Fundamentally Wrong: Market Pricing of Sovereigns and the Greek Financial Crisis

The unfolding of the Greek sovereign debt crisis beginning in late 2009 – and the euro-area crisis more generally – has called into question the extent to which the price of sovereign risk, as reflected in the interest rate spread on sovereigns, can be explained by macroeconomic fundamentals. In the run-up to Greece’s entry into the euro area in 2001, the 2-year spread between Greek and German sovereigns fell precipitously, from about 500 basis points in the late 1990s to about 40 basis points at the time when Greece became a member of the single-currency area on January 1, 2001; during that period, the spread on 10-year sovereigns fell from about 600 basis points to about 50 basis points. Over the following years, both the 2-year and 10-year spreads stabilized within a fairly narrow range of 10–50 basis points until the end of 2008, despite Greece’s large and growing fiscal and external deficits (as we explain below). Then, in October of 2009, a newly-elected Greek government stunned the markets with news that

in May 2010 a program that aimed to stabilize the debt dynamics. The self-reinforcing process finally came to an end in early 2012. By that time it had become clear that the debt dynamics were unsustainable. In March 2012, the Greek government restructured its debt and agreed to a second adjustment program with official lenders. Prior to those actions, the 10-year spread had reached 4000 basis points and, with an inversion of the yield curve (reflecting market expectations of a sovereign restruc-turing in the near term), the 2-year spread had peaked at 26,000 basis points.
A substantial empirical literature examining the contributions of economic fundamentals to spreads both for the euro area as a whole and for individual euro area countries has already emerged (e.g., De Santis (2012); Gibson et al., 2012;De Grauwe and Ji, 2013;Aizenman et al., 2013;Beirne and Fratzscher, 2013;Mink and de Haan, 2013). Typically, that liter-ature posits that, to the extent that sovereign credit risk cannot be explained by the economic fundamentals, factors related to contagionor, more generally, market psychologyaccounted for the unexplained portions of spreads. An earlier study by the present authors followed that approach (see Gibson et al., 2012). In that study, we examined the macroeconomic determinants of spreads between the 10year benchmark Greek government bond and the German 10-year sovereign. Our data sample was monthly and covered the period from January 2000 to September 2010. Thus, our data covered the pre-crisis period (i.e., the period prior to the fall of 2009) and the early part of the crisis period. Our results suggested that spreads were significantly below the levels that would have been predicted on the basis of the fundamentals during the mid-2000s, but significantly above what had been predicted by the fundamentals for much of 2010.
As in our previous study, in this paper we focus on the determinants of Greek sovereign spreads. However, in light of the intensification of the Greek financial crisis after the fall of 2010 (the end-point of our earlier sample period), here we extend the sample period through the first quarter of 2012. 3 Moreover, in addition to examining the determinants of 10-year spreads, we examine the determinants of 2-year spreads. In early-2011, 2-year spreads began to rise far above 10-year spreads, leading (as noted above) to an inverted yield curve. By examining the determinants of the 2-year spread, we are able to focus on the short-term risk (or volatility) that predominated in the markets.
