

Table 5 reports the trace and max eigenvalue statistics, respectively, along with their corresponding 5 and 1% critical values. If we look across all the panels, we generally see (from the trace and max-eigen statistics) that there is weak evidence for cointegration among all the CDS series.

Given that there are twelve series and a maximum of eleven possible cointegrated equations (‘At most 11’), the results here provide very scant evidence in favor of cointegration. In all, panels A, B and C have trace statistics and eigenvalue (max-eigen) statistics both of which provide some evidence of at least one cointegrating relationship. Trace statistics for panels D and E show no evidence of cointegration (albeit the max-eigen statistics for these panels supports the notion of at least one cointegrating relationship).

This weak evidence in favor of cointegration among the CDS markets is reconcilable by the fact that some countries may experience large fluctuations in their credit risks at particular points in time which deviate in magnitude from those of its peers. Thus, the relationship between all CDS markets, if nonlinear in nature, has a lower probability of being detected when using standard linear cointegration methodologies. Chan-Lau and Kim (2004) find no evidence of cointegration in the CDS and corresponding bond markets of various sampled emerging markets. Among other reasons, they argue that this is possible because market frictions or other technical factors limit the ability to exploit arbitrage opportunities across markets—a reason which may also be relevant to the sampled EU markets considered here. Other empirical findings which examine CDS markets with their corresponding bond markets, and in contra to their theoretical predictions, also find weak evidence for a long-run equilibrium cointegrating relation (Palladini and Portes 2011). In the context of cointegration between sovereign and bank CDS spreads, Alter and Schuler (2012) find that cointegration may exist in some cases while not in others.

In light of the results in Table 5, sub-sample analysis is undertaken to determine whether there exists a pattern in the cointegrating relationships. After inspecting across the economic regimes and across random sub-sample periods (not tabulated), it is ascertained that evidence for cointegration is generally weak and, at best, unstable and time-dependent. In light of this, the following section implements a VAR for the purpose of delineating transmission channels between the sampled countries’ CDS markets without a vector error correction representation.

3 Analytical framework

As mentioned, measuring contagion is problematic both from a statistical and theoretical point of view. A high correlation between markets, for example, does not necessarily provide a basis for causation. In other words, just because hypothetical countries A and B are highly correlated does not imply that shocks in one of them causes changes in another. Theoretically, establishing the transmission channels between markets is also problematic because we are oftentimes confined to discussing them in relatively abstract and unquantifiable ways. For example, if we argue that two markets are interlinked with one another due to geographic proximity and trade, we need to establish which country serves as the catalyst for shock transmissions to the other country. Is the supposed catalyst’s economy of such relative importance to the other market that a spillover is justified? Furthermore, is the shock transmission unidirectional or bidirectional? These are not easy questions to answer and any empirical model that presumes some relation from the onset may be contaminated by noise.

Bayoumi and Vitek (2013) argue that, although “at first blush, the solution to measuring spillovers across countries would seem fairly easy...although progress is being made, the financial sectors in large macroeconomic models are poorly developed and...there are no strong theories as to why financial markets are as closely linked as they appear to be in the data...” (p. 3). From a practical standpoint, it is very difficult to establish a priori which country or group of countries constitute the dominant transmission channels for other countries.

For this reason, an unrestricted VAR is estimated, which, unlike structural models with simultaneous regression equations, presumes no specific structure in the pattern of the transmission channels between countries. Instead, all that is hypothesized a priori is that all the countries’ credit risks affect each other in some way across time.

By using a VAR to describe transmission channels, we are at a vantage point where we can identify which country or group of countries serve as dominant transmission channels for credit risk (Chan-Lau et al. 2007). Without exogenous variables (the twelve CDS markets serve as endogenous variables), the VAR in (8) can be re-expressed compactly as follows:

$$\begin{aligned} Y_t =\mu +\sum \nolimits _{p=1}^k AY_{t-p} +\varepsilon _t \end{aligned}$$
(13)

whereby the set of endogenous \(\left( Y \right) \) variables consists of the weekly log-level CDS spreads from the twelve sampled EU countries. Using log-levels is consistent with Alter et al. (2012, p. 3448) who argue that “...if the tests do not clearly indicate that there is a long-run relation, we obtain the impulse responses from a VAR with the variables modelled in log-levels. Thus we do not cancel out the dynamic interactions in the levels, as opposed to modelling the variables in first differences, and leave the dynamics of the series unrestricted...”

