The Bank-Sovereign Nexus: Evidence from a non-Bailout Episode

We explore the interplay between sovereign and bank credit risk in a setting where Danish authorities first let two Danish banks default rather than bail them out and then left the country’s largest bank, Danske Bank, to recapitalize privately. We find that the correlation between bank and sovereign credit default swap (CDS) rates changed with these events, indicating that the non-bailout decisions and recapitalization helped to curb the feedback loop between bank and sovereign risk. Following the non-bailout events, the sensitivity to external shocks declined both for Danske Bank and for Danish sovereign debt, as measured by their CDS connection with CDS rates on the European banking sector. After Danske Bank was recapitalized, its exposure to the European banking sector reappeared, while that did not happen for Danish sovereign debt. This decoupling between CDS rates on sovereign and private bank debt indicates that the non-bailout policies succeeded in breaking the vicious circle generated by the risks on the bank and sovereign debts. Our results are reinforced by the use of an indirect testing approach and by focusing on CDS-quantiles. JEL codes : C21, G12, G21, G28.


Introduction
In the years following the 2007-2008 financial crisis, several countries decided to bail out their local banks, shifting losses from the financial sector to the government. Shortly after the bailout events, the credit risk on many of these countries' sovereign bonds started to rise. Since then, several studies have documented that the bank bailouts were an integral factor in fueling sovereign risk, see for instance Ejsing and Lemke (2011). It is even hypothesized that the bank bailouts backfired to some extent, as the subsequent rises in sovereign risks weakened the balance sheets of banks and thus re-ignited credit risk in the financial sector, as argued by for instance Acharya et al. (2014) and discussed by Arghyrou and Kontonikas (2012) and Fratzscher and Rieth (2015) in the context of the European sovereign debt crisis.
There are several more studies in this vein. Kallestrup et al. (2016) show that crossborder financial linkages affect sovereign risks to an extent that is beyond what can be explained by the simple exposure to common factors. Alter and Schuler (2012) document that bank bailout programs change the composition of both banks and government balance sheets, transferring the risks from the financial sector to the sovereign credit risk, while Alter and Beyer (2014) find evidence of an increase in bank-to-sovereign and sovereign-tobank spillover during the European sovereign crisis, as in Lane (2012). De Bruyckere et al. (2013) show in a sample of European data over the period 2007-2012 that the success of government interventions depends on the type of intervention. Also before the European debt crisis erupted, the bank-sovereign nexus was understood as a potentially problematic issue, for instance Gray (2009) argued that the feedback and spillover effects between the risk exposures of the banking and sovereign sectors were important but only incompletely understood. 1 Typical for the existing studies is that they are based on episodes where bailouts were undertaken. However, these analyses cannot necessarily tell much about the counter-factual evidence, namely what would have happened if banks had not been rescued, but instead had been left to fail or raise additional capital in the market. In this study, we focus on one such episode which took place in Denmark. Differently from most of the previous literature on the topic of sovereign and bank credit risk, which has mostly analyzed the problem of contagion at a systemic level, we focus on a single episode where the national authorities let distressed banks default and made the country's largest bank recapitalize privately. In 2011 two Danish banks, Amagerbanken and Fjordbank, defaulted on outstanding bonds. In both cases, senior bond holders incurred in substantial losses. The decision not to bail out these banks contrasted with the Danish crisis response in 2009, where the largest bank, Danske Bank, received considerable support. More broadly, the policy departed from the general Scandinavian practice of the early 1990s, where equity holders took most of the losses as banks collapsed, whereas bond holders were bailed out by the government, see e.g. Honkapohja (2009). Hence, the no-bailout decision was a sign of the Danish authorities' devotion to a more restrictive bailout policy than history would suggest. 2 The following market-based recapitalization of Danske Bank and restitution of the 2009 funding provided by the government supported this tougher policy stance.
A priori, as reflected in the introductory discussion above, it is not obvious what consequences these policies might have. On the one hand, weaker perceived government guarantees could leave the debt of private banks exposed to external aggregate funding shocks. On the other hand, with a weaker link to the government, the bank risk should become less strongly related to aggregate factors affecting the sovereign's solvency, and more dominated by idiosyncratic factors. Likewise, the sovereign debt might become more insulated from external disturbances if it is not expected to support its banks. However, if the lack of perceived bailout guarantees makes banks more vulnerable to external shocks, this could feed back to national balance sheets through tax base sensitivity to banking crisis. Hence, in this paper we seek to characterize how the sensitivity to external factors changed around the non-bailout events for Danish sovereign debt and the main Danish bank, Danske Bank. In particular, we provide empirical evidence to address whether private bank debt became more vulnerable after the non-bailout events and if the evolution of bank and sovereign debt became decoupled.
