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Journal of Banking & Finance 50 (2015) 308–325

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Journal of Banking & Finance
journal homepage: www.elsevier.com/locate/jbf

A macro-?nancial analysis of the euro area sovereign bond market q
Hans Dewachter a,b,c, Leonardo Iania a,d,?, Marco Lyrio e, Maite de Sola Perea a
a

National Bank of Belgium, de Berlaimontlaan 3, 1000 Brussels, Belgium Center for Economic Studies, University of Leuven, Naamsestraat 69, Leuven, Belgium c CESifo, Poschingerstr. 5, 81679 Munich, Germany d Louvain School of Management, Place de Doyens 1, bte L2.01.02 à 1348 Louvain-la-Neuve, Belgium e Insper Institute of Education and Research, Rua Quatá 300, S?o Paulo, Brazil
b

a r t i c l e

i n f o

a b s t r a c t
We estimate the ‘fundamental’ component of euro area sovereign bond yield spreads, i.e. the part of bond spreads that can be justi?ed by country-speci?c economic factors, euro area economic fundamentals, and international in?uences. The yield spread decomposition is achieved using a multi-market, no-arbitrage af?ne term structure model with a unique pricing kernel. More speci?cally, we use the canonical representation proposed by Joslin et al. (2011) and introduce next to standard spanned factors a set of unspanned macro factors, as in Joslin et al. (forthcoming). The model is applied to yield curve data from Belgium, France, Germany, Italy, and Spain over the period 2005–2013. Overall, our results show that economic fundamentals are the dominant drivers behind sovereign bond spreads. Nevertheless, shocks unrelated to the fundamental component of the spread have played an important role in the dynamics of bond spreads since the intensi?cation of the sovereign debt crisis in the summer of 2011. ? 2014 Elsevier B.V. All rights reserved.

Article history: Received 30 August 2013 Accepted 11 March 2014 Available online 25 March 2014 JEL classi?cation: E43 E44 E47 Keywords: Euro area sovereign bonds Yield spread decomposition Unspanned macro-factors Fair spreads

1. Introduction The creation of the European Economic and Monetary Union (EMU) in January 1999 led to an unprecedented convergence of government bond yields of eurozone countries,1 with remaining yield differentials being mainly attributed to differences in the levels of credit and liquidity risks among countries. The surge in the spreads between euro area sovereign bond yields and market risk-free rates, particularly since 2011, has raised questions about

q We thank Dennis Bams, Roberto De Santis, Peter Schotman, Raf Wouters, two anonymous referees, and seminar participants at the International Conference on Economics (Turkish Economic Association), VIII Annual Seminar on Risk, Financial Stability and Banking (Central Bank of Brazil), Conference on ‘‘The Sovereign Debt Crisis and the Euro Area’’ (Bank of Italy), CORE (UCL), and Maastricht University for many helpful discussions. The views expressed are solely our own and do not necessarily re?ect those of the National Bank of Belgium. All remaining errors are our own. Marco Lyrio is grateful for ?nancial support from the CNPq-Brazil (Project No. 303066/2010-5). ? Corresponding author. Tel.: +32(0)10 478439. E-mail addresses: hans.dewachter@nbb.be (H. Dewachter), iania.leonardo@ gmail.com (L. Iania), marco.lyrio@insper.edu.br (M. Lyrio), Maite. DeSolaPerea@nbb.be (M. de Sola Perea). 1 See Pagano and von Thadden (2004) for a detailed description of this process.

the underlying drivers of bond spreads and whether economic fundamentals (country-speci?c and international) alone are able to explain such dynamics. In this paper, we extend the approach proposed by Joslin et al. (2011) to a multi-market setting in order to decompose yield spreads of a set of euro area countries into a fundamental and a non-fundamental component. The fundamental component can be justi?ed by a set of country-speci?c factors, euro area economic fundamentals, and international factors. The non-fundamental part incorporates liquidity and political uncertainty effects, in addition to remaining common factors which might be proxying for redenomination risk, i.e. the fear by investors that at least one country would abandon the euro area.2 Our paper is part of a broad literature that studies the determinants of bond yield differentials in the eurozone. Despite its various approaches, we view this literature as divided in two main strands. The ?rst one relies mainly on regressions of yield spreads on a number of fundamental variables representing credit, liquidity, and international risks (see, for instance, Favero et al.
2 The term mispricing has been used to designate the non-fundamental component of sovereign bond spreads, i.e. the part of bond spreads not explained by differences in ?scal and macroeconomic fundamentals. See, for example, De Grauwe and Ji (2012) and Di Cesare et al. (2012).

http://dx.doi.org/10.1016/j.jbank?n.2014.03.011 0378-4266/? 2014 Elsevier B.V. All rights reserved.

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(2010)). Although there does not seem to be a clear consensus on the relative weight of each component, most studies in this strand of the literature point to the importance of both credit and liquidity risks in explaining differences in euro area bond spreads for the period before the start of the sovereign debt crisis in late 2009. Among the most recent studies, and particularly those focused on the sovereign debt crisis in the euro area, different approaches have been used to identify the extent to which bond spreads are justi?ed by macroeconomic and ?nancial fundamentals. Several papers have found evidence of the importance of a country’s macroeconomic situation in determining its sovereign bond yields, as these depend on its ?scal position and ability to honor its commitments. Bayoumi et al. (1995) ?nd evidence of the impact of the debt level on bond spreads for the U.S., while later studies reach similar conclusions for euro area countries (Hallerberg and Wolff (2006), Faini (2006), and others). Thus, the fundamental part (i.e. related to a country’s creditworthiness) of bond yields may be estimated using mainly country-speci?c indicators. Aizenman et al. (2011) develop a model of pricing of sovereign risk for a number of European and non-European countries where sovereign credit default swap (CDS) spreads are regressed on ?scal position indicators and other macroeconomic variables. According to their results, CDSs have been mispriced in euro area periphery countries, being excessively low in tranquil periods and too high during the recent sovereign debt crisis. Nevertheless, other factors may be behind movements in sovereign bond spreads, including the level of international risk aversion and ?nancial contagion, the latter being of particular relevance within a currency union. In the case of the euro area, market liquidity, cyclical conditions and risk appetite, which are related to the level of short-term rates, have been identi?ed as important factors behind the level of bond spreads (Manganelli and Wolswijk, 2009). Attinasi et al. (2011), for example, control for the effect of such factors on euro area sovereign bond spreads vis-à-vis German sovereign bonds. De Santis (forthcoming), on the other hand, considers the impact of contagion from events in Greece to other eurozone countries. He concludes that both sovereign solvency risk and contagion have played an important role in the increase of bond spreads in eurozone countries during the recent debt crisis. Giordano et al. (2013), in turn, distinguish between three types of contagion, with a ‘pure contagion’ not being justi?ed by fundamentals. They do not ?nd evidence of this kind of contagion during the debt crisis in the euro area. Finally, Caceres et al. (2010) also ?nd evidence of contagion originating in the most affected countries in the eurozone. A second strand of the literature includes papers that estimate multi-issuer, no-arbitrage, af?ne term structure models. For example, in order to analyze the dynamics of bond spreads of EMU countries, Düllmann and Windfuhr (2000) employ standard interest rate models using the short rate and the spread between risky and risk-free bonds as factors, while Geyer et al. (2004) rely on the estimation of purely latent factor models. Borgy et al. (2011), on the other hand, employ a multi-country af?ne term structure model making use of macroeconomic variables as factors.3 They estimate the joint dynamics of eight euro area government bond yield curves making use of three common euro area macro factors and one latent ?scal factor for each country. They focus on the effect of ?scal policy on the perceived sovereign default probabilities for each country and conclude that ?scal factors are the main determinants in the increase of yield spreads since 2008. Ang and Longstaff (2013) use a multi-factor af?ne framework to disentangle the systemic and country-speci?c shocks on CDS spreads of government
3 Amato and Luisi (2006) use a combination of macroeconomic and latent variables in an af?ne term structure model of defaultable bonds but their model is applied to U.S. corporate bond spreads.