Within this VAR framework, a ‘credit shock transmission’ can be defined as the fraction of H-week-ahead forecast error variance of one country’s log-level CDS spreads that can be accounted for by the innovations (i.e. shocks) in another country’s log-level CDS spreads.

The vector of constants, \(\mu \), is an \(n\times 1\) vector and A is an \(n\times n\) matrix of parameters to be estimated. The residuals, \(\varepsilon \), are an \(n\times 1\) matrix of serially uncorrelated disturbances and k is the order for the variables, Y. The estimates for A are determined by the following orthogonality conditions:

$$\begin{aligned} E\left\{ {\varepsilon _t } \right\} =0\hbox { and }E\left\{ {\varepsilon _t |Y_{t-p}^{\prime } } \right\} =0_{n\times n} ,\,p=1,2,\ldots ,k \end{aligned}$$
(14)

The most widely used method to achieve orthogonal decomposition of the \(\varepsilon \) vector in macroeconomic and financial time-series analysis is the Choleski decomposition method. This method, despite some of its potential weaknesses (discussed in more detail in Sect. 5), traditionally serves as the standard workhorse for time-series analysis which implements VAR methodologies and is thus the method used to draw discussable inferences here (Hamilton 1994; Wisniewski and Lambe 2015).

As is explained by classics such as Hamilton (1994), the choice of the ordering procedure, k, for the endogenous variables Y is atheoretical in nature. In the case of the twelve sampled CDS markets considered here, neither academic theories nor policymakers’ reports provide guidance as to which country may be a dominant transmission channel or which country’s market exerts relatively undue influence on another market.

To get some sense as to which of the few sampled countries ought to be first in the ordering procedure, k, pairwise Granger causality tests are conducted and reported for the full sample (Table 6), regime 2 (Table 7), which represents the 2008–2009 crisis, and regime 4 (Table 8), which represents the 2011–2013 crisis.

Table 6 Pairwise Granger causality tests, full sample; October 1, 2004–July 15, 2016 (N \(=\) 616)
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Table 7 Pairwise Granger causality tests, sample regime 2; March 7, 2008–June 26, 2009 (N \(=\) 69)
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Table 8 Pairwise Granger causality tests, sample regime 4; July 1, 2011–February 22, 2013 (N \(=\) 87)
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Table 9 Forecast error variance decompositions of CDS spreads, full sample; October 1, 2004–July 15, 2016 (N \(=\) 616)
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Table 10 Forecast error variance decompositions of CDS spreads, sample regime 1; October 1, 2004–February 29, 2008 (N \(=\) 179)
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Across each of the tables, there is no strict uniformity as to which country ought to be first or second in the ordering—a finding that is consistent with the notion of heterogeneity in credit risk transmission dynamics across economic regimes. The k ordering for the countries for the H-week-ahead forecast error variance decompositions reported in Tables 9, 10, 11, 12, 13 and 14 coincidentally are as follows (using their official abbreviations discussed in Table 1): BE, BG, DE, EL, ES, FR, HR, HU, IT, PT, RO, and SK. As is discussed in more detail in Sect. 4, BE and BG are dominant transmission channels for credit risk in the full sample (Table 9) while BE, BG, DE and EL are more important during the 2011–2013 crisis (regime 4 reported in Table 8). Although RO and SK are more important during the 2008–2009 crisis (regime 2 reported in Table 7), their respective GDP per capita (Fig. 2), in relation to their peers, are lowest—suggesting they may carry less economic influence relative to countries such as BE, BG and DE.Footnote 7

Table 11 Forecast error variance decompositions of CDS spreads, sample regime 2; March 7, 2008–June 26, 2009 (N \(=\) 69)
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Table 12 Forecast error variance decompositions of CDS spreads, sample regime 3; July 3, 2009–June 24, 2011 (N \(=\) 104)
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Table 13 Forecast error variance decompositions of CDS spreads, sample regime 4; July 1, 2011–February 22, 2013 (N \(=\) 87)
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Table 14 Forecast error variance decompositions of CDS spreads, sample regime 5; March 1, 2013–July 15, 2016 (N \(=\) 177)
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4 Results and discussion

The purpose of the multivariate VAR in (13) is to quantify credit shock transmissions from one country to another. As mentioned, a transmission can be defined as the fraction of H-week-ahead forecast error variance of one country’s log-level CDS spreads that can be accounted for by the innovations (i.e. shocks) in another country’s log-level CDS spreads.

