Regime-Dependent Sovereign Risk Pricing During the Euro Crisis

Previous work has documented a greater sensitivity of long-term government bond yields to fundamentals in Euro area stress countries during the euro crisis, but we know little about the driver(s) of regimeswitches. Our estimates based on a panel smooth threshold regression model quantify and explain them: 1) investors have penalized a deterioration of fundamentals more strongly from 2010 to 2012; 2) a key indicator of regime switch is the premium of the financial credit default swap index: the higher the bank credit risk, the higher the extra premium on fundamentals; 3) after ECB President Draghi’s speech in July 2012, it took one year to restore the non-crisis regime and suppress the extra premium.


Introduction
Financial market participants have a particular taste for locutions that describe the dynamics of asset prices. In 2011, when sovereign spreads for European peripheral countries successively soared, bond market participants asserted the presence of a cliff risk, the point at which a small shift in a bond's value can have a big impact on its price. 1 A similar pattern was emphasized by policymakers (with different terminology) when they complained about growing mistrust on the part of investors, a fact that drove self-reinforcing dynamics. 2 A way to picture these comments is to say that sovereign risk pricing is regime-dependent and subject to threshold effects.
It is clear from Fig. 1, which plots spreads between 10-year peripheral and German sovereign bonds, that the trend breaks after 2010, a break that is hard to reconcile with the gradual deterioration of economic conditions. 3 There is an extensive body of research examining sovereign bond prices in the context of the euro crisis, and we have learned several important lessons. First, the massive holding of peripheral sovereign bonds by the Eu-1 See for example "Bond investors fear cliff risks.", Financial Times, November 7, 2011. In this paper, we integrate these different pieces by exploring the possibility that the switch to the crisis regime was triggered by the deterioration of the banks' risk, the liquidity spirals, or both: two endogenous mechanisms potentially implying self-amplifying dynamics. We also control for alternative 4 "Irish bond yields leap after selling wave", Financial Times, 10 November 2010.
3 mechanisms, such as the rise of systemic risk in the market and the rise of volatility on several market segments. 5 These questions require testing for regime-switching dynamics in bond spread determination and investigating the triggers. To do so, we use the smooth transition regression model developed by Terasvirta (1996), extended in panel by González et al. (2005). Contrary to the alternative family of nonlinear models employed in previous works, the STR model offers a parametric solution to account for nonlinearity by allowing the parameters to change smoothly as a function of an observable variable. We exploit this advantage by taking an off-the-shelf model estimating the impact of economic fundamentals on the spread of sovereign bonds, and we consider potential threshold variables to account for the time variability of the estimated coefficients. We compute an original set of domestic and aggregate indicators for banking and liquidity risk. Our linearity tests establish a ranking among hypothetical drivers of self-reinforcing effects, and we identify the prominent driver of regime switch following Gonzalez et al.,  (2014)).
Technically our work imposes fewer constraints than previous work on the functional form of nonlinearities and allows parameters to change smoothly as a function of an observable variable. The innovations here are therefore 6 Again, we thank the referee for this suggestion.

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the identification of the amplification mechanisms; pinpointing the banksovereign nexus working through aggregate credit risk for financial names; quantifying the resulting change in the relative weight of the determinants; and documenting the reversion process after the crisis. More generally, documenting nonlinear dynamics in asset pricing during a crisis episode should contribute to a better understanding of drivers of financial instability.
The remainder of this paper is organized as follows. Section 2 reviews the abundant literature on sovereign bond pricing during the euro-crisis in order to specify our contribution. Section 3 introduces the PSTR specification methodology and the test procedure. Section 4 summarizes our data-set, and Section 5 discusses the estimation results. Section 6 concludes. investigation is by Coimbra (2014), who shows how the initial shock is exacerbated and feeds back to credit conditions. After a rise in sovereign risk, the banks' VaR constraint binds, which reduces their demand for sovereign bonds, thereby raising the sovereign risk premium. This in turn leads to adverse sovereign debt dynamics, which raise sovereign risk.  investors are more selective about the quality of assets they accept as collateral. Their demand for the sovereign bonds that are perceived to be more risky declines, thereby raising the sovereign risk premium. So there is a liquidity spiral: a falling sovereign bond market leads financial intermediaries to fly to liquidity, and this amplifies the effects of the initial price reduction.
Relatively small shocks can cause liquidity suddenly to dry up, leading to a major correction of asset prices.
We have learned, therefore, that banking credit risk and liquidity deterioration affected sovereign credit risk during the euro crisis. In addition, theoretical models point to endogenous amplification effects. Consequently, handling these variables as extra regressors in the sovereign risk-pricing model 8 Stiglitz (1982) and Geanakoplos and Polemarchakis (1986) initially pointed out this externality. Union. They also find significant differences in the coefficient weight of fiscal space in determining sovereign risk in peripherals versus core EMU members.
They attribute this difference to the fact that international investors perceive which EMU members legitimately qualify as Optimal Currency Area members. This is intellectually appealing, but the interpretation cannot be tested in their empirical framework because it does not allow them to test the potential drivers of observed nonlinearities. Our objective here is to relax linearity and allow the spread determination model to change according to an observable signal that sets off amplifying spirals. We now describe our empirical strategy.
for countries i = 1, . . . , N and t = 1, . . . , T . Here µ i represents individual fixed effects, X it is a set of variables that capture credit risk, liquidity risk and international risk aversion and u it are i.i.d. errors. g(.) is a continuous transition function bounded between 0 and 1. We use a logistic function of order 1 that has an S shape: where q is the observable threshold variable. The gamma parameter determines the smoothness, i.e., the speed at which the vector of coefficients goes cases, the test is non-standard, since the PSTR model contains unidentified nuisance parameters under H 0 (Davies, 1987). The solution is to replace the transition function, g(q it ; γ, c), with its first-order Taylor expansion around γ = 0 and to test an equivalent hypothesis in an auxiliary regression. We then obtain: In these auxiliary regressions, parameter θ 1 is proportional to the slope parameter γ of the transition function. Thus, testing linearity against the PSTR simply consists of testing H 0 : θ 1 = 0 in (3) for a logistic function 11 with the usual LM test. The corresponding LM statistic has an asymptotic Before proceeding to the estimation, we present our data.