We study the evolution of credit default swap (CDS) rates on the bonds of Danske Bank and on Danish sovereign debt. As Figure 1 shows, the Danske Bank CDS rates did indeed increase after the non-bailout events, in particular after the second event (Fjordbank's default on June 24, 2011). This indicates, as we would expect, that the variation in the perceived bailout guarantees was priced into CDS rates. Moreover, a similar pattern is seen for Danish sovereign debt, displayed in Figure 2. At face value this might seem to indicate that the non-bailout policies were unsuccessful as the reduction in bank guarantees were followed by greater bank and sovereign default risk. However, we also observe that both CDS rates decline toward the end of the sample and have remained low since Danske Bank was recapitalized. Hence, judging the merits of the non-bailout decisions from the immediate CDS responses would give a very different conclusion than a somewhat longerrun perspective. Several factors other than the non-bailout events may of course underlie such descriptive patterns, such as the European debt crisis in this specific period. For instance, even the CDS rates on German sovereign debt, by most standards a "safe haven asset", increased in mid-2011, as seen in Figure 3, a movement that obviously was not driven by Danish bailout policies. 3 For these reasons, we do not judge the effects of the non-bailout policies by the levels of Danish CDS rates alone. Instead, we develop an indirect testing strategy and study the sensitivity of Danske Bank and Danish CDS rates to the international CDS rates around the two non-bailout decisions and the subsequent recapitalization. We focus on the dynamics of the credit risk on a safe haven asset, as measured by the CDS on German sovereign bonds, and on the dynamics of the CDS index on the European banking sector. If the new non-bailout policy has affected market perceptions of credit risk determinants, that should turn up as time-variation in the regression coefficients of Danske Bank and Danish CDS rates on these variables.
We find that CDS rates on both Danske Bank and Danish sovereign debt became less sensitive to movements in CDS rates on the European banking sector immediately after Amagerbanken and Fjordbank were left to default. Later, after Danske Bank's private recapitalization, the sovereign bonds remained less exposed to EU banking risk than before the non-bailout episodes, whereas the Danske Bank sensitivity reverted to its pre-crisis levels. Hence, the overall effect of the non-bailout policy was to decouple sovereign from banking risk, but only after the private bank was recapitalized. Notably, the above results also emerge when we control for time varying sensitivity to CDS rates on German sovereign debt. The pattern of co-movement with the safe asset provided by German bonds is quite different from that with EU banking debt: the sensitivities of CDS rates on Danske Bank and Danish sovereign debt to German sovereign debt move together over the period we consider. The default episodes are not associated with a change in co-movement for either assets, while both Danske Bank and Danish sovereign CDS rates respond less to movements in German sovereign CDS rates after the Danske Bank recapitalization. Clearly, one may question if the empirical patterns are driven by the non-bailout events or other (domestic) factors that coincide in time. To deal with this problem, we control for an extensive set of variables, including the Danish housing price index and equity prices. Danske Bank equity prices are particularly important here, since bailouts primarily serve to shield debt holders rather than equity holders from losses. Hence, by controlling for swings in the Danske Bank stock price, we isolate the Danske Bank's CDS co-movement with the CDS of the German sovereign debt and of the European banking sector, that is not due to factors that affect the market's valuation of Danske Bank's assets. Similarly, for the Danish sovereign CDS, by controlling for overall equity prices, we control for the market's perception of the state of the Danish economy at large. Importantly, we also address non-linearities, as the co-movement between variables could be different in crisis times than in more normal periods. Indeed, bailout events generally take place during extreme market conditions or in exceptional company-specific circumstances. In these situations, the response variables are subject to extremely large realizations and a linear model could produce biased results, see, for example, Caporin et al. (2014). We therefore extend our analysis with quantile regressions, which facilitate detecting and testing for differential impacts of the explanatory variables across the quantiles of the dependent variable. We apply the method to assess whether the new non-bailout policy had particular effects in different parts of the CDS distribution. 4 The main findings from the non-linear analysis are consistent with the evidence obtained in a linear regression framework. Conditional upon being in high-volatility times, the co-movement between an average CDS of the larger European banks and Danske Bank CDS is markedly lower after the defaults of Amagerbanken and Fjordbank, whereas the co-movement of Danske Bank CDS and German CDS is stable. The same pattern emerges with Danish sovereign CDS rates. Then, after the Danske Bank recapitalization, the relationship of Danske Bank and Danish sovereign CDS rates with the European banking sector diverges with a positive significant coefficient for Dansk Bank and a flat zero coefficient for Danish CDS across quantiles. After the Danske Bank recapitalization, (i) CDS levels on both sovereign and private bank debt dropped, and (ii) sovereign and private bank risk were decoupled in their response to international banking risk. Taken together, these observations indicate that the entire non-bailout policy, including recapitalization, contributed to a curbing of the feedback loop between banking risk and sovereign risk.
