Separating Interdependence from Channels of Conta- Conta-gionConta-gion

Empirical Specification

We now analyze which economic variables explain the observed pattern of sovereign credit risk co-movements. Thereby, our approach allows us to separate interdependence from channels of contagion. The dynamic conditional correlation framework outlined in Section 1.3.1 provides us with estimates of daily credit risk co-movements (ρijt), which we aggregate to monthly averages denoted by ρijm. Monthly data still capture short-run variation in co-movements but smooth out high-frequency noise. This ap-proach is also in line with data availability regarding the explanatory variables (Table 1.3).

To investigate the determinants of credit risk co-movements, we use the DCCs as dependent variable in the following regression model (specification (I)):¹⁰

ρ_ijm =x⁰_ijmβ_I+u_ijm, (1.2)

where x_ijm denotes a vector containing the elements for all K explanatory variables (“determinants”) for a certain country pair (ij) and time period (m), βI is a vector containing the parameters, and u_ijm is the error term.

While this specification allows us to empirically assess the impact of global variables on sovereign credit risk co-movements, it controls neither for the full set of arbitrary

10Flavin et al. (2002) and Beine and Candelon (2011) use similar regression models applied to stock market correlations.

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global shocks nor for unobserved heterogeneity across country pairs. To overcome this shortcoming, country pair and time fixed effects are included inspecification (II):

ρ_ijm =z⁰_ijmβ_II+λ_ij +γ_m+v_ijm, (1.3)

wherez_ijm is a subset of x_ijm that contains the explanatory variables that vary across time and country pairs, λ_ij denotes country pair specific effects, and γ_m denotes time fixed effects.

The contagion indicator described in section 1.3.2 carries information about whether a country pair experienced a contagious episode at a certain point in time. Based on our definition, contagion means that shocks are transmitted more intensely than they are in tranquil times, leading to a significant increase in co-movements. Consequently, we call the channels through which this shock transmission occurs channels of conta-gion. These channels of contagion might be linkages that exist in tranquil times but abruptly change their strength or their role (or both) in turbulent times. Furthermore, they might be new channels that emerge in turbulent times and can be related to shifts in market sentiment. We refer to the first phenomenon as fundamentals based conta-gion and to the latter as non-fundamentals based contaconta-gion. We separate channels of contagion by adding interaction terms of the explanatory variables and the contagion indicator (specification (III)):

ρ_ijm =x⁰_ijmβ_III +x˜⁰_ijmδ_III × CI_ijm+φ_IV CI_ijm+u_ijm (1.4) wherex˜_ijm is a subset of the explanatory variablesx_ijm. A variable constitutes a chan-nel of contagion only if it affects the pattern of co-movements differently conditional on the occurrence of contagion, i.e., if the contagion indicator (CI_ijm) takes a value of one. In this case, the interaction term will have a significant effect. The equivalent specification including fixed effects is straightforward (specification (IV)):

ρ_ijm =z⁰_ijmβ_IV +z˜⁰_ijmδ_IV × CI_ijm+φ_IV CI_ijm +λ_ij+γ_m+v_ijm (1.5) Including the contagion indicator as explanatory variable in specifications (III) and (IV) leads to a bias in its coefficient (φ). The reason is that according to Section 1.3.2, the contagion indicator is derived endogenously from sovereign credit risk co-movements, which is the dependent variable in both specifications. However, following the identification strategy in Nunn and Qian (2013), interaction terms including one

Chapter 1: Sovereign Credit Risk Co-movements in the Eurozone

endogenous and one exogenous variable can be considered as exogenous.¹¹ Therefore estimation of the empirical specifications can yield insightful results on the channels of contagion. Clearly, the assumption of exogeneity of the explanatory variables entering the interaction term is key for the argument to hold. While exogeneity can be plau-sibly assumed for rather low-frequency macroeconomic and aggregate balance sheet variables, this might not be the case for high-frequency financial variables.

Choice of Explanatory Variables

We divide the explanatory variables into three groups based on their economic inter-pretation and theoretical considerations: (i) global controls, (ii) similarity in economic fundamentals, and (iii) direct and indirect linkages between countries. Table 1.3 shows the list of explanatory variables and their classifications.

