The state dependent impact of bank exposure on sovereign risk

Podstawski, Maximilian; Velinov, Anton Article — Accepted Manuscript (Postprint) The state dependent impact of bank exposure on sovereign risk Journal of Banking & Finance Provided in Cooperation with: German Institute for Economic Research (DIW Berlin) Suggested Citation: Podstawski, Maximilian; Velinov, Anton (2018) : The state dependent impact of bank exposure on sovereign risk, Journal of Banking & Finance, ISSN 0378-4266, Elsevier, Amsterdam, Vol. 88, pp. 63-75, https://doi.org/10.1016/j.jbankfin.2017.11.002 This Version is available at: https://hdl.handle.net/10419/231764 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0 The State Dependent Impact of Bank Exposure on Sovereign Risk This Version: September 12, 2017 Abstract The theoretical literature remains inconclusive on whether changes in bank exposure towards the domestic sovereign have an adverse effect on the sovereign risk position via a diabolic loop in the sovereign-bank nexus or reduce perceived default risk by acting as a disciplinary device for the sovereign. In this paper we empirically analyze the impact of exogenous changes in bank exposure on the risk position of the sovereign within a Markov switching structural vector autoregressive in heteroscedasticity (MSH-SVAR) framework for a set of EMU countries. We add to the methodological literature by allowing for regime dependent shock transmissions according to the volatility state of the financial system. Finding support for both, a stabilizing and a destabilizing effect, we document a clear clustering among the country sample: Rising bank exposure increased default risk for the EMU periphery, but decreased credit risk for the core EMU countries during times of financial stress. JEL classification: C32, E44, G10. Keywords: Markov-switching, heteroscedasticity, identification, sovereign-bank interlinkages, sovereign risk, credit default swap, contagion. This is the postprint of an article published in Journal of Banking & Finance 88 (2018), pp 63-75, available online at: https://doi.org/10.1016/j.jbankfin.2017.11.002 © <2020>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ 1 Introduction The most recent financial and European debt crises dealt a heavy blow to the financial stability of both governments and institutions alike. Throughout these crises two distinct phenomena were observed: First, sovereign and bank sector risk rose sharply and appear to move closely together. Second, the volume of domestic government debt held by the banking sector (which we will refer to as exposure in the following) has increased heavily (see Figure 1). bps 2004 2006 2008 2010 2012 2014 0 100 200 300 400 500 600 (a) CDS, Spain bps 2004 2006 2008 2010 2012 2014 0 100 200 300 400 500 600 (b) CDS, Italy bps 2004 2006 2008 2010 2012 2014 0 500 1000 1500 (c) CDS, Portugal Billions of Euro 2004 2006 2008 2010 2012 2014 100 150 200 250 300 (d) Exposure, Spain Billions of Euro 2004 2006 2008 2010 2012 2014 150 200 250 300 350 400 (e) Exposure, Italy Billions of Euro 2004 2006 2008 2010 2012 2014 5 10 15 20 25 30 35 (f) Exposure, Portugal Figure 1: Government (blue solid) and banking sector (red dashed) credit default swaps (CDS) in selected euro area countries (Source: Datastream) and banking sector exposure toward domestic sovereign in the Euro zone (Source: ECB). The role of bank exposure on financial stability is experiencing a lively debate in the literature. However, the literature appears to provide conflicting conclusions regarding the effect of increased domestic government debt holdings by banks on the government’s credit risk. In their seminal paper on the sovereign-bank nexus, Brunnermeier et al. (2011) point out that high exposure potentially increases the risk positions of both the sovereign and its domestic banking system, via a so-called diabolic loop. They argue that speculation about the solvency of either of the two sectors would affect the risk position of the other, thus feeding back into a higher default risk for the first. Therefore, increases in exposure make twin crises (banking 1 and sovereign) more likely and, thus, increase the probability of sovereign default. In contrast, the literature on sovereign default argues that bank exposure can act as a disciplinary device for the sovereign. Gennaioli et al. (2014) and Engler and Große Steffen (2016) show in the framework of theoretical models that a default is more costly to the sovereign if a relevant share of public debt is held by the domestic banking system. This triggers a credit crunch, thus reducing economic activity and worsening the sovereign’s budget prospects. Due to costs of default increasing in the domestically held share of public debt, they claim that default risk on government debt falls with rising exposure. These two somewhat contradicting hypotheses from the sovereign-bank nexus and sovereign defaults literature are discussed in greater detail in Section 2. In this paper we investigate the impact of exposure on sovereign risk from an empirical perspective for eight euro area economies. In particular, we aim to determine which of the competing hypotheses has more support in the data. We investigate this issue within a Markov Switching Structural Vector Autoregressive in heteroscedasticity (MSH-SVAR) framework. Such models are well suited for the purpose of our analysis for several reasons. Firstly, from Figure 1 it is apparent that the data display structural breaks, occurring around crisis periods. Such periods can be thought of as being different states of nature, which are arguably well modelled with the Markov switching methodology (see for instance Hamilton,1989). Our model is capable of endogenously determining different volatility states and, therefore, depicts crises as periods of increased volatility (see Velinov and Chen,2015). Secondly, the heteroscedastic feature of our model allows us to test structural identifying restrictions as, for instance, in Lanne et al. (2010) and others (see Section 5). This is of particular interest as there are no restrictions that are well established in the literature that we can make use of to identify the structural model. Thirdly, the theoretical literature this empirical investigation is built upon implicitly differentiates between states of the economy and the financial system when deriving implied effects of bank exposure on sovereign risk. The sovereign-bank nexus literature, on the one hand, mainly refers to twin crises of banks and sovereigns during a phase of financial turmoil. The disciplinary mechanism underlying the argument in the sovereign default literature, on the other hand, is also likely to gain importance with rising financial distress as market participants may increase awareness and monitoring efforts regarding the sovereign’s creditor 2 decomposition. The model used in this paper, therefore, extends the classical Markov-switching in heteroscedasticity framework to allow for state dependent contemporaneous impact effects and shock transmission. This paper contributes to the literature along two dimensions. Firstly, we empirically investigate the impact of bank exposure on sovereign credit risk (and hence, overall financial stability) in the euro area. As far as we are aware, this issue is not yet investigated from an empirical perspective, even though the role of bank exposure is at the center of an intense policy debate. Pockrandt and Radde (2012) identify a range of regulatory incentives fostering the large observed increases in bank exposure and argue that they should be repealed in order to break the link between risk positions in both sectors. This development is particularly pronounced in times of ample liquidity in the banking sector (see Shambaugh,2012), which was the case due to the European Central Bank’s (ECB) unconventional monetary policy. Another explanation linking exposure to policy actions is provided by Merler and Pisani-Ferry (2012), who see persuasion by politicians as driving the purchase of sovereign debt by domestic banks. Analyzing security purchases of 77 European banks from 2010 to 2012, Ongena et al. (2016) find econometric support for this channel. Given that the drivers of banking sector exposure identified in the literature are to a large extent at the discretion of policy makers, this renders the subject of investigation as highly policy relevant. Secondly, we make a methodological contribution to the existing MSH-SVAR literature (see for instance Herwartz and L¨utkepohl,2014) by allowing for regime dependent shock transmission along the lines of Bacchiocchi and Fanelli (2015). The existing literature makes the implicit assumption that changes in observed volatility are solely attributable to the variance of structural shocks. This is a strong assumption and there is no clear reason to believe that the shock transmission should remain unaffected if an economy, for instance, enters a state of financial turmoil. In this paper the appeal of our model extension is that it allows us to identify regime dependent impacts of increases in exposure on the risk positions of the sovereign sector. Based on the MSH-SVAR model, we find empirical support for the identifying restriction imposed on the system in order to identify the two shocks of interest, an exposure shock and a risk shock. Overall, our findings from the model with state invariant shock transmission point toward a destabilizing effect running from bank exposure to sovereign default risk in line 3 with the literature on the sovereign-bank nexus. Impulse responses from models that allow for state dependent shock transmission, however, reveal a more differentiated picture. While the reaction of sovereign credit risk to changes in bank exposure is found to be particularly strong during turbulent times for the EMU countries under fiscal stress in the sample analysed, it acts as a stabilizing device for the cluster of countries in our sample that were less affected by the recent crises, supporting the theoretical predictions by the literature on sovereign defaults. The remainder of the paper is structured as follows. The next section revisits the sovereignbank nexus and sovereign defaults literature, deriving the hypotheses that we empirically investigate. Section 3 introduces the data. In Section 4, we discuss the MSH-SVAR models and identification scheme used. Section 5 tests the identifying restriction using the data, presents smoothed state probabilities and assesses the hypotheses based on impulse responses. Finally, Section 6 concludes. 