In this paper, we aim to contribute to the existing literature on spreads during the euro-area financial crisis in several ways. First, in addition to investigating the relationship between spreads and economic fundamentals, we investigate the relationship between spreads and (a) political uncertainty and (b) sovereign credit ratings. Both of those factors appear, a priori, to have played an especially important role during the Greek financial crisis. As explained further below, political uncertainty in Greece underwent a sharp rise in 2008 and again in 2011 and early 2012; the latter period was marked by a political debate that had implications for Greece's remaining in the euro area, thereby introducing currency risk into inter-est-rate spreads. 4 With regard to credit ratings, as mentioned above, a succession of sovereign downgrades created negative feedback loops among (i) spreads, (ii) real economic activity, (iii) debt sustainability, and (iv) credit ratings. The impact of credit downgrades on debt sustainability appears to have been pronounced in the case of Greece since the country began the crisis with a very high debt-to-GDP ratio. Consequently, credit downgrades and the ensuing rises in spreads had the potential to set-off unstable debt-dynamics, leading to the need of debt restructuring, a potential that was, in fact, realized. In other words, debt dynamics in Greece were especially sensitive to credit downgrades and changes in spreads. Second, we examine the extent to which the determinants of spreads changed over time. In this connection, we use the Kalman filter to estimate the underlying time-varying coefficients of those determinants. By doing so, we are able to measure both the speed with which the impact of the determinants of spreads changed, and the timing of the changes that took place in the coefficients. To preview of our results, we find that for a number of years after Greece's entry into the euro area, mar-kets appeared to effectively discount the economic fundamentals in pricing Greek sovereign credit risk. With the collapse of Lehman Brothers in September 2008, and especially with the unexpected news about Greece's fiscal situation in the fall of 2009, the markets went through a process of learning as they increasingly priced credit (and, perhaps, currency) risk into Greek spreads, at times overpricing risk, thereby contributing to the self-reinforcing character of the crisis.
The remainder of this paper is structured as follows. Section 2 provides a brief overview of the recent literature on the macroeconomic determinants of spreads in the euro area. Section 3 describes our data. Section 4 presents our methodology and the empirical results. Section 5 concludes.

Related literature
The recent macro-international finance literature has focused on two presumably separate measures of sovereign risk -(1) spreads on government bond yields, and (2) CDS spreads. As Aizenman et al. (2013, p. 41) pointed out, however, recent studies suggest that both reference measures have common underlying determinants, rather than being entirely separate measures. 5 As is the case for the literature more broadly, studies that have focused on euro-area countries have found that mac-A common finding that has emerged from the literature dealing with spreads in the euro area is that there is a substantial difference between the effects of macroeconomic variables on sovereign risk when the sample period excludes the crisis per-iod and the effects of those variables when the sample period includes the crisis period. The precise dating of the start of the crisis period varies, however, depending upon whether the start of the period is considered to be the outbreak of the US sub-prime crisis in the summer of 2007, the collapse of Lehman Brothers in September 2009, or the eruption of the Greek sov-ereign debt crisis in the fall of 2009. Bernoth et al. (2012), treating the former (subprime) episode as the start of the crisis period, found that macroeconomic fundamentals were not significant determinants of spreads in the pre-crisis period but were significant if the sample is extended to include the crisis period. Von Hagen et al. (2011) found that, while bond yield spreads in the euro area before and during the crisis can be explained largely by fundamentals, the market has penalized fiscal imbalances much more severely in the period after the collapse of Lehman Brothers than in the period before that episode. Similarily, Afonso et al. (2012) found that euroarea bond spreads are well-explained by the macroeconomic fundamentals if account is taken of the onset of the global financial crisis in the summer of 2007, but spreads are not well-explained by the same fundamentals in the pre-crisis period.
An inference that can be drawn from the results of the above studies is that markets understatedor even overlookedthe role of some of the macroeconomic fundamentals in the determination of sovereign risk in the years leading up to the global financial crisis. In what follows, we investigate the reasons for this market behavior with respect to spreads on Greek sovereigns. In particular, we examine the relationship between macroeconomic fundamentals and Greek spreads, whether the fundamentals were important determinants of spreads prior to the outbreak of the Greek sovereign crisis, and, if not, whether and when they became significant determinants of spreads. In investigating the role of fundamentals, we control for potential independent influences stemming from political stability and ratings downgrades.