bonds for the U.S., individual U.S. states, and eleven euro area countries. Their ?ndings point to a stronger impact of systemic risk among European sovereigns than among individual U.S. states. This is interpreted by Battistini et al. (2013) as evidence of a possible breakup of the currency union. These authors estimate a dynamic latent factor model to identify the shocks driving the sovereign yields of each euro area issuer. They distinguish between a common (systemic) factor, capturing the perceived risk of a collapse of the euro system, and a country-speci?c factor, capturing each country’s credit risk. Using euro area data from 2008 to 2012, they conclude that yield differentials are mainly driven by country risk, particularly for eurozone periphery countries. The economic literature, therefore, ?nds evidence that both country-speci?c credit risk, contagion risk, and international risk factors are important in the determination of euro area sovereign bond spreads. Nevertheless, depending on the speci?c country under study, the effect of common risk factors not only is signi?cantly different in magnitude but also has opposite effects on bond spreads. Our model is part of the multi-issuer, no-arbitrage, af?ne term structure model literature and it differs from the extant papers in at least two points. First, we attempt to determine the fundamental component of bond spreads by using a relatively large set of observable macroeconomic factors. Our model therefore allows one to link the development of yield spreads with the evolution of the economic situation. Second, from an econometric setting, we adopt a relatively ?exible and simple methodology that overcomes most of the drawbacks related to existing af?ne term structure models. These shortcomings are related to the signi?cant amount of time necessary for the convergence of standard maximum likelihood algorithms4 and, more importantly, to the fact that the standard formulation implies that the macroeconomic risk factors are spanned by – i.e. can be expressed as a linear combination of – bond yields. This spanning condition is however overwhelmingly rejected by standard regression analysis, which shows that there is no perfect linear relation between yields and macroeconomic variables (see Joslin et al. (forthcoming)). To overcome these issues, we use the approach proposed by Joslin et al. (2011, forthcoming), extending it to a multi-issuer setting. We propose a multi-country, no-arbitrage, af?ne term structure model in which the countries share a common currency.5 Our goal is to identify the fundamental component of eurozone sovereign bond yield differentials. To this end, we estimate separately ?ve two-market models for Belgium, France, Germany, Italy, and Spain in which the Overnight Indexed Swap (OIS) rate is used as the reference rate, i.e. it serves as our benchmark market. We proceed as follows. We estimate the dynamics of a single risk-neutral measure in order to ?t the OIS yield curve and the yield curve of the respective country. This is achieved with the use of four spanned pricing factors computed as linear combinations of yields. Two of these factors are used to ?t the OIS yield curve and the other two to ?t the country’s bond yield differentials. In order to determine the effect of speci?c macroeconomic and ?nancial variables in the dynamics of bond spreads, we estimate a vector autoregressive (VAR) model combining the spanned factors with nine unspanned factors. Five of them represent country-speci?c fundamental factors, euro area economic measures, and other international in?uences. The other four factors capture the non-fundamental component of the sovereign spread, such as liquidity premia, political uncertainty,

4 For a description of the usual computational challenges faced by af?ne term structure models, see Duffee and Stanton (2008), among others. 5 Bauer and Diez de los Rios (2012) combine the methodology of Joslin et al. (2011, forthcoming) in a multi-country af?ne term structure model which includes unspanned macroeconomic risks. Their model, however, also includes foreign exchange risk.

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and common dynamics in the eurozone sovereign bond spreads. The VAR system allows for the assessment of the relative importance of economic fundamentals in the dynamics of the spanned factors and, hence, of yield spreads. We apply our model to monthly data of the mentioned countries over the period between August 2005 and May 2013. In all ?ve cases, our speci?cation is able to ?t both the OIS and the country’s yield curve rather well. Our main contribution, however, is related to the assessment of the relative importance of each group of factors for the dynamics of bond spreads. This is done by means of impulse response functions (IRFs), variance decompositions, and a historical decomposition of bond yield spreads. Our main result is clear. Both economic as well as non-fundamental risk factors are important sources of variation in bond yield spreads. Non-fundamental risk shocks are the main source of variation in bond spreads for short forecast horizons (up to one-month horizon), explaining between 35% (Germany, 5-year bond spread) and 82% (Belgium and France, 3-year bond spread) of such variation. This proportion decreases for longer forecast horizons. Overall, this proportion is the lowest for Belgium and the highest for France, where this group of factors accounts for most of the variation in bond spreads for all maturities and forecast horizons. Nevertheless, for all countries, such shocks are responsible for at least 20% of the bond spread variation for any maturity and forecast horizon. Shocks to economic fundamentals, on the other hand, gain in importance as the forecast horizon increases. For Belgium, Germany, and Italy, such shocks are the dominant source of variation in bond spreads for forecast horizons above one year. For France and Spain, those shocks also play an important role in long forecast horizons. We also illustrate the importance of each group of factors over time with a historical decomposition of bond yield spreads. Our results show that, overall, economic fundamentals are the dominant drivers behind yield differentials. Nevertheless, non-fundamental risk shocks have had a signi?cant impact on bond spreads since September 2011. The remainder of the paper is organized as follows. Section 2 presents the common-currency, multi-country, af?ne term structure model and the VAR system used to determine the in?uence of macroeconomic and ?nancial factors on bond spreads. Section 3 summarizes the data, describes the estimation method, and discusses the results. Section 4 analyses the historical decomposition of bond spreads and Section 5 concludes the paper.