2 Literature and hypotheses This section revisits two strands of literature that form the basis for competing hypotheses regarding the impact of bank sector exposure1on sovereign default risk. We begin by discussing the so-called sovereign-bank nexus literature, leading to a diabolic loop hypothesis. We then turn to the sovereign defaults literature, leading to a disciplinary device hypothesis. Finally, we conclude the section with the derivation of a third hypothesis, emphasizing the regime dependency of the relationship between bank exposure and sovereign risk. Literature on the sovereign-bank nexus As evident from Figure 1, there is a clear tendency for the credit risk of banks and their respective sovereigns to move together. This phenomenon triggered a large strand of literature investigating the linkages between both sectors, establishing a diabolic loop of risk contagion (Brunnermeier et al.,2011). We refer to this as the sovereign-bank nexus literature. A number of channels that connect both sectors together are identified. In what follows we discuss both directions separately, first the channels of contagion from the banking sector to the sovereign 1Note from Section 1 that we refer to exposure as the volume of national government debt held by the domestic banking sector. 4 and then vice versa. There are two main mechanisms identified as being responsible for potential contagion from the banking sector to the sovereign. Firstly, there is the credit supply channel. If the financial conditions of the banking sector were to deteriorate, banks may react by reducing credit supply to the real economy. This would lead to an economic slowdown or a deepening of an existing recession, which might severely harm the sovereign’s tax base. The worsened fiscal position would reduce the sovereign’s creditworthiness and, consequently, increase its default risk. Secondly, risks stemming from the banking sector might spill over to the national government via implicit bailout guarantees or, in a later stage, by explicit state promises (Ejsing and Lemke,2011;Alter and Sch¨uler,2012;Kallestrup et al.,2013). In the other direction, from the government to its banking sector, there is also risk contagion. It may take one of the following four channels. Firstly, given that banks generally hold nonnegligible amounts of public debt, an increase in the perceived likelihood of sovereign default would weaken the balance sheet positions of the banking sector. Angeloni and Wolff (2012), Buch et al. (2013) and De Bruyckere et al. (2013) provide evidence for the so-called portfolio channel during the European debt crisis. Secondly, a reduction of the market value of sovereign bonds has a direct negative impact on the funding conditions of banks, which use the bonds as collateral for refinancing operations (Kiyotaki and Moore,2005;Kaminsky et al.,2003); this is known as the collateral channel. Thirdly, Brown and Dinc (2011) and Demirg¨u¸c-Kunt and Huizinga (2010) point toward a guarantee channel: As soon as public debt default risk rises, government bank bailout and guarantee schemes become less valuable, which increases banking sector risk. Finally, Arezki et al. (2011) identify a sovereign rating channel. Since many rating agencies use public debt ratings as a ceiling for the private entities within an economy, a reduction in the sovereign rating may in turn lead to a reduction in the private rating. The channels of contagion noted above are summarized in Figure 2. Given that risk spillovers work in both directions via a number of different channels, Acharya et al. (2014) and Rieth and Fratzscher (2014) among others, empirically identify a two way feedback between sovereign risk and bank risk. The paths of contagion outlined above result from domestic sovereign bond holdings by the banking sector, which hence lie at the core of the sovereign-bank nexus. A measure to break the so called diabolic loop would have to target the amount of sovereign 5 Figure 2: Transmission channels and diabolic loop according to the sovereign bank nexus literature. bonds held by banks: If the banks would hold less or no sovereign bonds, the link between financial and sovereign credit risk would become a lot weaker or vanish completely (Pockrandt and Radde,2012). Conversely, increases in exposure intensify the link between the two sectors, thus making twin crises more likely and, consequently, increasing the probability of sovereign default. Summing up, the literature on the sovereign-bank nexus implies that banking sector exposure to the domestic sovereign should generally have a destabilizing effect on the economy. Hence, we derive the following hypothesis based on this literature. Hypothesis I (diabolic loop): Increases in bank sector exposure raise sovereign default risk via a diabolic loop of risk contagion. Literature on sovereign defaults Aside from the sovereign-bank nexus literature, another strand of literature related to this paper is on sovereign defaults. As opposed to private debt, where creditor rights in most countries are strong, it is not easy to enforce claims against governments in a similar manner. Therefore, sovereign debt can only exist because a default is costly to the government as the damage to the domestic economy (through the financial system) erodes the tax base. Borensztein and Panizza (2009) find