Data and stylized facts
Typically, studies that deal with the macroeconomic determinants of sovereign risk focus on fundamentals that capture fiscal sustainability and external sustainability and/or competitiveness. Measures of fiscal sustainability include the fiscal balance and public debt. Measures of external sustainability and/or competitiveness include the current account balance, external debt, relative prices, trade openness and real growth (an important determinant of the sustainability of a country's external obligations). Where appropriate, variables are specified as ratios to GDP. Note that the foregoing variables tend to be interrelated. For example, an expanding fiscal deficit is often accompanied by an expanding external deficit and growing external debt, while a deterioration in competitiveness, as defined by movements in relative prices, tends to be accompanied by growing external and fiscal imbalances. In addition to variables representing macroeconomic fundamentals, in our pre-vious study ( Gibson et al., 2012) we introduced a fiscal ''news'' variable in our specification of the determinants of Greek bond spreads on the supposition that unexpected (positive or negative) newsespecially a series of unexpected develop-mentsabout fiscal fundamentals can drive market dynamics, particularly in the short term. We found that the accumula-tion of fiscal news had a significant impact on Greek sovereign spreads, a finding corroborated in a different context (both in terms of the definition of a news variable and in terms of countries considered) by Beetsma et al. (2013).
We now turn to a description of the variables used in this study. Our sample period runs from January 2000 to March 2012; the data frequency is monthly. Fig. 1 shows the evolution of spreads during the period from January 2008 until March 2012. (Prior to January 2008, both 2-year and 10-year spreads remained in a fairly narrow range of 20-50 basis points.) With the collapse of Lehman Brothers in September 2008, 2-year and 10-year spreads both began to rise. That rise became highly accentuated with the news about Greece's fiscal situation in the fall of 2009. By May 2010, the time of the first Greek adjust-ment program, 2-year spreads had reached around 850 basis points and 10-year spreads had reached 565 basis points. The agreement of Greece's adjustment program contributed to a narrowing of spreads until the fall of 2010, under the presump-tion in the markets that the debt-dynamics had stabilized. However, in late 2010 it became increasingly evident that the adjustment program had gone off-track. Markets began to speculate that Greece would need to restructure its debt; spreads accelerated sharply upward, with the acceleration of the 2-year spread far outpacing that of the 10-year spread.
The above story is reflected in the yield curves. To capture the effects of the fundamentals (economic and political) on spreads, we use the following variables. We in-clude three measures of the fiscal situation.
(1) The ratio of government debt to GDP. The upper part of Fig. 3 shows the evolution of this variable. Greece entered the euro area with a debt ratio that was close to 100%. By 2006 that ratio had risen to about 110%, where it remained until 2009. The sustainability of the debt-to-GDP ratio was clearly dependent on the sustainability of robust real Source: ECB Statistical Data Warehouse (2) The government fiscal balance relative to GDP. The middle part of Fig. 3 shows the evolution of this variable. During much of the period from 2001 to 2006, the deficit exceeded 5% of GDP, despite the high GDP growth rates. This situation is explained by the fact that government spending was used to help generate economic growth. 7 By 2007, the deficit-to-GDP ratio began rising, peaking at 15½% in 2009. (3) Fiscal news. Since Greece's entry to the euro area in 2001, Greek fiscal data have been subjected to a number of revisions, sometimes several years after the initial (real-time) release of the data. These revisions have often involved upward revisions of the fiscal imbalances, generating negative surprises. In order to capture the news (or surprise) element that has figured prominently in the Greek experience, we construct real-time fiscal data. In particular, using the European Commission spring and autumn forecasts, we create a series of forecast revisions. We define, the revision in the spring 2001 forecasts, for example, as the 2001 deficit/GDP ratio in the spring compared to the forecast for 2001 made in the autumn of 2000. This procedure allows us to generate a series of revisions which, when cumulated over time, provides a cumulative fiscal news variable. As shown in the lower part of Fig. 3, the fiscal news variable deteriorated throughout 2000-2010, especially during the latter part of the period.
We use three variables to capture competitiveness.
(1) Relative prices. With Greece's nominal exchange rate fixed against those of the other euro-area countries, we use the Greek consumer price level relative to that of Germany as a measure of the change in competitiveness. The top part of In addition to fundamentals dealing with the fiscal and external situations, we use the following variables.