yield curve. Subsequently, in line with Joslin et al. (forthcoming), we model the dynamics of the yield portfolios under the historical measure by means of a standard VAR, including (next to the yield curve portfolios) both macroeconomic and ?nancial variables. Based on the VAR dynamics, and the af?ne yield curve representation implied by the risk-neutral dynamics, we assess the relative contribution of the respective macroeconomic and ?nancial variables in the yield curve dynamics. In this analysis, we focus on the (ir)relevance of macroeconomic fundamentals in explaining the yield (spread) curve dynamics in the euro area bond market. We proceed in two steps. First, we present the common-currency, multi-country af?ne yield curve model. We then present the speci?c assumptions imposed in the VAR system. 2.1. A multi-market af?ne yield curve model This section builds on Joslin et al. (2011) who introduce af?ne yield curve models using observable yield portfolios as factors spanning the yield curve. We discuss a multi-market version of this model. We assume the existence of K fundamental and unobserved pricing factors for the yield curve of all markets, X k;t ; k ? 1; . . . ; K , collected in the vector X t ? ?X 1;t ; . . . ; X K ;t ?0 . As explained below, these factors re?ect fundamental sources of risk. They can be either common (affecting all markets) or market-speci?c (affecting a subset of markets) risk factors. The dynamics of these factors under the unique risk-neutral measure (Q) is modelled by means of a maximally ?exible af?ne VAR(1) dynamics (see Dai and Singleton (2000)):
Q Q Xt ? CQ X ? UX X t ?1 ? RX et ;
Q X

eQ t $ N ?0; IK ?;

?1?

where U is a diagonal matrix containing the distinct eigenvalues of Q Q Q UQ X ; UX ? diag ?k1 ; . . . ; kK ?, and RX is a lower-triangular matrix. We assume that the K factors determine each of the m market-speci?c, short-term interest rate in market m; rm;t , with m ? 1; . . . ; M. The dependence of the short-term interest rate of market m on the pricing factors is given by the 1 ? K vector q1 m:
1 r m ;t ? q 0 m ? qm X t :

?2?

2. The model We extend the standard af?ne yield curve model to a multimarket, single-pricing kernel framework. This framework is particularly useful in addressing issues related to the euro area sovereign bond market. Speci?cally, in the context of a common currency, it allows us to model a ?nancially integrated market by imposing a unique pricing kernel while at the same time acknowledging the possibility of country-speci?c (default) risks. The model hence features a parsimonious representation of the yield spread dynamics, allowing for both common and country-speci?c risk factors. As shown by the empirical results, the model is able to capture the most salient features of the euro area sovereign bond market, both in the cross-sectional as well as in the time series dimension. A parsimonious representation of the yield curve dynamics is obtained by focusing on the latent version of the af?ne yield curve model. This type of model imposes the no-arbitrage restriction in the context of Gaussian and linear (latent) state space dynamics under the risk-neutral measure. Following Joslin et al. (2011), we use a limited set of spanned factors – the so-called yield portfolios – to model in a consistent way the cross-sectional features of the

As such, the model allows us to introduce simultaneously several bond markets, all conditioned on the same risk-neutral probability measure. The differences across bond markets depend on the market-speci?c factor sensitivities to the respective fundamental factors, q1 m . We use a two-market setup (M ? 2?, where market 1 is a benchmark market and market 2 is the sovereign bond market of a speci?c country in the euro area. In this setting, we assume that the benchmark (risk-free) short-term interest rate is given by a constant and the sum of the ?rst two common factors, i.e. r 1;t ? q0 1 ? ?1; 1; 0; 0?X t , and the market-speci?c, short-term sovereign yield of the speci?c bond market is given by 0 r2;t ? q0 1 ? q2 ? ?1; 1; 1; 1?X t . The latter two factors drive the movements of the instantaneous spreads and can be interpreted as re?ecting market-speci?c default risk or liquidity factors; see e.g. Duf?e and Singleton (1999). As mentioned in Joslin et al. (2011) and Dai and Singleton (2000), the framework consisting of Eqs. (1) and (2) leaves open some identi?cation issues. To econometrically identify all parameters, additional restrictions need to be imposed. We follow one of the identi?cation schemes proposed by Joslin et al. (2011) (see their Proposition 2). In particular, in the context of the A0 ?n? type of model proposed in Eq. (1), we impose the following restriction on the Q-dynamics: C Q X ? 0. As a result, and imposing stationarity on the Q-dynamics, the parameter q0 m becomes proportional to the unconditional average of the short rate in each market. Furthermore, due to the latent structure of the model, we also need

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to ?x the loadings of the short-term rates on the factors X t by set1 1 ting the parameter vector q1 m to q1 ? ?1; 1; 0; 0? and q2 ? ?1; 1; 1; 1? (see also the discussion above). Conditional on this identi?cation scheme, the Q-dynamics of the canonical multi-country yield curve model can be summarized by a parameter vector for market m conn o Q Q 0 1 1 sisting of Hm ? C Q X ; UX ; RX ; qm ; qm , where C X and qm are ?xed for reasons of identi?cation. Given the risk-neutral dynamics (Eq. (1)) and the de?nition of the short-term interest rate for each market (Eq. (2)), zero-coupon bond yields can be written as an af?ne function of the state vector (see e.g. Dai and Singleton (2000)). Denoting the time-t yield in market m and maturity n by ym;t ?n?, the yield curve can be written as an af?ne function of the factors:

Mt Pt

!

? C P ? UP

! M t?1 ?R P t ?1

"

eP M ;t eP P ;t

# ?7?

where R is a lower-triangular matrix implied by the Cholesky identi?cation of structural shocks. The identi?cation is performed by ?rst including the more exogenous variables, representing international and euro area conditions, then the country-speci?c macroeconomic factors, and, ?nally, the country-speci?c yield spread factors. This allows for an immediate impact of shocks in the macroeconomic and ?nancial variables on sovereign bond spreads. In the next section, we detail the variables included in the vectors of unspanned and spanned factors. 2.3. Estimation method Three main characteristics distinguish the estimation of our common-currency, two-market af?ne yield curve model from standard macro-?nance models (see, for example, Ang and Piazzesi (2003)). First, we select a group of observed yield portfolios (spanned factors) to ?t the yield curves of the country under study and the benchmark market (the OIS rate in our case). Second, we choose a set of macroeconomic and ?nancial variables (unspanned factors) which might (i) have predictive content for excess bond returns over and above that of the spanned factors and (ii) help us discriminate between the relevant determinants of bond yield spreads. Finally, we focus on the dynamics of bond yield spreads with respect to the benchmark market. Our estimation procedure follows the two-step procedure proposed by Joslin et al. (2011). This procedure uses an ef?cient factorization of the likelihood function, arising from the use of yield portfolios as pricing factors. In ? ?0 particular, the likelihood function for the data vector Z t ? M 0t ; P 0t is factored into two components:

ym;t ?n? ? Am;n ?Hm ? ? Bm;n ?Hm ?X t ;

? 3?

where the functions Am;n ?Hm ? and Bm;n ?Hm ? follow from no-arbitrage difference eq. (see Duffee (2002),Dai and Singleton (2000) and Ang and Piazzesi (2003)). Assuming there are N yields per market, we collect all market-speci?c yields in a vector ? ?0 ym;t ? ym;t ?1?; . . . ; ym;t ?N? . De?ning

Am ?Hm ? ? ?Am;1 ?Hm ?; . . . ; Am;N ?Hm ??0
and

? ?0 Bm ?Hm ? ? Bm;1 ?Hm ?0 ; . . . ; Bm;N ?Hm ?0 ;
the market-speci?c yield curve is given by:

ym;t ? Am ?Hm ? ? Bm ?Hm ?X t :

? 4?