that banking crises and credit crunches driven by debt defaults are particularly costly to the sovereign. The severity of such costs depends mainly on the extent 6 of bank sector exposure. Losses from default are more severe if debt is held by the domestic banking system. Gennaioli et al. (2014) set up a model of sovereign default in which government defaults are costly because of the adverse effect on domestic banks’ balance sheets. Consequently, their model predicts that sovereign default probability decreases in banking sector exposure. In addition, they find panel econometric evidence for sovereign defaults being less likely, the more exposed the domestic banking sector is. Similarly, Kohlscheen (2010) and Van Rijckeghem and Weder (2004) find governments are less likely to default on domestic creditors than foreign ones. Based on this line of reasoning, Engler and Große Steffen (2016) argue that incentives for sovereign default originate in wealth transfers by defaulting on foreign held debt. The fundamental point from this strand of literature is that bank exposure can act as a disciplinary device for the sovereign. Such a device would lead to a lower perceived sovereign default risk when more domestic debt is held by the banking system.2 On a related point, the sovereign default literature helps explain the sharp increase in bank exposure observed in Figure 1. In particular, Broner et al. (2014) argue that sovereign bonds deliver a higher expected return to domestic creditors than to foreign creditors. Given that debt default is more costly to the sovereign if its debt is held domestically, government bonds offer a higher expected return to domestic creditors, especially during turbulent times. Therefore, public debt crises trigger a buy up of bonds by domestic creditors – most importantly banks. Overall, the sovereign default literature points toward bank sector exposure acting as a disciplinary device. In other words, the greater the exposure of the domestic banking system, the less likely the government is to default on its debt. We formulate this in the following hypothesis. Hypothesis II (disciplinary device): Increases in bank sector exposure raise the cost of default for the sovereign and, therefore, decrease sovereign default risk. State dependency From the above noted literature we further observe a certain degree of state dependence in 2It should be noted that additional demand through bank purchases of sovereign bonds ceteris paribus reduce yields, potentially leading to arbitrage opportunities for (institutional) investors to simultaneously sell bonds and CDS protection, a common proxy for default risk. This could also result in a negative relation between sovereign bond purchases and their CDS spreads as postulated by the literature on sovereign defaults. 7 use the following matrix specification of equation (5) BINV = b11 0 b21 b22  , Q(1) =  0 0 0 0 and Q(St) =  q11(St)q12(St) 0 0  ∀St>1.(6) This means that the upper right element, b12(St) of B(St), is unrestricted for St>1, or, in other words, for high volatility states (see Section 5.2). We use the specification in equation (6) for several reasons. Firstly, over the course of the most recent crises market participants have become more sensitive toward potential risk contagion between banks and sovereigns. This has arguably induced closer monitoring than before. We, therefore, feel more comfortable imposing the restriction only for the lower volatility (first) state. In this framework the market would be allowed to instantaneously react to all shocks that occur in higher volatility states. For example, in a two state model, where the first state is the lower volatility state, b12(1) = 0 and b12(2) 6= 0. This specification may be seen as a more general version of the state invariant Bmatrix since it allows us to relax the restriction. Secondly, we also need to relax this restriction due to practical considerations, so as to provide the model with enough flexibility in order to investigate the third hypothesis. Put differently, if we keep the zero restriction in all states, the responses we are interested in (namely those of sovereign CDS toward exposure shocks) remain invariant up to scaling. Finally, we assure that the necessary and sufficient conditions for (local) identification of the model are satisfied, given the set of restrictions that we impose.10 10In order to check the rank condition we follow Bacchiocchi and Fanelli (2015) and check whether the K(K+ 1) ×amatrix given by (I2⊗D∗ K)(B⊗IK) 0K2×K2 (B+Q)⊗IK(B+Q)⊗IK SBSI 0K2×aCSQ has full column rank (see Bacchiocchi and Fanelli,2015, equation (27)), where ais the number of free parameters in the structural impact matrices Band Q,SB,SQand SIsummarize the linear restrictions on B,Qand crossrestrictions on Band Q, respectively, and D∗ Kis the Moore-Penrose inverse of the duplication matrix D. We draw 10,000 matrices from the uniform distribution on the interval between -10 and 10 and find the rank condition satisfied for every draw. 14 4.2 Estimation and Bootstrapping We now discuss parameter estimation for both types of model specifications, with and without a state invariant Bmatrix, and we briefly describe how we test the identifying restriction in equation (4). This section concludes with a note on bootstrapping. The