Before proceeding to discussing the variance decompositions in Tables 9, 10, 11, 12, 13 and 14, it is worth reviewing the pairwise Granger causalities in Tables 6, 7 and that were briefly mentioned in the preceding section because they describe the direction of interdependency channels in credit risk transmissions among all the sampled countries. As mentioned, in panel A, pairwise Granger causalities are reported for the full sample while panels B and C report for regime 2 and regime 4, respectively. For each of the panels, Granger causality tests are conducted using one, two, three and four lags. Finally, for each of the panels, and given that they are pairwise causality tests (involving two countries at a time), there are a total of sixty six pairwise tests that are estimated: 1. (BE \(\leftrightarrows \) BG), 2. (BE \(\leftrightarrows \) DE), 3. (BE \(\leftrightarrows \) EL), 4. (BE \(\leftrightarrows \) ES), 5. (BE \(\leftrightarrows \) FR), and so on, until all countries have been tested with one another (i.e. all sixty-six pairwise combinations have been examined).

Bearing in mind that the null hypothesis for the Granger causality test is that there is no causality (i.e. Country A does not Granger cause Country B), let us turn our attention to the full sample results (panel A) whereby lag length = 1. If we look at the CDS market of, say, Belgium (BE), we can see that it Granger causes changes in the CDS markets of HR, FR, DE, EL, HU, IT and SK, respectively. Thus, BE causes changes in seven out of eleven possible markets (approx. 64% of cases). Likewise, there is no evidence BE causes changes in the CDS markets of BG, ES, PT and RO—the remaining four countries (the remaining 36% or so of cases where the null of no causality is not rejected). Of the seven markets that BE causes, none of those countries Granger cause BE (i.e. the direction of causality between BE and the seven aforementioned countries is unidirectional).

If we look at the case of Germany (DE) in panel A whereby lag length = 2, we see that DE respectively causes BE, FR, EL and SK (four out of eleven possible markets, or, about 36% of cases). Of these four markets, BE, FR and SK Granger cause DE. Thus, there is a bidirectional causality pattern between DE and, respectively, BE, FR and SK.

From the full sample in panel A, we see that Greece (EL) does not cause any other CDS market when there is one lag. When there are two lags, EL causes BE and ES while, for three and four lags, respectively, EL causes BE. Overall, for the full sample, EL does not appear to be a dominant transmission channel for credit risk. However, BE, BG and ES consistently serve as channels for credit risk across all four lag lengths. Relative to the causality results with one and two lags, RO and SK become more active credit risk transmission channels when there are three and four lags.

In Table 7, which represents the 2008–2009 crisis, we see that BG and RO serve as dominant transmission channels across all lag lengths. HR and SK are dominant transmission channels when there is one lag. Across all lag lengths, DE does not Granger cause a single CDS market while EL Granger causes two markets across all lag lengths.

Finally, let us turn our attention to Table , which is the fourth regime that represents the 2011–2013 European debt crisis. Compared to panel B (the 2008–2009 crisis), we see that EL now serves as a relatively stronger transmission channel for the other countries. This is not surprising given that it has been implicated as the catalyst for the Eurozone crisis. However, we can see that when lag length \(=\) 1, EL transmits to about 63% of countries—a percentage that is still lower than BE, BG, PT and equivalent to that of FR. Keeping in mind that, for one lag, DE transmits to about 55% of markets, we can conclude conservatively that, at a minimum, EL does not disproportionately channel credit risk to its EU peers any more than DE, FR, or any other major market does. When we inspect causality results for two, three and four lags, we see that the percentage of its (outbound) transmission channels, compared with its peers, are relatively fewer and, at best, nothing out of the ordinary.

Tables 9, 10, 11, 12, 13 and 14 report forecast error variance decompositions for the full sample (Table 9) and each of the regimes (Tables 10, 11, 12, 13 and 14). For each of the countries, 2-, 4-, 6-, 8- and 10-week forecast horizons are considered. Instead of tabulating all the A coefficients from the VAR in (13), a more compact and intuitive way of determining how shocks in one CDS market affect other CDS markets is to estimate variance decompositions. As mentioned, shock transmissions are the fraction of H-week-ahead forecast error variance of one country’s log-level CDS spreads that can be explained by shocks in another country’s log-level CDS spreads. The variance decomposition tables (Tables 9, 10, 11, 12, 13 and 14) tell us, in relative terms, the importance of each random shock within the VAR system. To estimate the variance decompositions, the Choleski method is used (the merits of this procedure are revisited in Sect. 5).