This paper is organized as follows. Section 2 provides an overview of the data and the institutional setting. Emphasis is on how failing banks typically have been dealt with in Scandinavia and the particular events in Denmark that we study. Section 3 describes the results of our analysis applying both linear regression and quantile regression models. Section 4 concludes. trials where the interest is in how subjects respond to a specific treatment.
2 Data and Institutional Setting

Setting and Events
After the real estate crisis in the late 1980s and early 1990s, the Scandinavian governments, particularly in Norway and Sweden, nationalized defaulting banks by creating the system of so-called "bad banks". In a nutshell, the shares of the bad banks lost their value while debt was repaid by the government. Hence, stock holders suffered all the losses, whereas bond holders were largely guaranteed, see e.g. Honkapohja (2009). The impression that bank bonds were protected by the government was strengthened during the financial turmoil of 2007-2008, where the governments in Scandinavia, as in many other economies, stepped in to support their largest banks with emergency credit lines. In 2009 the Danish government implemented a credit aid package intended to support Danske Bank, among other financial institutions. In particular, Danske Bank raised a perpetual hybrid loan of 26 billion Danish Krone (DKK) (equivalent to some 4.8 billion US Dollars at the time) with the Danish government, which allowed the bank to maintain its capitalization well above regulatory requirements (Standard and Poor's, 2012). 5 Despite the support measures of the government, the Danish economy further deteriorated after 2009, and real estate prices plummeted. The collapse in house prices brought additional problems to the Danish banking sector. On February 6, 2011, the relatively small bank Amagerbanken was unable to meet its obligations and forced a 41% loss on its senior bond holders. The fact that the Danish government chose not to bail this bank and its senior bond holders out marked a shift in bailout policy and contrasted sharply with previous experience. On June 24, 2011, this restrictive policy line was confirmed when Fjordbank was left to default, and senior bond holders suffered substantial losses once again. On October 30 2012, Danske Bank initiated a significant recapitalization, with a DKK 7 billion equity rights issue. The recapitalization was a main ingredient in a new three-year plan of the group to improve its earnings capacity. The issue was partly motivated by tighter future regulatory capital requirements, and partly by the fact that the government support measures from 2009 were about to expire, and the cost of repaying the government was set to increase sharply after May 2014. Notably, in contrast to the case of the US government support to the local banks, the extraordinary 2009 government measures were temporary. They had a precise deadline when funding was supposed to be repaid, in line with EU competition law. Part of the 2009 funding (DKK 2 billion) was repaid already in 2012.

Data
Similarly to Kalbaska and Gatkowski (2012), the evolution of the credit risk is analyzed by means of the prices of the CDS contracts, which can be obtained from Datastream. We use daily observations of the stock prices (P DB ) and CDS rates (CDS DB ) of Danske Bank, covering the period December 2007 to April 2014. CDS contracts are designed to transfer the credit exposure of fixed income products between parties. The buyer of a credit default swap receives credit protection from the seller. In doing so, the risk of default is transferred from the holder of the fixed income security to the seller of the swap. Higher CDS values imply higher risk. Hence, the CDS rates proxy for the risk that Danske Bank will default on its debt. We also collect daily data on Danish sovereign CDS rates (CDS DK ) with 5 years maturity, along with the German sovereign CDS rates with 5 years maturity (CDS DE ), and a CDS index for the European banking sector (CDS EU ). The latter is computed by Thomson-Reuters as the weighted average CDS spread of the constituents, with weights based on total debt outstanding at the index construction date. 6 We develop our analysis based on a few assumptions: A1 German bonds are safe assets.