model parameters in equation (1) are estimated by means of the Expectation Maximization (EM) algorithm (see Hamilton,1994, Chapter 22). In the Expectation step the model filtered, smoothed and transition probabilities are estimated.11 In the Maximization step all other parameters in (1) are estimated, as well as the B, Λ and Qparameters described in sections 4.1.1 and 4.1.2. To estimate the parameters of the state invariant Bmatrix in equation (3) and of Λ(St), St>1, we use a similar algorithm as that described in (Velinov and Chen, 2015, Appendix). To estimate the parameters of the state dependent specification (equation (5)) we use the following concentrated out log likelihood function l(BINV , Q(2), Q(3) ...,Q(M)) = 1 2 M X m=1 b Tmlog(det(B(m)B(m)0)) + tr(B(m)B(m)0)−1 T X t=1 b ξmt|Tbutbu0 t, where ξmt|T, m = 1, . . . , M, t = 1, . . . , T are the model smoothed probabilities and Tm= PT t=1 ξmt|T. The hat denotes estimated parameters from the previous step/iteration. Note that in order to maximize this function subject to the constraints in (6) we use a nonlinear solver.12 Once the EM algorithm has converged, standard errors of the point estimates of the parameters are obtained through the inverse of the negative of the Hessian matrix evaluated at the optimum. With the standard errors in hand, we use Likelihood Ratio (LR) tests to determine whether the pairwise parameters of at least one of the Λ(St), St= 2, . . . , M matrices are distinct. As noted in Section 4.1.1, if that is the case then the Bmatrix is identified up to changes in sign and column ordering. Hence, any additional restrictions as in equation (4) 11Note the filtered and smoothed probabilities represent the conditional expectation of Stgiven information available up to time period tand Trespectively. The transition probabilities are given by pij =P(St=j|St−1= i), i, j = 1, . . . , M. 12We made use of Matlab R2014a to program and estimate the model. The code for the estimation of the model is available upon request. 15 become over-identifying and can be tested by means of an LR test.13 Finally, we would like to mention the theoretical aspects of the bootstrapping procedure we use for generating confidence bands for our impulse responses (see Section 5.3). In particular, given the heteroscedastic nature of the data,14 classical residual based bootstrap techniques may be problematic in generating reliable confidence intervals for impulse responses (IRs). Any resampling scheme needs to preserve the second order characteristics of the data. We therefore use a fixed design wild bootstrap according to u? t=ϕtbut, where ϕtis a random variable, independent of ytfollowing a Rademacher distribution. In other words, ϕtis either 1 or -1 with a 50% probability. Davidson and Flachaire (2008) show that using the Rademacher distribution for wild bootstrapping is superior to the two-point distribution proposed by Mammen (1993), even if the residuals are not symmetrically distributed.15 5 Results This section presents the empirical results of both models (see Section 4.1.1 and Section 4.1.2) for eight euro area countries. Impulse responses (IRs) are presented to assess the three hypotheses. The section starts with a discussion of the model specification and smoothed probabilities. 5.1 Model selection In our analysis we consider two-state Markov Switching Structural Vector Autoregressive in heteroscedasticity (MSH-SVAR) models. The use of two states is for several reasons. Firstly, due to a limited number of observations, we prefer parsimonious model specifications. Secondly, two states are sufficient to formally test the identifying restriction imposed on the model (see Section 4.1). Thirdly, provided one state is interpretable as a tranquil and the other as a crisis state, two states suffice for testing the third hypothesis that refers to a state dependent shock transmission. Finally, a third state would mainly pick up outliers, rendering the parameters for this state difficult to estimate due to few observations. 13Note that the LR test is only applicable to the specification described in section 4.1.1. We do assume however, that if the restriction holds for that specification it is plausible that it holds for the state invariant part of the contemporaneous impact matrix, BINV in section 4.1.2. 14ARCH tests strongly indicate the presence of heteroscedasticity in the data. 15See MacKinnon (2014) for a further discussion of Wild bootstrap auxiliary distributions. 16 We follow the literature on MS-VAR models and select the lag order of the endogenous variables, p(see equation (1)), based on the linear VAR model. To keep the models as parsimonious as possible we follow the Bayesian information criterion (BIC) and choose one lag for Spain, Italy, Portugal, Belgium and Germany and two lags for France, The Netherlands and Austria. In addition, we set n=p, that is we use the same lag length for the exogenous variables. Table 2: Log-Likelihood, Akaike and Bayesian information criteria for model selection based on a Markov-switching model with two states and different sets of switching parameters linear Σ(St) Σ(St), ν(St) Σ(St), Ai(St) Σ(St), Ai(St), ν(St) Spain LogLik -713.103 -684.159 -676.579 -679.323 -662.563 AIC 1570.206 1432.318 1421.158 1430.646 1437.125 BIC 1568.930 1511.227 1504.999 