Data description
The estimation of the model of Eq.(1) is subject to two major data constraints. On the one hand, macroeconomic fundamentals have a low frequency (annual, quarterly or monthly), while our financial data are daily.
Therefore we transform all series to monthly data. We calculate the monthly average of the daily series and we transform quarterly to monthly using

Determinants of the sovereign bond spread
Our dependent variable is the long-term government bond spread, which prices the country risk. It is defined as the difference between country i's government bond yield and the risk-free rate of the same maturity. For each country in the sample, we use the long-term German yield, which is the benchmark risk-free rate for the Euro area (Dunne et al., 2007), and the government yield of this country at the same maturity. We rely on daily observations of 10-year bond yields provided by Bloomberg, from which we compute a monthly average. 11 The descriptive statistics of our variables are presented in Table 1.
A key choice is the set of explanatory variables included in X t in Eq (1). The government bond yield spread represents the risk premium paid by governments relative to the benchmark government bond 12 . From a theoretical perspective, these instruments can be priced by decomposing the risk premium into credit risk and liquidity risk. 13  14 ables are economic activity and the country's competitiveness. We proxy economic activity with four alternative variables: unemployment has an expected positive sign, the manufacturing production index, the new housing permits (from Eurostat) and the industrial production index (IMF) have all the expected effect to reduce the spread when they increase (negative coefficient). The country's competitiveness is proxied with the real effective exchange rate defined as the relative price of domestic to foreign consumer price index (source: IFS). An increase is an appreciation, so a deterioration of competitiveness implying that the expected coefficient is positive. In addition we use the trade balance, which is expected to have a negative coefficient (Eurostat). 15 Second, we include a variable for liquidity risk, proxied by the bid-ask spread of the dependent variable; it is expected to have a positive coefficient, because an increase of the bid-ask spread is a deterioration of liquidity. Because the liquidity effects were mixed in previous studies, we also use the country's share of total outstanding Euro-denominated long-term government securities issued in the Euro zone. The sign of the coefficient is ambiguous: it is expected to be negative because a higher ratio means a higher liquidity, but it may turn positive because it also means a higher relative stock of debt. Data are available on a monthly basis from the European Central Bank (ECB), while the bid-ask spread is taken from Bloomberg. We include the CBOE Volatility Index (VIX) as a measure of international risk aversion, because it is often considered to be the world's premier barometer of investor sentiment and market volatility (e.g., Rey, 2013). The coefficient is expected to be positive.
Last, we control for the effect of non-standard monetary measures adopted by the ECB during the crisis. In May 2010, the ECB decided to start the Securities Markets Programme (SMP) with large securities purchases in order to address tensions in certain market segments. 16 We use the amount of se-

Endogenous drivers of nonlinearities, two hypotheses
We present the set of financial data used to capture our two hypotheses, . The more bearish the market, the closer to 1 the indicator.
• Euribor-OIS spread is calculated as the difference between the Euro Interbank Offered rate and the overnight indexed swap rate.
This indicator must be taken with some caution because of the alleged manipulation of the Euribor rate.