A2 The credit risk on the Danish sovereign bonds does not influence the credit risk of German bonds.

A3
The credit risk on the Danske Bank bonds does not influence the credit risk of European banks.
Assumption A1 is perhaps an exaggeration as there could be risks associated with German debt too (otherwise the CDS price would be zero). This assumption should be interpreted as the German sovereign bonds being the safest, relatively to the other bonds and it carries the baseline credit risk. A2 and A3 are motivated by the share volume of debt, and the size of the economies. The sovereign debt of Germany is more than eighteen times the sovereign debt of Denmark. 7 The total debt of Danske Bank is less than 1.5% of the total loans of the European banks. 8 In addition, we use daily data on four other international risk related measures: the Euro Stoxx 50 Index (STOXX), the Euro Stoxx 50 Volatility Index (VSTOXX), the Oil price (OIL), and the liquidity risk in the money market computed as the difference between the 1-month Euribor and the Repo spread (LIQ). The role of liquidity for credit risk is quite controversial. Early papers, such as Codogno et al. (2003), find a limited impact, 6 We also tried to use a total connectedness index of the CDS of the 52 largest European banking institutions, see Figure A.2. Results were qualitatively similar. 7 In 2014 the GDP of Denmark was about 257 billion Euro and its debt-to-GDP ratio was 44.8%. For Germany, these numbers were 2904 billions and 74.7%, respectively. We recover these data from Eurostat. 8 In 2014 the total debt of Danske Bank was below 200 billion Euro relative to more than 16 trillion Euro in all of Europe, as reported by Danske Bank and ECB. while more recent contributions, such as Manganelli and Wolswijk (2009) and Beber et al. (2009), show that "...while the bulk of sovereign yield spreads is explained by differences in credit quality, liquidity plays a nontrivial role...". We also control for Danish house prices, using a monthly Danish house price index (HS) that we interpolate to the daily frequency. The effects of the recapitalization of Danske Bank in October 2012 are evident in the CDS, as it returns to its pre-2011 level after the recapitalization. This is natural, as more bank capital implies less risk for bond holders. Importantly, the patterns in Figure 4 could stem from several other factors than the defaults of Amagerbanken and Fjordbank. We therefore study the dynamic interplay between the CDS rates across countries and companies by means of the total connectedness index of Diebold and Yilmaz (2014). The TCI is defined as

Preliminary analysis
where N denotes the number of variables in the system, andd i,j is the i, j entry of the standardized connectedness matrixD. The matrixD is defined as with where A h is the impulse-response matrix at horizon h associated with a VAR(p) model, Σ is the covariance matrix of the errors, and e i , e j are N × 1 selection vectors. By construction, N j=1d i,j = 1 and N i,j=1d i,j = N . Equation (3) defines the generalized forecast error decomposition, as introduced by Pesaran and Shin (1998). In other words, the TCI measures the average portion over N variables of the forecast error variation of variable i coming from shocks arising from the other j = 1, . . . , N − 1 variables of the system. The TCI provides a characterization of the connectedness of a system that is richer than the one obtained with a simple linear correlation coefficient. Indeed, the TCI combines the information coming from both the contemporaneous and the dynamic dependence structure of the system trough Σ and A h , respectively. Moreover, by estimating the VAR model over rolling windows, it is possible to characterize the evolution of the dependence structure between two or more variables by looking at the variations of the TCI over time. Figure 5 reports the pairwise rolling TCI between ∆ log CDS DB , ∆ log CDS DE , ∆ log CDS DK , and ∆ log CDS EU . 9 After the non-bailout event of Fjordbank and before the recapitalization of Danske Bank, the rolling TCI between ∆ log CDS DB and ∆ log CDS DK increased, but only after a decline at the beginning of the sample. After the recapitalization, the TCI index plunged and remained low and stable until the end of the sample. A similar pattern also arises from the TCI of ∆ log CDS DB and ∆ log CDS DE . The connectedness between ∆ log CDS DB and ∆ log CDS EU , the latter capturing systemic risk of other European banks, increases towards the end of the period while, it is very low between 2011 and 2012. This indicates that, after the recapitalization, the dynamic behavior of credit risk associated with Danske Bank is connected with that of the rest of the European banking sector. Finally, the graphs in the bottom panels of Figure 5 display a general downward trend in the TCI between the CDS of Denish, German and the European banking sector without notable breaks after the recapitalization of Danske Bank. In the following section, we assess to what extent the non-bailout episodes and the recapitalization of Danske Bank have lead to changes in the co-movement between Danske Bank's CDS and German sovereign CDS rates.  (2014), based on a VAR with two lags (p=2) and a horizon of H = 12 days for the impulse-response functions.