Stacking the yields and the functions Am ?Hm ? and Bm ?Hm ? across the h i0 ? ?0 M markets, Y t ? y01;t ; . . . ; y0M;t , A?H? ? A1 ?H1 ?0 ; . . . ; AM ?HM ?0 , and ? ? 0 B?H? ? B1 ?H1 ?0 ; . . . ; BM ?HM ?0 , we obtain the multi-market, noarbitrage yield curve representation:

f ?Y t ; Z t jZ t?1 ? ? f ?Z t jZ t?1 ; C P ; UP ; R? ? f ?Y t jPt ; H?:
The ?rst component, f ?Z t jZ t?1 ; C P ; UP ; R?, is the prediction density for the state vector, Z t , which is implied by the VAR(1) model in Section 2.2:

Y t ? A?H? ? B?H?X t :

? 5?

The fundamental pricing factors, X t , are unobserved. However, a suitable rotation based on yield portfolios can be used to identify an equivalent, observable, yield curve representation. These yield portfolios, de?ned as linear combinations of yields (possibly across different markets), are assumed to be perfectly priced by the noarbitrage restrictions. Formally, the lth yield portfolio with yield P l;t is de?ned by a time-invariant weight function wl such that P l;t ? wl Y t . Assuming there are (at least) K such yield portfolios, stacked in the K ? ?NM ? matrix W, the vector of yield portfolios is given by P t ? WY t . In addition, assuming zero measurement errors on the yield portfolios allows us to re-express the fundamental af?ne yield curve model in terms of the observable yield portfolios Pt . It is straightforward to show that the representation in terms of observable yield portfolios becomes:

Z t ? C P ? UP Z t?1 ? ReP Z ;t ;

eP Z ;t $ N ?0; IK ?:

?8?

The second component, f ?Y t jP t ; H?, refers to the yield curve density and is obtained from the no-arbitrage af?ne yield curve model:

Y t ? ap ?H? ? bp ?H?Pt ? RY eY ;t ;
where the loadings

eY ;t $ N?0; ILY ?;

?9?
and

h i ap ?H? ? I ? B?H??WB?H???1 W A?H?

h i Y t ? I ? B?H??WB?H???1 W A?H? ? B?H??WB?H???1 P t :
2.2. Decomposing yield curves

bp ?H? ? B?H??WB?H???1 are obtained by rotating the loadings of Eq. (5) (see Eq. (9)). This factorization allows for an ef?cient twostep maximum likelihood estimation procedure, which can be summarized as follows.  Step 1: We estimate the prediction equation (see Eq. (8)) using standard OLS regressions. This is possible since all factors included in this VAR system are observable and because there are no restrictions in the VAR dynamics. This results in the estimation of C P and UP and in a initial estimate for R which is used in step 2.  Step 2: Using a QML procedure and ?xing the parameters C P and UP of the prediction equation, we estimate the remaining 0 parameters in Eq. (9), namely UQ X ; RX ; qm , in order to ?t the yield curves of both markets. We use the OLS estimates of R as a starting value for RX , as in Joslin et al. (2011). Then, we maximize the likelihood function by a mixture of simulated annealing and simplex procedures.

? 6?

We use a standard ?rst order Gaussian VAR representation to assess the relative importance of macroeconomic and ?nancial shocks in the yield curve dynamics while maintaining the condition of no-arbitrage. This type of decomposition can be performed using the yield curve representation in Eq. (6). Given that yields are af?ne functions of the observable yield portfolios, it becomes equivalent to a decomposition of the yield portfolios, P t . Denoting the set of unspanned macroeconomic and ?nancial factors by Mt , our VAR(1) model can be written as:

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Fig. 1. Unspanned and spanned common factors. Note: VIX is the Chicago Board Options Exchange (CBOE) Market Volatility Index; ESI is the European Commission’s Economic Sentiment Indicator; F2S is the spread between the yield on the German government guaranteed bond (KfW) and the German sovereign bond, averaged across maturities; POL is the European Economic Policy Uncertainty Index; PC(Eur_spr, 1) and PC(Eur_spr, 2) are the ?rst two principal components of the standardized spreads between bond yields of the ?ve countries included in our sample and the OIS yield curve; ?nally, PC(OIS, 1) and PC(OIS, 2) are the ?rst two principal components of the ?ve OIS rates. For all series, the sample period goes from August 2005 to May 2013.

3. Empirical results 3.1. Data The model is estimated on monthly data over the period from August 2005 to May 2013 (94 observations per time series). The data used can be sorted in two groups. 3.1.1. Common factors One group consists of variables used across all markets and for all countries analyzed. It includes (i) the Chicago Board Options Exchange (CBOE) Market Volatility Index (VIX ), obtained from Datastream, which expresses the implied volatility of the Standard & Poor’s (S&P) 500 stock market index options, as a measure of global ?nancial volatility or uncertainty in ?nancial markets; (ii) the European Commission’s Economic Sentiment Indicator (ESI), a forward-looking variable which re?ects expectations regarding the euro area economic outlook; (iii) the Overnight Indexed Swap (OIS) rates for maturities of 1, 2, 3, 4, and 5 years, from Bloomberg, which re?ects the evolution of the risk-free interest rate for all euro area countries, and is also used as a reference rate to calculate the spreads of sovereign bonds at the respective maturities; (iv) the spread between the yield on the German government-guaranteed KfW (‘Kreditanstalt fur Wiederaufbau’, a government-owned development bank) bond and the German sovereign bond (from Bloomberg), averaged across maturities, which measures the liquidity premium, and can be interpreted as a common liquidity or ?ight to safety (F2S) factor across the euro area bond market6 (see De Santis (forthcoming)); and (v) the European Economic Policy
6 In the remaining of the paper, we refer to the terms ?ight to safety and ?ight to liquidity interchangeably.

Uncertainty Index (POL), produced by Economic Policy Uncertainty, which measures economic uncertainty related to policies. This index, proposed by Baker et al. (2013), is constructed based on newspaper coverage of policy-related economic uncertainty and the disagreement among economic forecasters on future economic indicators for France, Germany, Italy, Spain, and the United Kingdom. In this paper, this index is used as a general measure of political risk in the euro area. 3.1.2. Country-speci?c data Country-speci?c data series include three macroeconomic variables, obtained from Datastream7: (i) the annual growth rate of real gross domestic product (GDP); (ii) the annual in?ation of the Harmonized Index of Consumer Prices (CPI); and (iii) the annual growth rate of the public debt to GDP ratio (D/GDP), which is used to estimate the impact of the change in the ?scal position of each country on government bond spreads. Both GDP and D/GDP are available only on a quarterly basis, so they are interpolated to obtain data at a monthly frequency. Besides these macroeconomic data series, country-speci?c data include the per annum zero-coupon yield for government bonds of each of the ?ve countries analyzed for maturities of 1, 2, 3, 4, and 5 years. 3.2. Spanned and unspanned factors We now specify the vector of spanned factors or yield portfolios, Pt , de?ned in Section 2.1, which is used to explain the dynamics of the yield curves in our two-market setup. As mentioned before, we estimate the model separately for each of the ?ve countries having
7 For the series such as in?ation and GDP, the releases of May 2013 were not available. We used instead the forecasts made by the International Monetary Fund.