(i) Global controls: Common macroeconomic shocks that affect all countries at the same time, such as changes in risk aversion or liquidity risk, are likely to affect the structure of credit risk co-movements in sovereign debt markets. We control for these global factors by including the VDAX implied volatility index and the Euribor-Eonia spread in specifications (I) and (III).¹² We expect increases in risk aversion and de-creases in liquidity risk to lead to stronger credit risk co-movements. Macro shocks of any kind are implicitly controlled for by the time fixed effects in specifications (II) and (IV).

(ii) Similarity in economic fundamentals: Because the creditworthiness of a sovereign is connected to economic fundamentals, two countries with similar economic fundamen-tals should exhibit a higher degree of credit risk co-movement. This justifies the inclu-sion of similarity measures based on GDP growth, public debt, and foreign reserves held by the (national) central bank. We also include similarities in the size of the banking system and common portfolio exposure, where the first is proxied by banks’ total assets and the latter by the correlation of bank equity prices. The rationale behind the inclu-sion of these banking sector-related variables is to capture the interdependence between sovereign and bank credit risk as an important feature of the Eurozone debt crisis. Such interdependence might arise through risk transfers from banks to sovereigns and the impact of sovereign credit risk on banks’ holdings of sovereign debt (Acharya et al., 2014). We expect sovereign credit risk to co-move more strongly for two countries that

11In their 2012 working paper version (Nunn and Qian, 2012), the authors write: “Our instrument, which is constructed by interacting an arguably exogenous term (. . .) with one that is potentially endogenous (. . .), can be interpreted as exogenous since we directly control for the main effect of the endogenous variable (. . .).”

12We use the VDAX implied volatility index rather than the VIX because we consider it to be the more relevant measure in our analysis which focuses on the Eurozone.

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are more similar to each other in specifications (I) and (II). By interacting the similar-ity measures with the contagion indicator in specifications (II) and (III), we can test for the presence of “wake-up call” contagion. This might arise if weak fundamentals in one country make investors aware of (similar) structural problems in other countries.

In such a case, similarities in economic fundamentals constitute a channel of contagion.

(iii) Direct and indirect linkages: Variables related to direct linkages between coun-tries account for simple interdependence in specifications (I) and (II). They comprise linkages associated with the real and financial sector. The real linkage is captured by bi-lateral trade flows. As banks hold sovereign debt on their balance sheets, they are likely to play a critical role in the transmission of shocks related to sovereign debt markets.

We thus compute the financial linkage using bilateral data on banks’ foreign claims from the Bank for International Settlements. In tranquil times, the financial linkage is assumed to improve international risk sharing and thus to reduce co-movements in sovereign credit risk (Kalemli-Ozcan et al., 2013). However, direct real and financial linkages might constitute channels of contagion in two respects. First, thestrength of the linkages can fluctuate if trade flows collapse, banks rebalance their portfolios via asset sales, international interbank markets freeze, and bailouts take place. Second, the role of the linkages can change. While the linkages can enhance risk sharing and financial stability in tranquil times, it can foster the transmission of shocks and thus channel contagion in turbulent times. In both cases, we would expect an increase in credit risk co-movements. Bolton and Jeanne (2011) provide a theoretical framework for this state-dependent role of financial (or banking sector) integration in the trans-mission of shocks in sovereign debt markets.¹³ By interacting both linkages with the contagion indicator in specifications (III) and (IV), we can test for this channel of con-tagion, which we callfundamentals based contagion.

In addition to direct linkages, sovereign debt markets might also be connected via more indirect or non-fundamental linkages. These linkages are often not prevalent in tranquil times but emerge in turbulent times. From a theoretical point of view, they can be related to concepts such as herding behavior, changes in market sentiment and the occurrence of “bad equilibria” or “risk panics” (Bacchetta et al., 2012; Masson, 1999). Even though non-fundamentals are generally not observable, proxies do exist.

We choose the GDP weighted stock market volatility as a measure of common market sentiment for a given country pair. We do not expect the non-fundamental linkage to have a strong impact on credit risk co-movement in tranquil times. A significant

13The relation between the degree of market integration in general and the vulnerability to transmis-sion of shocks and/or contagion is addressed in many papers and usually found to be non-monotonic.

While a comprehensive literature review is out of scope of this paper, we refer to Allen and Gale

Chapter 1: Sovereign Credit Risk Co-movements in the Eurozone

impact of this variable when interacted with the contagion indicator in specifications (III) and (IV), however, would be a strong indication that sovereign debt markets have been subject to non-fundamentals based contagion.