1519.419 1575.216 Italy LogLik -751.353 -705.828 -709.990 -722.241 -692.472 AIC 1626.705 1475.655 1487.979 1516.483 1496.945 BIC 1622.644 1557.715 1575.167 1608.799 1640.548 Portugal LogLik -955.411 -867.543 -866.453 -865.692 -867.327 AIC 2054.821 1799.086 1800.906 1803.383 1846.655 BIC 2053.545 1881.146 1888.093 1895.700 1990.258 Belgium LogLik -692.793 -635.920 -632.459 -633.967 -641.484 AIC 1529.585 1335.839 1332.918 1339.933 1394.968 BIC 1528.309 1417.899 1420.106 1432.250 1538.572 Germany LogLik -686.307 -599.297 -596.326 -595.661 -557.502 AIC 1516.614 1262.593 1260.653 1263.321 1227.005 BIC 1515.338 1344.652 1347.841 1355.638 1370.608 France LogLik -617.171 -564.962 -560.691 -557.654 -544.697 AIC 1350.341 1201.925 1197.382 1203.309 1217.393 BIC 1346.542 1293.864 1294.429 1315.679 1380.842 Netherlands LogLik -641.081 -599.545 -599.173 -599.47 -554.362 AIC 1398.162 1271.091 1274.347 1286.940 1236.724 BIC 1394.363 1359.026 1367.168 1394.416 1393.053 Austria LogLik -720.102 -641.481 -640.311 -629.650 -624.506 AIC 1576.204 1354.962 1356.622 1347.300 1377.012 BIC 1574.999 1446.902 1453.669 1459.671 1540.461 Notes: Σ(St) – only covariance matrix switching; Σ(St), ν(St) – covariance matrix and intercept switching; Σ(St), Ai(St) – covariance matrix and slope parameters switching; Σ(St), Ai(St), ν(St) – all reduced form parameters switching. The bold formatting denotes the model chosen by the respective criterion. Table 2 reports information criteria for different specifications regarding the linearity of the model. Clearly, non-linear models are preferred over linear specifications, according to 17 log-likelihoods and information criteria. The AIC usually favors models with more parameters switching, but based on our preference for parsimonious model specifications, we opt for the more restrictive BIC. In all cases except for Spain this criterion strongly favors a model structure with only switching covariance matrices. Therefore, we use a Markov Switching Structural Vector Autoregressive in heteroscedasticity (MSH-SVAR) model for all countries considered.16 Such a specification is in line with the findings from ARCH tests for conditional heteroscedasticity in the data. These tests strongly reject the null hypothesis of no heteroscedasticity. 5.2 Smoothed state probabilities Figure 3 plots the smoothed probabilities of state 2, the high volatility state, for all eight countries based on the MS model with the state invariant instantaneous impact matrix.17 Clearly, each MS model is well capable of capturing the crisis phases, which are always indicated as being in state 2.18 The upper four panels of Figure 3 show the countries that were affected somewhat more by the crisis (Spain, Portugal, Italy and Belgium). Their smoothed probabilities appear to be relatively stable. The lower four panels of the figure show the more stable countries (France, Germany, The Netherlands and Austria), where Germany was even regarded as a safe haven during the European debt crisis. The smoothed probabilities of Germany, The Netherlands and Austria show more volatile patterns. This is likely attributable to less volatility in data, making both states not very different from each other. In order to test the identifying restriction in equation (4), we first need to determine whether the pairwise diagonal elements of Λ(2) are distinct (see Section 4.1.1 and Section 4.2). Table 3 clearly shows that this is the case according to Likelihood Ratio (LR) tests (the null hypothesis is λ11(2) = λ22(2)).19 This means that all of the estimated models are over-identified since 16Given the complicated structure of the likelihoods of the MS-VAR models, that the information criteria are based upon, together with the estimation uncertainty of their parameters, the criteria should not be viewed as providing a strict guideline, but rather as well informed indications towards a preferred specification. 17Note that the smoothed state probabilities for the model with a state dependent instantaneous impact matrix look quite similar, but are not identical. 18Note that the states are not directly comparable among different countries. For instance, volatility may be higher in the second state for some countries than for others indicating that they were hit more strongly by the crisis. 19We follow the literature on identification via heteroscedasticity regarding the assumptions on the asymptotic distribution of the test statistic. It should be noted, however, that according to personal communication with 18 Jan07 Jan08 Jan09 Jan10 Jan11 Jan12 Jan13 Jan14 0 0.2 0.4 0.6 0.8 1 Jan07 Jan08 Jan09 Jan10 Jan11 Jan12 Jan13 Jan14 0 0.2 0.4 0.6 0.8 1 (a) Spain Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 (b) Portugal Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 (c) Italy Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 (d) Belgium May06 May07 May08 May09 May10 May11 May12 May13 0 0.2 0.4 0.6 0.8 1 May06 May07 May08 May09 May10 May11 May12 May13 0 0.2 0.4 0.6 0.8 1 (e) France Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 Apr06 Apr07 Apr08 Apr09 Apr10 Apr11 Apr12 Apr13 0 0.2 0.4 0.6 0.8 1 (f) Germany Mar07 Mar08 Mar09 Mar10 Mar11 Mar12 Mar13 0 0.2 0.4 0.6 0.8 1 Mar07 Mar08 Mar09 Mar10 Mar11 Mar12 Mar13 0 0.2 0.4 0.6 0.8 1 (g) Netherlands May06 May07 May08 May09 May10 May11 May12 