Table 9 provides variance decompositions for the full sample. In the first column are each of the twelve CDS markets while in the second column are the H-week ahead periods corresponding to each respective market. The standard error (S.E.) corresponding to each horizon is in the third column. The columns that follow are each of the predictor variables in the VAR system. For the sake of explaining the decomposition table, let us look at, say, Germany (DE) when it serves as the response variable. We can see that in the 2-week horizon, a significant fraction of its forecast variance is explained by its own lagged shocks (76%). Lagged shocks in Belgium (BE) and Bulgaria (BG) explain 18 and 4% of its forecast variance, respectively. Greece (EL) explains a mere 0.04% while Croatia (HR) explains almost 0%. If we were to sum all these percentage variance decompositions across any of the respective horizons, they sum to 100% by construction. Thus, we can see for any given country at any given horizon, the proportion of forecast variance explained by shocks in each of the CDS markets in the VAR system.

Looking down the columns in Table 10 (regime 1), we can see that specific countries (such as DE, EL, HR, PT, RO, SK) uniformly contributed a small proportion of forecast variance to other countries (in all cases, and as is expected, each country responds to lagged innovations in its own CDS market). Other countries, particularly BE and BG, appear to have a disproportionate impact on some countries while a negligible effect on others. For example, shocks in BE explains 34–40% of the forecast variance in ES across the various week horizons. Shocks in BG explain 73–81% of the forecast variance in HR, 43–50% of the forecast variance in HU and 55–74% of the forecast variance in RO, to name only a few examples.

Results for regime 2, which corresponds with the 2008–2009 financial crisis, are reported in Table 11. Again we see that BE and BG appear to have a disproportionate impact on some markets. One notable difference in regime 2 compared to regime 1 is the contributions of EL to the forecast variances of the other countries increased. For example, EL explains 20–23% of the forecast variance in ES and 15–19% of the forecast variance in IT. When EL is the response variable, we see that BE, BG and DE (in that order) are the largest contributors to its forecast variance (excluding shocks in its own lags).

Regime 3 (Table 12) is comparable to regime 1 in the sense that BE and BG tend to dominate, relative to their peers, in terms of explaining forecast variances of other countries. EL tends to appear uniform and relatively modest in explaining forecast variances of other countries, with the exception of Portugal (PT) where it explains 13–34% of its forecast variance. For the sake of comparison, DE and FR both explain between 1 and 3% of the forecast variance in PT.

Regime 4 represents the 2011–2013 European debt crisis (Table 13) where Greece made headline news and was insinuated as a catalyst for the Eurozone crisis. As we discussed in Table 8, Greece had a relatively higher tendency to Granger cause shifts in other CDS markets during this period (when compared with the percentage of cases it Granger causes during regime 2 and the full sample). We see however that it explains very little of the forecast variance of other countries.

Finally, regime 5 (Table 14) represents our present-day state of affairs where EL is uneventful in explaining other countries’ forecast variances. One notable difference with Table 13 is the case of ES. In regime 5, ES accounts for 33–38% of the forecast variance for IT and 21–26% of the forecast variance for PT.

Impulse response graphs to Cholesky one standard deviation (S.D.) innovations (and a 95% confidence band) are illustrated in Figs. 4 and 5 for regime 4 only. Impulse responses reveal how one country’s CDS market responds to a unit shock in another CDS market. The purpose of focusing on regime 4, the 2011–2013 European debt crisis, is to focus more on the dynamic interactions between CDS markets and the extent to which shocks in Greece’s credit risks can affect other markets. While Fig. 4 show the response of each countries to a shock in Greece, Fig. 5 show the response of Greece to shocks in other countries.

Fig. 4
figure 4

Impulse response to Cholesky one S.D. innovations ± 2 S.E. Response of \(\hbox {Country}_\mathrm{j} \) to impulse EL. Sample regime 4; July 1, 2011–February 22, 2013 (N \(=\) 87)

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Visual inspection of the figures suggests heterogeneity in the decay patterns of the impulse responses; specifically, some innovations (impulses) decay (or ‘die out’) for response countries at different times. For example, the response of Hungary to Greece is most pronounced during the 5th week even though the innovation finally begins to decay at around the 12th week. Now, if we look at the response of Portugal to Greece we observe very different behavior; at first the impulse response appears to decay by the 4th week then begins to show some small signs of transmission shocks after the 12th week (although they are very small in magnitude).Footnote 8

Focusing on how Germany and Greece react to one another’s innovations further reinforces this notion of heterogeneity in impulse decay behavior; in Fig. 4 we see the response of Germany to Greece while in Fig. 5 we see the response of Greece to Germany. In the former case, innovations in Greece appear to decay by the 9th week but then shift behavior after the 12th week. In the latter case, innovations in Germany decay by the 5th week. In terms of magnitudes, however, the size of the shock from Germany to Greece is larger than the shock from Greece to Germany (based on the scales of each graph).