Dependence on systemic risk after the non-bailout episodes
In order to further study the dynamics of credit risk in the Danish economy relative to the credit risk of the European system before and after the non-bailout events, we explore the sensitivity of Danske Bank and Danish sovereign CDS rates to movements in the CDS rates on European banks and German sovereign debt, ∆ log CDS EU t and ∆ log CDS DE t . We first consider a linear specification of the following form: where i = DB, DK. DB stands for Danske Bank and DK for Denmark, and the dependent variable is the log change in the CDS of Danske Bank or Danish sovereign debt; ε t is the error term; and j = 1, 2, 3 refer to the three periods we consider. These are: the period up to the default of Fjordbank (from December 18, 2007to June 24, 2011, the period between the default and the recapitalization of Danske Bank (from June 25, 2011 to October 30, 2012), and the period after the recapitalization (from November 1, 2011 to April 29, 2014). Note that we choose to use the Fjordbank default and not that of Amagerbanken, as it was only after the Fjordbank event that the CDS of Danske Bank reacted. This likely reflects that the market, only after the second event, interpreted the absence of bailout as a structural change in government policy. The covariates are the log changes of German CDS, the log changes of the European banking sector CDS, the returns of Danske Bank equity, and the changes in the Danish housing index (∆ log HOU S). Furthermore, W t contains other financial variables related to global risk that are used as controls, ∆ log OIL t , ∆ log ST OXX t , ∆ log V ST OXX t , and ∆LIQ t .
The results in Table 1 show that the estimated coefficient on ∆ log CDS DE t is significantly positive in the two regressions, both in the first period and in the second period. Moreover, the values of the coefficients in the two samples are very similar. The credit risk on debt issued by both Danske Bank and the Danish government co-moves with the German CDS rate, suggesting the relationship of the two assets with the safe haven has been constant. The observed signs make economic sense, since a general increase in global risk is likely to raise riskiness of the Danske Bank, and the Danish and German sovereign debts at the same time. In the last period, ∆ log CDS DE t has hardly moved, see Figure 3, which can explain why both the coefficients are close to zero here.
The evidence is different when focusing on the co-movement with ∆ log CDS EU t . The coefficients for both regressions are always positive and significant in the three periods 10 , but with large differences across periods and between the two dependent variables. We find a substantial decrease of the coefficient in the second period for both dependent variables, from 0.741 to 0.156 and from 0.278 to 0.058 for DB and DK respectively, indicating that the exposure of Danske Bank and Danish government debt to international shocks decreased after the default of Fjordbank. We interpret this drop in co-movement as a sign that, after the non-bailout episode, the systemic component became relatively less important than the idiosyncratic (company specific) component of Danske Bank's perceived riskiness. The pattern is consistent with the hypothesis that, under a regime with a strong implicit bailout guarantee, bank debt is ultimately backed by the government and hence only sensitive to systemic risk, not idiosyncratic risk, even if the latter risk may be far greater than the former. 11 Then, once the bailout guarantee is weakened, holders of bank bonds become more strongly exposed to idiosyncratic risks instead of systemic risks. Before its recapitalization, Danske Bank's idiosyncratic risks were likely perceived as considerable.
Notably, also the Danish sovereign CDS became less tightly correlated with the foreign banking sector after letting Fjordbank default, indicating that once bailouts were less likely, banking risk became less important for perceived sovereign risk. Importantly, after the recapitalization of Dansk Bank was finalized, the coefficients for the two parties diverge: for Danske Bank the coefficient increases toward the value it had before Fjordbank defaulted, whereas for the Danish CDS, it remains low and hardly significant. This indicates some success of the policy changes: The recapitalization leaves Danske Bank less exposed to idiosyncratic factors, and hence its perceived riskiness is again primarily driven by the credit risk of the international banking sector, but has no such effect for the Danish government. Under bailout guarantees perceived as weaker, the government remains less exposed to the international banking sector even though its largest bank still is.