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Fig. 2. Unspanned country-speci?c macroeconomic factors. Note: For every country, GDP is the year-on-year growth rate of the real GDP index, CPI is the year-on-year growth rate of the Consumer Price Index, and D/GDP is year-on-year change in the debt-to-GDP ratio. For all series, the sample period goes from August 2005 to May 2013. Quarterly data are interpolated in order to obtain monthly series.

Fig. 3. Spanned country-speci?c factors. Note: For every country, PC(spr, 1) and PC(spr, 2) are the ?rst two principal components of the yield spreads between the sovereign bond yields and the OIS rates for the ?ve maturities considered. For all series, the sample period goes from August 2005 to May 2013.

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Fig. 4. Fit of the 5-year OIS rate in each of the ?ve cases. Note: The ?gure shows the ?t of the 5-year OIS rate resulting from the separate estimation of the model for each country. For all series, the sample period goes from August 2005 to May 2013.

the OIS rate as our benchmark bond market. We then describe the unspanned factors, M t , used to assess the driving forces behind yield spread movements. 3.2.1. Spanned factors We adopt a total of four spanned factors to ?t the OIS and the country-speci?c yield curves. The ?rst two factors are used to explain the dynamics of the OIS yield curve. In principle, we could choose any linear combination of observed yields to form such portfolios. Nevertheless, to avoid ?tting perfectly a set of speci?c yields and under?tting the others, we opt for extracting the ?rst ;1 two principal components of the ?ve OIS rates (PC OIS and t ;2 PC OIS ). Since these yield portfolios refer to the benchmark rate, t they are the same in the separate estimations for each of the countries. The last two factors are used to ?t the country’s bond yield spreads. We follow the same principle used for the ?rst two factors and extract for each country the ?rst two principal components of the yield spreads between the country’s sovereign yields and the ;1 ;2 OIS rates for the ?ve maturities considered (PC spr and PC spr ). As t t a result, we obtain the following vector of yield portfolios:

bond yields of the ?ve countries included in our sample and the spr ;1 spr ;2 8 OIS yield curve (PC Eur and PC Eur ). The last factor in this t t sub-group is our measure for the political uncertainty in the euro area (POL). The ?nal sub-group includes three standard economic variables related to the overall ?scal sustainability of the country. They are the growth rate of real GDP, the growth rate of the Consumer Price Index, and the growth in the debt-to-GDP ratio, GDP, CPI, and D/GDP, respectively. The vector of unspanned factors can then be represented as:

h i0 Eur spr;1 spr ;2 Mt ? VIX t ; ESIt ; F 2St ; PC t ; PC Eur ; POLt ; GDPt ; CPIt ; D=GDPt : t ?11?
All 13 factors for the ?ve countries can be seen in Figs. 1–3. Fig. 1 shows the variables which are common to all countries, i.e. the ?rst six unspanned and the ?rst two spanned factors. Fig. 2 shows the macroeconomic data speci?c to each country and Fig. 3 depicts the last two spanned factors, which are also speci?c to each country. The OIS rates and bond yield data are shown in the next section when we evaluate the yield curve ?t for each country. 3.3. Model evaluation The model ?ts the yield curve of the ?ve countries rather well. An illustration of this can be seen in Figs. 4 and 5. Fig. 4 shows the ?t of the 5-year OIS rate resulting from the separate estimation of the model for each of the ?ve countries and Fig. 5 displays the ?t of the 5-year bond yield spread for each country. Finally, Table 1 reports summary statistics concerning the bond spread ?t for all maturities and countries. Except for the last column in this table, all values are expressed in basis points. The statistics for the yield ?tting errors are presented in the last three columns. Although both the mean and standard deviation of the ?tting errors are quite low, the ?rst-order autocorrelation seems remarkably high in some
8 We have a total of 25 series of bond yield spreads since we use ?ve maturities for each of the ?ve countries in the sample.

h i0 ;1 ;2 ;1 ;2 Pt ? PC OIS ; PC OIS ; PC spr ; PC spr : t t t t

?10?

3.2.2. Unspanned factors We include a total of nine unspanned factors in the assessment of the macroeconomic and ?nancial determinants of sovereign bond yield spreads, which can be sorted in three sub-groups. The ?rst one consists of variables capturing the global tension in the ?nancial market and the expectation regarding the European economic situation, VIX and ESI, respectively. The second sub-group contains four factors which account for non-fundamental risks in the euro area bond market. The ?rst one is our common liquidity factor in the eurozone bond market (F2S). The next two non-fundamental factors capture the common dynamics of euro area sovereign bond yield differentials. They are obtained as the ?rst two principal components of all the standardized spreads between

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Fig. 5. Fit of the 5-year bond yield spread for each country. Note: The ?gure shows the ?t of the spread between each country 5-year bond yield and the 5-year OIS rate. For all series, the sample period goes from August 2005 to May 2013.

Table 1 Diagnostic statistics of the estimated models Mean Data (bp) Belgium spread1yr spread2yr spread3yr spread4yr spread5yr France spread1yr spread2yr spread3yr spread4yr spread5yr Germany spread1yr spread2yr spread3yr spread4yr spread5yr Italy spread1yr spread2yr spread3yr spread4yr spread5yr Spain spread1yr spread2yr spread3yr spread4yr spread5yr 17 31 41 48 57 ?1 8 13 17 21 ?8 ?11 ?11 ?7 ?7 76 104 119 127 131 86 108 119 129 137 Emp (bp) 18 30 40 49 56 ?1 10 11 15 23 ?9 ?9 ?9 ?9 ?7 76 104 120 128 131 86 107 120 129 136 Std Data (bp) 38 56 61 62 66 18 18 22 26 28 11 12 11 13 13 113 135 143 147 150 120 139 147 159 164 Emp (bp) 43 52 59 64 66 17 17 21 26 31 10 11 11 12 14 115 132 143 148 149 121 137 148 157 165 Fitting error Mean (bp) 0 1 0 ?1 1 1 ?2 2 2 ?2 1 ?1 ?2 2 0 0 1 0 ?1 0 0 1 ?1 ?1 0 Std (bp) 8 6 6 3 4 3 4 4 1 4 4 4 4 3 3 7 7 7 3 6 5 7 8 5 6 Auto 0.754 0.683 0.741 0.650 0.777 0.755 0.728 0.721 0.446 0.826 0.375 0.443 0.442 0.699 0.557 0.486 0.413 0.719 0.641 0.654 0.504 0.522 0.702 0.801 0.522

Note: Mean denotes the sample arithmetic average and Std the standard deviation, all expressed in basis points. Auto denotes the ?rst-order monthly autocorrelation and Emp the empirical result from the model.