Fig. 5
figure 5

Impulse response to Cholesky one S.D. innovations ± 2 S.E. Response of EL to impulse \(\hbox {Country}_\mathrm{j}\). Sample regime 4; July 1, 2011–February 22, 2013 (N \(=\) 87)

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5 Robustness tests and other ad hoc findings

As mentioned in footnote (7), the ranking order of the countries was changed in accordance with their GDP per capita in order to check that there were no sensitivities in the variance decompositions reported in Tables 9, 10, 11, 12, 13 and 14. In addition to this, a generalized variance decomposition á la Koop et al. (1996) and Pesaran and Shin (1998) is implemented for the sake of comparison and in order to extract generalized impulse response functions.

The advantage of generalized variance decompositions is that they do not rely on an ordering pattern for variables in the VAR system (i.e. they are order invariant). If there are no criteria for establishing an ordering procedure for the variables, a generalized variance decomposition method may prove useful because no such ordering is required. The disadvantage of this approach, however, is that structural shocks are not orthogonalized. In an analysis involving country spillover effects, IMF (2016) shows that Cholesky methods of decomposition yield qualitatively similar findings with the generalized approach. Given their advantages and disadvantages, one cannot prove theoretically that a generalized method is superior to a Cholesky method, or vice versa, given that such a comparison is data-dependent.

Fig. 6
figure 6

Generalized impulse responses to one S.D. innovations ± 2 S.E. Impulses and Responses between DE, EL, ES and FR. Sample regime 4; July 1, 2011–February 22, 2013 (N \(=\) 87)

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For the sake of some comparison, generalized impulse response functions are illustrated in Fig. 6 for Greece, Germany, France and Spain. Even with generalized impulse responses, we can see that shock transmissions from Greece to Germany, France and Spain, respectively, are somewhat smaller in magnitude relative to the shock transmissions Greece receives. It seems that shock transmissions from Greece to the other countries begins to decay by the 8th week while shocks transmissions from the other countries to Greece may experience a shift in behavior after the 10th week. This latter point is illustrated when looking at the “response of EL to ES” and the “response of EL to FR” graphs.

Finally, and separate from the generalized variance decomposition approach, a Bayesian VAR methodology á la Litterman (1986) and Sims and Zha (1998) is also considered. Relative to traditional VAR approaches, Bayesian VAR models address the problem of over-parameterization which can occur in the presence of many variable series in the VAR system. The problem of potential over-parameterization is addressed via the use of information priors that reduce the VAR to a more parsimonious model which, theoretically, can help to improve variance forecasts.

Variance decompositions and impulse response functions (not tabulated) using the Litterman/Minnesota and Sims-Zha priors do not lead to any qualitative changes in the results which merit specific discussion. In fact, many of the patterns and behaviors we observed (such as BE and BG dominating in terms of explaining forecast variance for other countries) manifests in the same manner even when using a Bayesian VAR.

6 Summary and concluding remarks

The purpose of this paper is to examine the dynamic interdependencies between CDS markets among several of the major EU countries which have an active and liquid CDS market. Specifically, the countries examined are, Belgium, Bulgaria, Croatia, France, Germany, Greece, Hungary, Italy, Portugal, Romania, Slovakia, and Spain. The motivation for this paper lies in the fact that Greece has featured, disproportionately relative to its peers, in the media as the instigator (or catalyst) for the Eurozone crisis. Thus, the idea in this paper is to test, using a VAR methodology, whether Greece disproportionately channels credit risk transmissions to other markets (i.e. Greece is the ‘black swan’) or whether Greece is being ostracized for Europe’s general economic problems given its idiosyncratic hapless economic conditions (i.e. Greece is the ‘black sheep’).

Despite Greece’s sovereign problems, it is yet to be proven empirically that it serves as a catalyst for the problems that grip Europe at large. This is important to identify because, as discussed earlier, news headlines and media outlets have a significant impact on the behavior of market participants. Despite the heterogeneity in credit risk transmission channels across time, the results here show that, at a minimum, it cannot be shown empirically that Greece serves as a dominant transmission channel for credit risk any more than France, Germany or any of the other major EU players.

Instead of the media trying to find a black sheep to explain our dire international state of economic affairs, more attention and research needs to be devoted into examining why there has been a systemic buildup in risks across our international financial and banking community.