We note that the above results hold when we control for both Danish house prices and for Danske Bank equity prices. Hence, the results do not seem driven by variation in the dynamics of house prices or in any other factor that might affect the market valuation of Danske Bank's assets.
In principle, the reduced weights on German CDS in the third sample might be driven by the German CDS and the European banking CDS index proxying similar risks in the third sample, in which case the CDS index of European banks is enough to capture foreign shocks to the Danish economy. We therefore document the co-movement between these two series, regressing ∆ log CDS DE t on ∆ log CDS EU t using the three-period regressions in (4). The results in Table 1 show that the co-movement between the German CDS and the European banking sector decreases over time and becomes statistically insignificant at the end of the sample. Hence, correlation between these two series does not seem to be behind the declining weights on the German CDS in Table 1. More likely, the very low coefficients on German CDS at the end of the sample are related to the fact that changes in the German CDS were very limited and ∆ log CDS DE t is very often close to zero in this period, see also Figure 3. 12

Default probabilities under different market conditions
Bailout events typically occur during extreme market conditions or under exceptional company-specific circumstances. In these scenarios our object of interest, the credit risk of bonds, might reach extreme values. Consequently, it display a correlation structure with the credit risk on the bonds issued by other European countries that differs from the pattern in normal times. Our linear regression approach from the previous section ignores such possible different market conditions, and they might therefore bias our estimates and provide weak identification. Hence, we extend the analysis to assess if the time-variation in default-risk sensitivities occurred in particular parts of the distribution of credit risk. ; log differences of a CDS index for the European banking sector computed by Thomson-Reuters, ∆ log CDS EU t ; log-returns on Danske Bank stocks, ∆ log P DB t ; differences of Danish real estate index, ∆HOU SE t . The coefficients are period-specific and refer to the three periods we consider in the analysis (P1, P2, and P3), namely: from the beginning of the sample up to the default of Fjordbank; from the default up to the recapitalization of Danske Bank; from the recapitalization up to the end of the sample. The regressions also include a set of control variables (coefficients available upon request): log differences of oil prices; log returns of the Euro 50 Stoxx Index; log differences of the Euro Stoxx 50 Volatility Index; difference of the liquidity risk in the money market computed as the difference between the 1-month Euribor and the Repo spread. Significant coefficients, computed with the Newey-West standard errors, are indicated as follows: 1%=a, 5%=b, and 10%=c. The last row reports the adjusted R-squared coefficients.
In particular, we are interested in whether they are more pronounced in the tails, so as to understand if there are different responses under normal circumstances than in more turbulent periods.
To this end we adopt a quantile regression method, where we hypothesize that a specific quantile of the density of the target variable (the CDS-change) is a linear function of a set of covariates. In recent years, financial applications of quantile regression methods have become increasingly common, see for instance Boyson et al. (2010), Baur (2013), and Caporin et al. (2014), among many others. We thus consider the quantile regression estimation of model (4), where the estimated parameters are associated with a specific quantile (τ ). This allows recovering the τ -quantile of the dependent variable conditional on the set of covariates. The model is defined as where, similarly to the linear case, W t contains several explanatory/control variables such as returns in the housing market and is included in all model specifications considered in this section. The quantile regression specification is comparable, in terms of choice of regressors, to that of equation (4). Therefore, the parameters of interest are still the same as those in (4), but they are now separately estimated for each particular quantile τ . For details on quantile regression estimation, see Koenker (2005). In our analysis, we consider values of τ ranging from 5% to 95% with a 5% step. We start by analysing the quantile regression (5) for the CDS of Danske Bank. Panel a) of Figure 6 shows the coefficients associated with the German CDS, the CDS of EU banks and Danske Bank stock returns over the three periods. 13 The relation with the German CDS changes over the three periods. In the first period, the relationship is present throughout the quantile distribution. In period two, it is only present for upper quantiles, while for period three it disappears for all quantiles. Hence, the removal of the implicit bailout guarantee made Danske Bank riskier, and its correlation with the German CDS vanished. The only exception is those instances when the CDS on Danske Bank were in the riskiest quantile (right tail) in the second period. In this case, a positive increase in the German CDS was positively associated with the perceived credit risk of Danske Bank.