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Table 2 Diagnostic statistics of the estimated models – R-squared. Mat. (years) OIS rate Belgium France Germany Italy Spain 1 0.9996 0.9996 0.9996 0.9996 0.9996 2 0.9993 0.9994 0.9994 0.9993 0.9994 0.9889 0.9679 0.8841 0.9971 0.9973 3 0.9995 0.9995 0.9994 0.9995 0.9995 0.9914 0.9712 0.8539 0.9979 0.9971 4 0.9999 0.9999 0.9999 0.9999 0.9999 0.9978 0.9921 0.9321 0.9994 0.9990 5 0.9994 0.9994 0.9994 0.9994 0.9994 0.9957 0.9924 0.9535 0.9984 0.9988

3.4. Impulse response functions IRFs allow us to visualize the relationship between each of the 13 variables included in the model and movements in the yield curve. The ordering of the variables included in the VAR in Eq. (7) is as follows:

h F t ? VIX t ; ESIt ; F 2St ; PC Eur t

Bond yield spreads Belgium 0.9506 France 0.8773 Germany 0.8643 Italy 0.9967 Spain 0.9982

Eur ; PC t i0 ;1 ;2 CPIt ; D=GDPt ; PC spr ; PC spr : t t

spr;1

spr;2

;1 ;2 ; PC OIS ; PC OIS ; POLt ; GDPt ; t t

?12?

Note: The table shows the R2 of the OIS rates and bond yield spreads for each of the estimated models.

As mentioned before, we start with the more exogenous variables, representing international and European wide variables, and then include the country-speci?c factors. As a result, the ?rst eight variables are common to all countries and the last ?ve are country speci?c. We therefore estimate the following VAR(1) system:
P P Ft ? CP F ? UF F t ?1 ? RF eF ;t ;

?13?

cases, potentially indicating the presence of a missing factor. Notwithstanding this, the model ?ts well both the OIS yield curve and the country-speci?c spreads. A con?rmation of the good ?t of the model is found in Table 2, which reports the R2 ’s of the OIS rates and bond yield spreads for the ?ve estimated models. The R2 ’s of the OIS rates are equivalent across models, suggesting that, independently of the country considered, the model consistently ?ts the OIS yield curve. The R2 ’s of all bond yield spreads are well above 90%, except in three cases. These high values imply that two factors are able to capture most of the recent movements in bond spreads for all countries. Overall, we conclude that, despite the small number of spanned factors, our model is able to capture the evolution over time of OIS rates and government bond spreads across maturities.

where RF is a lower-triangular matrix implied by the lower triangular identi?cation of the shocks. Figs. 6–12 illustrate the IRFs for the 5-year bond spreads of all countries for a shock of one standard deviation to some of the 13 factors. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively, and the horizontal axis is expressed in months. Despite the high dimension of the VAR system, most of the IRFs are in line with economic intuition. We comment on some of the cases shown in these ?gures. We start by analyzing the response of bond spreads to common economic factor shocks. We see in Fig. 6 that a one-standard deviation shock to the VIX index, and therefore an increase in the uncertainty in ?nancial markets, initially increases bond spreads for all countries, except Germany, where the spreads decrease. We ?nd a signi?cant initial response (below 6 months) that is

Fig. 6. Impulse response function: response of 5-yr yield spreads to a VIX shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a one standard deviation VIX shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard bootstrapping procedure.

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Fig. 7. Impulse response function: response of 5-yr yield spreads to an ESI shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a one standard deviation ESI shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard bootstrapping procedure.

Fig. 8. Impulse response function: response of 5-yr yield spreads to a F2S shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a one standard deviation F 2S shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard bootstrapping procedure.

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Fig. 9. Impulse response function: response of 5-yr yield spreads to a PC(Eur spr, 1) shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a one spr ;1 standard deviation PC Eur shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard t bootstrapping procedure.

Fig. 10. Impulse response function: response of 5-yr yield spreads to a PC(Eur spr, 2) shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a spr ;2 one standard deviation PC Eur shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard t bootstrapping procedure.

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Fig. 11. Impulse response function: response of 5-yr yield spreads to a Pol. Risk shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a one standard deviation POL shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard bootstrapping procedure.

Fig. 12. Impulse response function: response of 5-yr yield spreads to a D/GDP shock. Note: The ?gure shows the impulse responses of 5-year bond yield spreads to a one standard deviation D=GDP shock. The dark and light shaded areas show the 66% and 90% con?dence intervals, respectively. Error bands are obtained by standard bootstrapping procedure.

320 Table 3 Variance decomposition of bond yield spreads. Horizon 1-yr bond spread Eco Belgium 1m 1 yr 3 yr 5 yr 7 yr 10 yr France 1m 1 yr 3 yr 5 yr 7 yr 10 yr Germany 1m 1 yr 3 yr 5 yr 7 yr 10 yr Italy 1m 1 yr 3 yr 5 yr 7 yr 10 yr Spain 1m 1 yr 3 yr 5 yr 7 yr 10 yr 0.09 0.35 0.40 0.40 0.40 0.40 0.01 0.34 0.37 0.38 0.38 0.38 0.26 0.40 0.53 0.54 0.54 0.55 0.16 0.39 0.50 0.51 0.51 0.52 0.12 0.21 0.28 0.36 0.37 0.37 Idios 0.29 0.34 0.31 0.30 0.30 0.30 0.32 0.18 0.16 0.14 0.14 0.14 0.27 0.17 0.13 0.11 0.11 0.11 0.26 0.18 0.17 0.17 0.17 0.17 0.34 0.20 0.17 0.15 0.15 0.15

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3-yr bond spread Non-f 0.62 0.31 0.29 0.30 0.30 0.30 0.67 0.48 0.47 0.48 0.48 0.48 0.48 0.43 0.34 0.35 0.35 0.35 0.58 0.43 0.33 0.32 0.32 0.31 0.53 0.59 0.54 0.49 0.48 0.48 Eco 0.06 0.47 0.57 0.57 0.57 0.57 0.03 0.30 0.38 0.39 0.39 0.39 0.22 0.40 0.56 0.56 0.56 0.56 0.18 0.42 0.54 0.56 0.56 0.56 0.13 0.25 0.37 0.45 0.46 0.46 Idios 0.12 0.25 0.21 0.21 0.21 0.21 0.14 0.07 0.05 0.05 0.05 0.05 0.16 0.10 0.07 0.06 0.06 0.06 0.27 0.14 0.16 0.16 0.16 0.16 0.31 0.18 0.13 0.11 0.11 0.11 Non-f 0.82 0.28 0.22 0.22 0.22 0.22 0.82 0.64 0.57 0.57 0.56 0.56 0.62 0.50 0.37 0.38 0.38 0.38 0.55 0.44 0.31 0.28 0.29 0.28 0.56 0.58 0.50 0.43 0.42 0.42