Liquidity spirals
• Aaa/10-year Bund spread denotes the spread between European corporate bonds rated Aaa and the 10-year German Bund. It is a standard measure of liquidity premium, because even the highest-rated corporate bonds tend to be less liquid than Treasury securities. All corporate bond indices are Markit i-boxx European corporate bonds, taken from Datastream.
• High-yield bond/Baa spread denotes the spread between "junk bonds", i.e. bonds with too low a rating to be considered investmentgrade, and Baa-rated corporate bonds, the lowest-rated bonds considered as investment-grade. High-yield bonds are issued in smaller quantities and traded by a limited set of investors (institutional investors are banned from the market) in comparison with Baa-rated bonds, implying a liquidity premium to compensate investors for holding the less liquid asset.
• 10-year swap spread. The fixed-rate payment leg of a swap is expressed as the Treasury yield plus a spread that compensates investors for the fact that claims on fixed-rate payments are considerably less liquid than Treasury securities.
During a liquidity run, investors fly to quality because of asymmetry of information, so we complement our set with the following: • StockbondsCorr measures the correlation between domestic stock total return indices and the total return German Bund index. The correlation between stock and government bond returns is usually significantly negative during financial crises, because investors consider government bonds safer. We compute the correlation over rolling three-month periods using the domestic stock index of each country of our panel and the 10-year Bund index taken from Datastream. We use the negative values of the correlations, so that an increase in the measure corresponds to higher flightto-quality.
• Cross-section dispersion bank computes the cross-section dispersion of bank stock returns to capture uncertainty about the relative quality of banks and to proxy asymmetry of information.
The intuition is that the larger the cross-section dispersion, the larger proportion of returns is unexpected, so the larger the information asymmetry. It is calculated using daily data on the S&P banks in terms of market value. 19

Control Variables
We control for alternative mechanisms, such as the rise of systemic risk in the market and the rise of volatility on several market segments

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• DomsticIndex is the matrix of the domestic stock returns indices of the five countries in our panel (PSI, IBEX, ATHEX, FTSEMIB, ISEQ).
• RvolBonds captures bond market volatility using the 10-year German government bond index. It is the realized volatility computed as the monthly average of absolute daily rate changes.
• Rvol Nonfi is the realized volatility of domestic non-financial sector stock market indices taken from Datastream.
• Rvoldoll, Rvolyen and Rvolpound are the realized volatility of three bilateral euro exchange rates for the US dollar, the Japanese yen and the British pound respectively.

Estimation results: Nonlinear dynamics in the European sovereign market
We recall that the PSTR specification of the spread is as follows: for i = 1, ..., n and t = 1, ..., T, X represents the vector of determinants, µ i the country fixed effects, g(.) the threshold function, q it the threshold variable, γ the smooth parameter, c the location parameter. 21

The changing composition of the yield spreads over time
In order to test the linearity assumption and select the optimal threshold variable, we need a single specification for the whole set of threshold variables. Selecting explanatory variables by linear models might not be appropriate, since some variables could be important in a nonlinear way. 21 So we select the common specification using a time-varying PSTR (TV-PSTR) which allows the coefficients to vary with time. It has both advantages of allowing non-linearity and not imposing a particular observable threshold variable. To proceed, we estimate a TV-PSTR on alternative specifications and select the optimal specification according to information criteria. 22 The linearity test results reported at the bottom of Table 2 21 We thank the anonymous referee for this comment. 22 We test the largest possible vector of determinants by simultaneously including several proxies of the same effect (for example we include the real exchange rate and the trade balance together). The only exception is the four alternative proxies for economic activity because of their strong correlation.

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vestors have priced sovereign risk differently during the crisis, and the transition from the non-crisis to the crisis regime has taken two years. The information criterion suggests that the second specification including the manufacturing production index is optimal (Schwarz = -0.65). In the following we focus on this specification to comment on the changing composition of the spread determinants over time.  )). So far we have allowed the coefficients to vary over time, but we argue that the regime shift may be endogenous due to self-reinforcing dynamics. What are the drivers of regime shift? In the following, we answer by relaxing the linearity assumption again and we allow the coefficients to vary with the different observable variables that capture the bank-sovereign nexus, liquidity risk, and the controls.