The coefficient associated with the CDS on the European bank system is always positive and significant in the first period. In the second period, the coefficients are substantially smaller than in the first period, and significant for the upper quantiles only. This aligns with the prior hypothesis that the large bank's credit risk becomes more dominated by idiosyncratic factors when bailout is less likely, factors which were considerable for Danske Bank before the recapitalization. After the recapitalization, these idiosyncratic risks nec-essarily fall in magnitude, and the coefficient on European-wide banking risks increases across all quantiles, returning to values comparable to those of period one. The third line of the panel shows that the relationship between the Danske Bank credit risk and the bank's stock prices is never significant, confirming that changes in perceived credit risk were not driven by omitted factors correlated with stock prices.
To statistically validate the previous graphical evidence, we consider a more general model using dummy variables and derive a testing procedure from that model. The approach we follow comes from the extensive use of quantile regression methods in treatment effects analysis, typical of clinical trials, where the interest is in the response of subjects to a specific treatment. Quantile regression allows detecting the so-called quantile treatment effect that postulates a possible different impact of the treatment across quantiles. Direct estimation of the quantile treatment effect is possible by means of dummies that identify subjects that have received the treatment. In this way, it is possible to disentangle the different impacts of the treatment: the absence of impact, when dummy coefficients are all zero across quantiles; a simple location shift, with dummy coefficients that are constant across quantiles; the scale shift case, where dummy coefficients are symmetric; and the location and scale shift, where coefficients are not constant across quantiles nor symmetric. In our setting, we might identify two different treatments: the absence of a government bailout and the recapitalization. Our interest is whether these treatments affect the relation between the CDS changes and the various covariates. We thus rewrite the model in (5) in the following way: where i = DB, DK, while D 1,t , D 2,t , and D 0,t = 1 − D 1,t − D 2,t are step dummies. D 1,t = 1 after the default of Fjordbank and up to the recapitalization of Danske Bank, D 2,t = 1 after the recapitalization of Danske Bank, and both are zero otherwise. 14 The estimation of model (6) for a given quantile τ allows testing a null hypotheses of parameter stability across periods. We thus proceed to test the following null hypotheses i) H 0 : β 1,j,τ = β 2,j,τ ii) H 0 : β 1,j,τ = β 3,j,τ .
for j = 1, 2. The Wald-type test statistics can be easily derived given the asymptotic properties of quantile regression estimators, see Koenker (2005). The results to the left in Table 2 show that, for Danske Bank, the coefficients on German 14 We also consider a version of the test associated with a model specification in which the covariates ∆ log CDS DE t and ∆ log CDS EU t and the intercept are excluded. Results are qualitatively similar. The three columns refer to the three subsamples we consider. The plot reports the estimated coefficients across quantiles and the 95% confidence interval obtained by a boostrapping approach.
sovereign debt are significantly different only in the lower end of the quantile distribution, and these differences are primarily significant for period 3. In contrast, for period 2 the coefficients on European banks are significantly different from period 1 across the quantile distribution, while the difference is insignificant for period 3. This is the same pattern as we saw in Figure 6.  Table 2: Wald test for zero restrictions for the coefficients of the main covariates in equation (6). The null hypothesis is that covariates impact on the dependent variables (∆ log CDS DB t and ∆ log CDS DK t ) equally across periods, as in equations (4) and (5). Column P2 compares the estimates in the second period in our analysis to estimates in the baseline first period, the null hypothesis in (4); column P3 compares estimates in the third period to estimates in the baseline first period, as in the null hypothesis (5). The covariates that we restrict and test are ∆ log CDS DE t and ∆ log CDS EU t . Bold numbers indicate p-values below 5%.
Next, we consider the quantile regression for the CDS of the Danish sovereign bonds. Panel b) of Figure 6 (and Table A.3 in Appendix) shows that the major difference from the results for Danske Bank is related to the coefficient on the European banking sector in period three. Across the quantiles considered the coefficient seems to drop from period one to period two. It then stays low from period two to period three. Hence, the dependence between the risk on the Danish government debt and that on the foreign banking sector has disappeared after the non-bailout episodes, while it was present before the non-bailout events. The coefficients are approximately zero for some of the central quantiles. The Wald tests in Table 2 confirm the graphical evidence and imply that we can reject the null of equal coefficients for most quantiles when comparing the first with the third period. Moreover, the coefficient changes for the German sovereign CDS are statistically significant across the quantile distribution. This is also supported by the evidence on the upperright panel of Figure 6. Overall, the combined non-bailout and recapitalization events were associated with a clear break in the relation between Danish sovereign risk and the covariates, indicating that the sovereign risk became less closely related to other risk factors.