5-yr bond spread Eco 0.06 0.50 0.61 0.61 0.61 0.61 0.09 0.27 0.38 0.39 0.39 0.40 0.26 0.37 0.50 0.51 0.52 0.52 0.19 0.43 0.55 0.57 0.57 0.57 0.14 0.27 0.40 0.48 0.49 0.49 Idios 0.17 0.24 0.20 0.19 0.19 0.19 0.33 0.07 0.05 0.05 0.05 0.05 0.39 0.25 0.17 0.13 0.13 0.13 0.30 0.13 0.15 0.16 0.16 0.16 0.32 0.18 0.13 0.11 0.11 0.11 Non-f 0.77 0.26 0.19 0.20 0.20 0.20 0.58 0.66 0.57 0.57 0.56 0.56 0.35 0.38 0.33 0.36 0.35 0.35 0.51 0.44 0.30 0.27 0.27 0.27 0.54 0.55 0.47 0.41 0.40 0.40

Note: Eco, Idios, and Non-f denote the component due to economic, idiosyncratic, and non-fundamental shocks, respectively.

particularly strong for Italy, around 10 basis points, but weaker for the other countries, being below 5 basis points in absolute value. Fig. 7, on the other hand, shows that an increase in the euro area con?dence (ESI) only marginally affects bond spreads, initially decreasing bond spreads for Italy and Spain but increasing for the other countries. We now turn to the response of bond spreads to common nonfundamental factor shocks. From Fig. 8, we see that ?ight to safety (F 2S, or ?ight to liquidity) shocks increase bond spreads of all countries, with the exception of Germany, where the spreads decrease. The magnitude of this response is small for all countries, below 5 basis points, and is signi?cant for a short horizon for France, Germany and Belgium. Innovations to the ?rst principal spr ;1 component of euro area spreads (PC Eur ?, shown in Fig. 9, signift icantly increase bond spreads of all countries. This reaction is signi?cant up to about 3 months after the shock in most cases. The magnitude of the reactions is large relative to the other shocks. For example, for Spain and Italy, we observe an initial increase of about 15 basis points. Turning to the innovations to the second spr;2 principal component of euro area spreads (PC Eur ), Fig. 10 shows t that a positive shock to this factor increases bond spreads of Belgium, Italy, Spain and France (the latter with a lag), and decreases those of Germany. The magnitude of the reactions is large for the peripherical countries (Italy and Spain) while is small for the other three countries. Lastly, the effect of political uncertainty (POL) shocks on bond spreads can be seen in Fig. 11. For short horizons, an increase in political uncertainty has a positive but marginal

impact on spreads of most countries. For horizons above one quarter, the impact of a political shock is more marked for peripheral countries such as Italy and Spain, with a signi?cant increase of bond spreads above 5 basis points. Finally, we analyze the response of bond spreads to countryspeci?c economic factor shocks, and in particular to D/GDP (Fig. 12). In most of the cases an increase in the D/GDP ratio generates a positive and signi?cant reaction of bond spreads over long horizons, the only exception being Italy, where positive shocks to the D/GDP ratio induce a counterintuitive negative reaction of yields’ spreads. 3.5. Variance decompositions We now perform a variance decomposition in order to identify the main drivers behind movements in sovereign bond yield spreads. The model includes a total of 13 factors, four observable factors spanning the yield curve (P t ) of each country and other nine unspanned factors (M t ). To facilitate interpretation, these factors are divided in three groups: (i) economic factors summarize the information concerning the global and euro area environments and the economic situation of each country. This group includes the following variables: VIX ; ESI; GDP ; CPI; D=GDP , PC OIS;1 , and PC OIS;2 ; (ii) idiosyncratic factors represent country-speci?c conditions that cannot be captured by the economic and ?nancial variables included in the model, i.e. PC spr;1 and PC spr;2 ; and (iii) non-fundamental risk factors measure the euro area dynamics of

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Fig. 13. Variance decomposition of 5-year bond yield spreads. Note: The ?gure reports the variance decomposition of the 5-yr yield spreads for the ?ve countries in our dataset. The forecasting horizon considered is 1-m, 1-yr, 3-yr, 5-yr, 7-yr and 10-yr. Economic groups the following shocks: VIX, ESI, GDP, CPI, D/GDP, PC(OIS, 1) and PC(OIS, 2); idiosyncratic groups the following shocks: PC(Spr, 1) and PC(Spr, 2); Non-fundam. groups the following shocks: F2S, PC(Eur_spr, 1); PC(Eur_spr, 2) and POL.

sovereign bond spreads which should not be present in a wellfunctioning monetary union and include the remaining variables (F 2S; PC Eur spr;1 ; PC Eur spr;2 , and POL). The variance decomposition is performed for bond spreads with maturities of 1, 3, and 5 years and for a forecast horizon of up to 10 years. The results can be seen in Table 3. As an illustration, we also present the results for the 5-year bond spread decomposition in Fig. 13. A number of observations emerge from these results. First, both economic and non-fundamental risk shocks are signi?cant sources of variation in bond yield spreads. Non-fundamental risk shocks are the main source of yield spread variation for short forecast horizons (up to one-month horizon), where this type of shock explains between 35% (Germany, 5-year bond spread) and 82% (Belgium and France, 3-year bond spread) of the bond spread variation. The effect of this type of shock is, however, also signi?cant for long forecast horizons. For all countries, nonfundamental risk shocks are responsible for at least 20% of the bond spread variation for any maturity and forecast horizon. This proportion is the lowest for Belgium and the highest for France,

where this group of factors accounts for most of the variation in bond spreads for all maturities and forecast horizons. Among the four non-fundamental risk factors, the ?rst principal component of euro area bond spreads (PC Eur spr;1 ) plays a dominant role, suggesting the presence of spillover (contagion) effects across countries. The political uncertainty factor (POL) seems to have a minor in?uence in the variation of bond yield spreads.9 Economic shocks, on the other hand, gain in importance as the forecast horizon increases. For Belgium, Germany, and Italy, such shocks are the dominant source of variation in bond spreads for forecast horizons above one year. For France and Spain, those shocks also play an important role in long forecast horizons. Finally, in most cases, country-speci?c shocks play a minor role in the variance decomposition of bond yield spreads. One notable exception is the case of Belgium, where this type of shock is responsible for 20% or more of the bond spread variation for any maturity.
9 The speci?c contribution of each factor to the forecast variance is available upon request.

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Fig. 14. Historical decomposition of bond spreads – Belgium. Note: The ?gure shows the historical decomposition of 5-year Belgian bond yield spreads with the shocks grouped as follows: Economic Component – VIX , ESI, GDP , CPI, D=GDP, PC OIS;1 , and PC OIS;2 ; Idiosyncratic Component – PC spr;1 and PC spr;2 ; and Non-fundamental Component – F 2S; PC Eur spr;1 ; PC Eur spr;2 , and POL.

Fig. 15. Historical decomposition of bond spreads – France. Note: The ?gure shows the historical decomposition of 5-year French bond yield spreads with the shocks grouped as follows: Economic Component – VIX , ESI, GDP, CPI, D=GDP , PC OIS;1 , and PC OIS;2 ; Idiosyncratic Component – PC spr;1 and PC spr;2 ; and Non-fundamental Component – F 2S; PC Eur spr;1 ; PC Eur spr;2 , and POL.