Linearity tests: the prominent role of the bank-sovereign nexus
We now run linearity test on the optimal specification (3 in Table 2) using observable threshold variables instead of time. The linearity test results reported in Table 3 clearly reject the null hypothesis of a linear relationship, regardless of which threshold variable is included in the specification. To 24 This effect is confirmed in two out of four specifications reported in Table 2 identify the prominent determinants of bond pricing shifts, we select the best threshold variables, which as suggested by González et al. (2005), are those which leads to the strongest rejection of the linearity hypothesis.
The ranking of the test statistics reveals that four out of the five proxies indicator CmaxFi is more efficient (Table 4). So in the last step of our empirical investigation, we estimate the two specifications to examine the variation of coefficient loads. This finding leads us to split our sample into two sub-samples, one including

Heteroegeneity in the sample
Italy, Spain and Portugal, the other Greece and Ireland. The smaller subsample still has 162 observations, which is sufficient for reasonably precise and stable estimates.
We re-estimate the model in each sub-sample (Tables 5 and 6). We obtain a parsimonious specification by adopting a general-to-specific modeling approach, where we eliminate variables based on their statistical significance and the Schwartz information criterion.

Italy, Portugal and Spain
Results in Table 5  in this sub-sample: when we plot the evolution of the weight, we observe that the increase is very limited. 25 In sum, the market discipline effect works through a higher sensitivity to the countries' perceived competitiveness rather than the fiscal situation. Last, the SMP program does not have the expected negative effect on the yield spread.

Greece and Ireland
The results of the second sub-sample including Greece and Ireland reported Table 6 also indicate that the yield spreads have become more sensitive to fundamentals since 2010. Figure 4 plots the smooth transition to the crisis regime. The fact that the transition is smooth and not sharp in this sample may be due to the presence of Greece, the epicenter of the crisis from which contagion effects then spread.
Contrary to the previous sample, we find that an extra premium is applied to fiscal imbalances: the coefficient of debt-to-GDP increases dramatically in the second regime (β 1 +β 2 = 0.868 versusβ 1 = −0.22) as well as the absolute value of the coefficient of fiscal balance (β 1 +β 2 = −0.56, negative 25 The graph is available upon request. as expected, versusβ 1 = 0.34). So the higher sensitivity to fiscal imbalances seen in the larger sample was driven by the presence of Greece and Ireland, two counties that have faced fiscal deterioration to a much larger extent than Italy, Spain and Portugal. In addition, a higher sensitivity is detected for competitiveness (the real effective exchange rate and trade balance have both a higher absolute coefficient in the second regime) and economic activity (manufacturing production index). We do not detect a significant effect of the SMP program in this sub-sample either.
In total, splitting the sample highlights that an extra premium on fiscal deterioration is applied in Greece and Ireland only.

Robustness
To check the robustness of our results, we proceed to alternative estimates: • In the first sub-sample (including Italy, Spain and Portugal), overall amplification effects are confirmed when Cmax Fin is used as a threshold variable in an alternative specification reported in Table 5.
In particular, these estimates confirm that fiscal imbalances are not priced more severely in the crisis.
• Banking CDS and sovereign bonds may price the same information, which would raise an endogeneity bias due to simultaneity. To address this, we re-estimate our optimal model by lagging the threshold variable. Linearity is strongly rejected (LM = 179.9), and amplification effects are confirmed.
• Last, we check that our nonlinearity finding does not result from omitting the financial CDS index as an explanatory variable so that a linear regression would be enough. 26 Our results are not affected by the introduction of the financial CDS index in the vector of determinants (X it in Eq. 1), and its coefficient is not significant.  26 We thank the referee for this comment.

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of our optimal specification in both sub-samples up until March 2014, the maximum date with available data. 27 The takeaway is that the evolution of the coefficient load is very similar to the previous estimation period and the same regime-shifting mechanism operate in reverse. Indeed, Figure 5

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We estimated the sovereign spread of five peripheral members of the euro area using panel non-linear estimation methods. Our objectives were threefold: 1) test for nonlinear sovereign bond pricing 2) discriminate between two potential drivers of non-linearity, the sovereign-bank nexus and liquidity spirals and 3) quantify the threshold effects and coefficient regime shifts in order to draw lessons for economic policy.
Our PSTR estimations confirm the previous finding that the changing sensitivity of bond yields to fundamentals is necessary to explain yields dur- Beyond the specific Eurozone crisis event, our findings may contribute to a better understanding of financial instability, with macroprudential lessons.
The financial price determination models prevailing in normal times may be invalid during crises; the risk pricing of financial assets is fundamentally state-dependent. Our empirical framework gives a simply implementable method to track regime changes and identify the trigger. It is key to act on it quickly. When the risk trigger is systemic, the central bank can change the state to restore the pricing dynamics, by virtue of its unique role as lender of last resort.  Debt − to − GDP 0.137 * * *   Debt − to − GDP 2 0.000 (−1.14) 0.001 * * * significant at the 5% level and (***): significant at the 1% level.β 1 and β 2 correspond to the coefficient in Eq (11). β 1 is the coefficient in the first extreme regime . The coefficient in the second extreme regime is β 1 + β 2 . Debt − to − GDP −0.222 * *