To further dissect the empirical findings, we perform two specification tests on the outcomes of the quantile regression in equation (5). First, we verify coefficient stability across quantiles (the so-called "slope equality test), contrasting the coefficients of the median with the coefficients of the upper 90% and 95% quantiles. The null hypothesis is the equality of the quantile regression coefficients at the three quantile levels, and its rejection suggests that the covariates have different impact at the different quantiles of the dependent variable. Table 3 reports results for the tests of stability of the coefficients associated with German CDS, European bank CDS, and Danske Bank log returns in the three periods. In the case of Danske Bank CDS, in the first period the coefficients associated with the three variables are stable across quantiles. For the second period, however, the coefficients for ∆ log CDS DE t and ∆ log CDS EU t are not stable, and the null is rejected. The evidence is opposite for the third period where the null hypothesis of coefficient stability is not rejected for any variable. The results are similar for the Danish sovereign CDS.
Second, we focus on a test that evaluates the symmetry of the coefficients. In particular, this test evaluates if the slope of the coefficients changes when moving from the left side of the median to the right side. Similarly to the previous set of tests considered, we are interested in evaluating if there is an asymmetric response after specific events. The quantile symmetry test is based on 0.05, 0.10, 0.50, 0.90, 0.95 quantiles, and the null hypothesis is symmetry in the impact of the covariates on the dependent variable, i.e., β(0.05) + β(0.10) + β(0.90) + β(0.95) = 4β(0.5), where β(τ ) = [β 1,τ , β 2,τ , . . . , β N,τ ] is the vector of parameters at a given quantile. The results reported in Table 3 provide a clear answer: as for the slope tests, the rejections only occur in the second period for the German CDS and European banking CDS.
The change in the bailout policy associated with the two defaults increases the idiosyncratic risk of Danske Bank, but, if the Danske Bank CDS is in its upper tail, then increases in the German CDS and European banking CDS will affect Danske Bank, as one might expect. For the other two periods, the responses are more uniform across quantiles. Therefore, it seems that the defaults of Amagerbanken and Fjordbank resulted in a location and scale shift; the recapitalization of Danske Bank restored normality for Danske Bank and a new regime for Danish government CDS. Our quantile regression analysis confirms that these results are not just driven by market conditions.

Conclusion
New regulations limit the scope for governments to bail their banks out from financial stress. These regulations are at least partly motivated by the hypothesis that bank bailouts might fuel sovereign risk and backfire as greater sovereign riskiness weakens the banks' balance sheets and thus re-ignites credit risk in the financial sector. We shed light on this channel in a setting where the authorities decided to let distressed banks default and left the main bank to privately recapitalize. Our evidence suggests that the no-bailout policy helped to curb the feedback between bank and sovereign risk and reduce the exposure of the government to external conditions in the banking sector. This conclusion is based on an indirect testing approach to deal with endogeneity problems. This approach is based on both linear regressions and quantile regressions which account for possible asymmetries between crisis periods and normal times. We also present quantile regressions as a treatment effect approach. The purpose of this is to study whether the new policy was associated with a location shift, a slope shift, or both. The latter turns out to be the case. Our analysis offers empirical support to regulation policies that limit bank bailouts and encourage market based solutions, such as recapitalization. It also provides new tools, based on indirect testing and quantile regressions, to investigate the interplay between sovereign and private banking risks.  Table A.1: Quantile regression results for delta-logs Germany Sovereign CDS across a range of quantiles (first column). The conditional quantile specification includes control variable whose coefficients are not included in the present table. Coefficients reported refers to the intercept and the Delta-logs of EU Banks CDS across the three subsamples of our analysis. Significant coefficients are indicated as follows: 1%=a, 5%=b and 10%=c.  Table A.3: Quantile regression results for delta-logs Danish sovereign CDS across a range of quantiles (first column). The conditional quantile specification includes control variable whose coefficients are not included in the present table. Coefficients reported refers to the intercept, the Delta-logs of EU Banks CDS, the Delta-Log of Germany Sovereign CDS, the Danske Bank equity return, and the Housing index changes, across the three subsamples of our analysis, P1=first period, P2= second period, P3=third period. Significant coefficients are indicated as follows: 1%=a, 5%=b and 10%=c. Standard errors computed by bootstrap.   (2014), based on a VAR with two lags (p=2) and an horizon of H = 12 days for the impulse-response functions.