May13 0 0.2 0.4 0.6 0.8 1 May06 May07 May08 May09 May10 May11 May12 May13 0 0.2 0.4 0.6 0.8 1 (h) Austria Figure 3: Smoothed probabilities of state 2, the high volatility state, from the Markov switching VAR models with invariant structural impact matrices 19 Σ(1) 6= Σ(2). Table 4 summarizes the LR tests of the restriction b12 = 0 (equation (4)), versus the alternative of an unrestricted Bmatrix. As noted earlier, this test is only applicable to the state invariant specification discussed in section 4.1.1. The imposed restriction is not rejected by the data, except in the case of the Spanish model. We consider this result as a strong signal in support of our structural shock identifying assumption and therefore, assume that this restriction is plausible for BINV in (6), i.e. bINV 12 = 0. Finally, since most elements of Λ(2) are larger than unity (i.e. the volatility of the first state), we refer to the second state as the crisis state.20 Table 3: Diagonal elements of Λ(2) with standard errors in parentheses. Likelihood Ratio test for distinct elements of Λ(2). The null hypothesis is λ11(2) = λ22(2). Spain Italy Portugal Belgium Germany France Netherlands Austria λ137.948 70.229 199.978 62.552 14.488 144.096 35.651 10.064 (7.992) (8.942) (8.006) (9.685) (11.282) (19.714) (9.121) (4.796) λ20.178 1.95 5.635 0.993 78.043 1.497 0.151 135.828 (0.065) (0.635) (1.759) (0.326) (28.672) (0.51) (0.058) (15.764) LogLik -698.079 -731.333 -896.997 -666.566 -602.575 -588.94 -610.905 -654.854 χ227.84 51.01 58.908 61.292 6.558 47.956 22.72 26.747 p-value 0.000 0.000 0.000 0.000 0.010 0.000 0.000 0.000 Table 4: Likelihood ratio test of the restriction in equation (4) versus an unrestricted Bmatrix. Spain Italy Portugal Belgium Germany France Netherlands Austria Restr. -691.520 -705.905 -867.549 -636.376 -599.319 -564.967 -599.723 -641.481 Unrestr. -684.159 -705.828 -867.543 -635.920 -599.297 -564.962 -599.545 -641.481 χ214.723 0.154 0.011 0.912 0.044 0.009 0.356 0.000 p-value 0.000 0.695 0.916 0.340 0.833 0.925 0.551 0.982 5.3 Impulse Responses We turn to impulse response (IR) analysis to formally test the hypotheses outlined above. We evaluate Hypotheses I and II using the state invariant Bmodel, since they do not refer Helmut L¨utkepohl recent research finds the assumptions for the asymptotic distributions of the test statistic to be not quite correct. Therefore, these tests should be interpreted with some caution. Tentative evidence indicates that the LR statistic for a bivariate VAR model has an asymptotic χ2(2) distribution under the null. Based on the critical values of the χ2(2) distribution the test would indicate identification. In addition, the (bootstrapped) IRs stemming from the models identified via heteroscedasticity do not indicate any lack of identification since error bands are well behaved. 20Note that we are mainly interested in λ1, the CDS volatility in the second state, which is always greater than one (see Table 3). 20 to a regime dependent shock transmission. We assess Hypothesis III by means of the regime dependent Bmodel. 5.3.1 State invariant Bimpulse responses Figure 4 reports the IRs in state 1 of sovereign CDS to a positive one standard deviation exposure shock. Note, the IRs of state 2 are the same in shape, sign and significance, only differing in the scaling on the vertical axis. All countries exhibit a significant increase in credit risk in response to a shock in bank exposure. Risk shock Gov 0 5 10 15 20 0 2 4 6 8 10 Exp Shock Gov 0 5 10 15 20 −1 0 1 2 3 Risk shock Exp 0 5 10 15 20 −0.4 −0.2 0 0.2 0.4 Exp Shock Exp 0 5 10 15 20 0 1 2 3 4 5 6 (a) Spain Risk shock Gov 0 5 10 15 20 0 2 4 6 8 10 Exp Shock Gov 0 5 10 15 20 0 5 10 15 Risk shock Exp 0 5 10 15 20 −1.5 −1 −0.5 0 Exp Shock Exp 0 5 10 15 20 0 2 4 6 8 (b) Portugal Risk shock Gov 0 5 10 15 20 0 1 2 3 4Exp Shock Gov 0 5 10 15 20 0 2 4 6 8 Risk shock Exp 0 5 10 15 20 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 (c) Italy Risk shock Gov 0 5 10 15 20 0 1 2 3 4 Exp Shock Gov 0 5 10 15 20 0 1 2 3 4 Risk shock Exp 0 5 10 15 20 −0.1 −0.05 0 0.05 0.1 0.15 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 (d) Belgium Risk shock Gov 0 5 10 15 20 0 0.5 1 1.5 Exp Shock Gov 0 5 10 15 20 −1 −0.5 0 0.5 1 1.5 2 Risk shock Exp 0 5 10 15 20 −0.1 −0.05 0 0.05 0.1 0.15 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 (e) France Risk shock Gov 0 5 10 15 20 0 1 2 3 4 5 Exp Shock Gov 0 5 10 15 20 0 0.5 1 1.5 Risk shock Exp 0 5 10 15 20 0 0.2 0.4 0.6 0.8 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 (f) Germany Risk shock Gov 0 5 10 15 20 0 1 2 3 4Exp Shock Gov 0 5 10 15 20 −2 −1 0 1 2 3 4 Risk shock Exp 0 5 10 15 20 −1.5 −1 −0.5 0 Exp Shock Exp 0 5 10 15 20 −5 0 5 10 (g) Netherlands Risk shock Gov 0 5 10 15 20 0 0.5 1 1.5 2 2.5 Exp Shock Gov 0 5 10 15 20 −0.4 −0.2 0 0.2 0.4 0.6 0.8 Risk shock Exp 0 5 10 15 20 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 (h) Austria Figure 4: State invariant Bimpulse responses of sovereign CDS to an exposure shock with 68% confidence intervals based on 1000 bootstrap replications The overall responses are not only statistically significant, they are also economically significant. The countries in the upper panel of the figure that were hit harder by the sovereign debt 21 crisis exhibit particularly strong responses. For