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Fig. 16. Historical decomposition of bond spreads – Germany. Note: The ?gure shows the historical decomposition of 5-year German bond yield spreads with the shocks grouped as follows: Economic Component – VIX , ESI, GDP , CPI, D=GDP, PC OIS;1 , and PC OIS;2 ; Idiosyncratic Component – PC spr;1 and PC spr;2 ; and Non-fundamental Component – F 2S; PC Eur spr;1 ; PC Eur spr;2 , and POL.

Fig. 17. Historical decomposition of bond spreads – Italy. Note: The ?gure shows the historical decomposition of 5-year Italian bond yield spreads with the shocks grouped as follows: Economic Component – VIX , ESI, GDP, CPI, D=GDP, PC OIS;1 , and PC OIS;2 ; Idiosyncratic Component – PC spr;1 and PC spr;2 ; and Non-fundamental Component – F 2S; PC Eur spr;1 ; PC Eur spr;2 , and POL.

4. Historical decomposition of bond yield spreads The variance decompositions discussed above point to the importance of both economic as well as non-fundamental risk fac-

tors in the forecast variances of bond yield spreads. To visualize the contribution over time of each group of factors to the total bond yield spread, we perform a historical decomposition of bond spreads. Figs. 14–18 show the historical decomposition of 5-year

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Fig. 18. Historical decomposition of bond spreads – Spain. Note: The ?gure shows the historical decomposition of 5-year Spanish bond yield spreads with the shocks grouped as follows: Economic Component – VIX , ESI, GDP, CPI, D=GDP , PC OIS;1 , and PC OIS;2 ; Idiosyncratic Component – PC spr;1 and PC spr;2 ; and Non-fundamental Component – F 2S; PC Eur spr;1 ; PC Eur spr;2 , and POL.

bond yield spreads for each country over our sample period.10 Each panel shows the contribution of one group of shocks to the total yield spread. We ?nd that, in all cases, economic shocks are responsible for a substantial part of bond yield spreads. This can be seen, for example, for the cases of Italy and Spain, shown in Figs. 17 and 18, respectively. Non-fundamental risk shocks also had a signi?cant impact on government bond spreads especially after the intensi?cation of the debt crisis in September 2011. This corroborates the ?ndings of previous studies which report evidence that yield spreads of EMU countries are not justi?ed based only on ?scal and macroeconomic fundamentals (see De Grauwe and Ji (2012) and Di Cesare et al. (2012)). For example, in September 2011 the non-fundamental component explains 283 basis points of the 5year Italian bond spread (Fig. 17, bottom panel), which represents about 46% of the total spread. We observe similar patterns for Belgium, France, and Spain. As mentioned in the analysis of the variance decomposition, the two principal components capturing the common dynamics of euro area sovereign bond yield differentials (PC Eur spr;1 and PC Eur spr;2 ) are the two most important non-fundamental factors.11 Finally, country-speci?c shocks had overall a smaller impact on bond spreads, with the exception of Italy and Spain around the middle of 2011 and 2012. In summary, although we identify an increase in bond spreads due to non-fundamental risk shocks after the intensi?cation of the debt crisis in September 2011, our results show that, in general, economic fundamentals are the dominant drivers behind bond yield spreads. As an illustration of the contribution of non-fundamental shocks to sovereign bond spreads, Table 4 presents a decomposition of 1-, 3-, and 5-year bond yields for each country as of May

Table 4 Bond yield decomposition – May 2013. Mat. Spread component Eco Belgium (% p.a.) 1 yr ?0.046 3 yr 0.088 5 yr 0.185 France (% p.a.) 1 yr ?0.063 3 yr ?0.043 5 yr ?0.011 Germany 1 yr 3 yr 5 yr (% p.a.) ?0.050 ?0.060 ?0.060 Idios 0.004 0.035 0.058 0.010 0.054 0.100 0.000 ?0.013 ?0.040 ?0.406 ?0.106 0.041 0.109 0.223 0.273 Non-f 0.007 0.091 0.149 0.044 0.116 0.193 0.001 ?0.013 ?0.039 0.518 0.853 0.948 0.202 0.633 0.818 Level OIS 0.074 0.302 0.631 0.074 0.302 0.631 0.074 0.302 0.631 0.074 0.302 0.631 0.074 0.302 0.631 Obs 0.095 0.462 1.049 0.079 0.391 0.930 0.044 0.193 0.511 0.839 2.215 3.131 1.099 2.675 3.341 Fund 0.088 0.370 0.900 0.036 0.275 0.736 0.043 0.206 0.550 0.321 1.363 2.182 0.897 2.042 2.523

Italy (% p.a.) 1 yr 0.602 3 yr 1.255 5 yr 1.471 Spain (% p.a.) 1 yr 0.822 3 yr 1.453 5 yr 1.736

Note: Eco, Idios, and Non-f denote the component due to economic, idiosyncratic, and non-fundamental shocks, respectively. Obs denotes the observed level of bond yields and Fund its fundamental value, computed as the observed level (Obs) minus the non-fundamental component of bond spreads.

10 The results for 1- and 3-year bond yield spreads are qualitatively similar and are available upon request. 11 This can be seen in a decomposition of the non-fundamental component of bond yield spreads, which is available upon request.

2013. Columns 2–4 show the contribution of each spread component to the total bond spread, column 5 shows the level of the OIS rate, and columns 6 and 7 display the observed and fundamental levels of bond yields at that date, respectively. The fundamental level is computed as the observed level minus the non-fundamental component. Notice that the sum of the three

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spread components (columns 2–4) plus the OIS rate (column 5) differs slightly from the observed bond yield (column 6) due to ?tting errors. The table shows, for example, that at the end of May 2013, while the observed level of the Italian 5-year bond yield was 3:13%, its fundamental level was only 2:18%. 5. Conclusion We present an empirical approach to identify the component of euro area sovereign bond yield spreads due to non-fundamental risks. Put differently, we assess the effect on government bond yields due to the probability of a country leaving the euro area. The yield spread decomposition is achieved with the use of a common-currency, two-market, no-arbitrage af?ne term structure model. The model is based on the methods proposed by Joslin et al. (2011, forthcoming), which are computationally faster than standard likelihood-based methods and allow the inclusion of unspanned macro-factors. This avoids the likely misspeci?cation of standard formulations which only incorporate spanned macro-factors. The model is applied to yield curve data from Belgium, France, Germany, Italy, and Spain over the period 2005–2013. Bond spreads are computed with respect to the OIS rate. The model includes a total of 13 factors, four observable factors spanning the OIS rates and the yield curve of each country and nine unspanned factors. To simplify interpretation, these factors are classi?ed as economic, idiosyncratic, and related to non-fundamental risk. Overall, we ?nd that economic fundamentals remain the dominant drivers behind euro area sovereign bond spreads. Nevertheless, non-fundamental risk shocks have played an important role in the dynamics of yield spreads for all countries and maturities analyzed following the intensi?cation of the debt crisis since the summer of 2011. More speci?cally, between July 2011 and August 2012, the impact of non-fundamental risk shocks resulted in a strong widening of sovereign bond spreads relative to the OIS rate which cannot be associated with macroeconomic and ?nancial conditions in the euro area as a whole or in the country under study. References
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