instance, the model indicates an increase in CDS of up to 10 basis points for Italy and more than 20 basis points for Portugal. In addition, for those countries, the responses do not show signs of mean reversion at the 20 month horizon plotted in the figure. Note that the response for Spain differs in that it is insignificant over all time horizons. However, the results for Spain should be interpreted with some caution given that the identifying restriction was rejected for the Spanish model (see Table 4). Finally, for Germany, The Netherlands, Austria (and France to a lesser extent) the IRs also show longer lasting impacts, but with a clear reversion toward mean after a couple of months. The Austrian model shows a similar pattern for the response to an exposure shock, however, it is not significant. Overall, we conclude that the results from models with state invariant structural impact matrices seem to point more strongly toward the diabolic loop story (Hypothesis I), thereby rejecting competing Hypothesis II, the disciplinary device mechanism hypothesis. 5.3.2 State dependent Bimpulse responses We now turn to the state dependent Bmodel results in order to investigate Hypothesis III. These allow for contemporaneous reactions of the sovereign CDS markets to changes in banks’ balance sheets (i.e. increases in bank exposure toward the sovereign) during crises times. Figure 5 and Figure 6 plot these IRs for the low and high volatility states, respectively. Note that for tranquil times, the contemporaneous restriction still holds, identifying the exposure shock as argued in Section 4.1.2. A number of findings arise from Figure 5. Firstly, the IRs of state 1, the tranquil state, are qualitatively very similar to the ones from the state invariant Bmodel. This is as expected, given that the identification has not changed for the tranquil state. We therefore, assume that it is plausible for b12(1) = bINV 12 = 0. Note however, the notable exception of Spain (and to a lesser extent Austria). For Spain the same conclusion holds as above, in that we cannot be sure whether the shocks are correctly identified, although in this case the response seems much more plausible. Secondly, for state 2, the crisis state, the impact responses plotted in Figure 6 are all different from zero — due to the higher degree of freedom in estimating the 22 Risk shock Gov 0 5 10 15 20 −2 0 2 4 6 Exp Shock Gov 0 5 10 15 20 0 1 2 3 4 5 6 Risk shock Exp 0 5 10 15 20 −4 −3 −2 −1 0Exp Shock Exp 0 5 10 15 20 0 1 2 3 4 5 (a) Spain Risk shock Gov 0 5 10 15 20 −2 0 2 4 6 Exp Shock Gov 0 5 10 15 20 0 2 4 6 8 10 12 Risk shock Exp 0 5 10 15 20 −4 −3 −2 −1 0Exp Shock Exp 0 5 10 15 20 0 2 4 6 8 10 12 (b) Portugal Risk shock Gov 0 5 10 15 20 0 1 2 3 4 5 6 Exp Shock Gov 0 5 10 15 20 0 2 4 6 8 10 12 Risk shock Exp 0 5 10 15 20 −1.5 −1 −0.5 0 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 (c) Italy Risk shock Gov 0 5 10 15 20 0 1 2 3 4 Exp Shock Gov 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 Risk shock Exp 0 5 10 15 20 −0.8 −0.6 −0.4 −0.2 0 Exp Shock Exp 0 5 10 15 20 −1 0 1 2 3 (d) Belgium Risk shock Gov 0 5 10 15 20 0 0.5 1 1.5 Exp Shock Gov 0 5 10 15 20 −1 −0.5 0 0.5 1 1.5 2 2.5 Risk shock Exp 0 5 10 15 20 −0.6 −0.4 −0.2 0 0.2 Exp Shock Exp 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 (e) France Risk shock Gov 0 5 10 15 20 0 0.5 1 1.5 2 2.5 3 3.5 Exp Shock Gov 0 5 10 15 20 0 0.5 1 1.5 2 Risk shock Exp 0 5 10 15 20 −2 −1 0 1 2 3 4 Exp Shock Exp 0 5 10 15 20 −2 0 2 4 6 (f) Germany Risk shock Gov 0 5 10 15 20 0 0.5 1 1.5 2 Exp Shock Gov 0 5 10 15 20 −0.5 0 0.5 1 Risk shock Exp 0 5 10 15 20 −1 −0.5 0 0.5 1 Exp Shock Exp 0 5 10 15 20 −5 0 5 10 (g) Netherlands Risk shock Gov 0 5 10 15 20 0 1 2 3 4 5 6 7Exp Shock Gov 0 5 10 15 20 −1 0 1 2 3 Risk shock Exp 0 5 10 15 20 0 1 2 3 4 5 6 7 Exp Shock Exp 0 5 10 15 20 −2 −1 0 1 2 3 4 5 (h) Austria Figure 5: State dependent Bimpulse responses of sovereign CDS to an exposure shock for the low volatility state with 68% confidence intervals based on 1000 bootstrap replications impact matrix.21 This figure shows that the impulse responses portray a clear clustering of the countries, dividing them by the sign of the impact response into a group that was hit hard by the crisis and a group with sovereign finances less affected by the crisis. Sovereign credit risk rises strongly in Spain, Portugal and Italy in response to an exposure shock. The impulse responses exhibit a clear pattern of regime dependence and point toward a strong diabolic loop effect at play in the crisis hit countries. On impact, an increase in exposure of one standard deviation leads to a jump of between 20 and 40 basis points in credit 21 Note that this does not contradict the LR test results in Table 4(where the null of b12 = 0 is accepted) since, as discussed before, this test is only applicable to the specification in Section 4.1.1. Further, b12(2) 6= 0 is also not a contradiction since the specification in Section 4.1.2 assumes that Λ(St) = I2∀Stmeaning that only the elements of B(St) are responsible for the decomposition of Σu(St), the state dependent reduced form covariance matrix. Thus the only way for Σu(St) to differ over states would be if B(St) differed over states. 23 Herwartz, H. and H. L¨utkepohl (2014). 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