(1) Real GDP growth. High real growth helps improve debt sustainability; therefore, all other factors held equal, we expect higher growth to reduce spreads. Fig. 5 Fig. 6. We assign values of 1-22 to different possible ratings (higher values represent a deterioration in ratings); changes in the ratings variable are based on which of the three agencies moved first. In this way, we capture what might be termed ''important'' rating downgrades or upgrades. However, ratings are dependent, in part, on the economic fundamentals. To deal with the issue of endogeneity, we regress our ratings variable against the economic fundamentals and use the residuals in our spreads' equations as a measure of the impact of ratings agencies, purged of economic fundamentals. The objec-tive is to examine the extent to which rating downwards may themselves have exerted an independent influence on spreadsover-and-above the influence of the fundamentals. (4) Political uncertainty. We use the IFO World Economic Survey Index of political stability for Greece. The evolutions of the above variables tell a coherent story. Upon entry into the euro area, Greece benefited from a low-interest rate environment, which contributed to high real growth rates. Nevertheless, the Greek economy walked a razor's edge between debt sustainability and unsustainability. Throughout the period 2001-2009, fiscal imbalances built up, despite robust real growth rates and low interest rates, and competitiveness deteriorated. Until late 2009, however, spreads dis-played little sensitivity to the warning alarms embedded in the fundamentals. Did the markets pay attention to any of the foregoing fundamentals? If so, which fundamentals? When did the markets begin to use the fundamentals to price risk into spreads? What roles did political uncertainty, SMP interventions, and rating downgrades play in the determination of spreads, over-and-above the role of the economic fundamentals? To answer these questions, we now turn to a formal analysis.

Empirical results
We begin by testing for cointegration among the above variables for both the 10-year and the 2-year spread, assuming that the SMP dummy is exogenous. The results are reported in Table 1 for the 10-year spread and Table 2 for the 2-year spread. For the 10-year spread there is strong evidence of up to six cointegrating vectors. As shown in Table 2 for the 2-year spread, there is evidence of at least fiveand possibly six (using the trace statistic)cointegrating relationships. Again, the hypothesis that spreads are exogenous is rejected. An implication of these results is that we can treat spreads as endogenous. We now proceed to an investigation of their determinants.
We begin with a simple static regression, which we interpret as the long-run determination of spreads. Given our above intuitive account of the evolution of the fundamentals and spreads, we do not expect this relationship to necessarily exhibit stable parameters and we are not especially concerned with the economic interpretation of each of the fundamentals. Our objective here is simply to use the basic specification as a point of departure for a time-varying analysis. The results for the 10-year and 2-year spreads are reported in Tables 3 and 4, respectively. 8 The main findings can be summarized as follows. For the 10-year spread equation, seven variables are correctly signed and significantthe debt-to-GDP ratio, fiscal news, real growth, oil prices, political uncertainty, the SMP program, and the residuals of an equation in which the economic fundamentals are used to determine ratings (see Appendix A). 9 The remaining four variables (the current account def-icit-to-GDP ratio, relative prices, and fiscal deficit-to-GDP ratio) are either insignificant or incorrectly signed. This finding is not surprising; these three variables are measures of either the fiscal situation or competitiveness. Hence, they are collinear with other variables in the regression. For the 2-year spread equation, six variables are significant and correctly signedfiscal news, growth, oil prices, political uncertainty, the SMP program, and the residuals from the ratings equation. 10 In interpreting these results, several points merit comment. First, to the extent that ratings were determined by the exist-ing fundamentalsand not the expected future fundamentalsratings downgrades appear to have played a very important effect on spreads, over-and-above the impact of the economic fundamentals. To explain, consider that for the 10-year spread regression, the adjusted R-squared without the residuals from the ratings equation is 0.733 (see Appendix A), with the resid-uals from the ratings equation included the adjusted R-squared rises to 0.916. For the 2-year-spread equation, the adjusted 8 In interpreting these results, note that both the current-account balance and the fiscal balance (as percentages of nominal GDP) are treated in the following way. Declines in the current account and fiscal deficits should reduce spreads; hence, the signs on both variables are expected to be negative. 9 The results are also economically significant. Thus, for example, a one standard deviation rise in the debt-to-GDP ratio (equivalent to a rise of 17.5% points) leads to a rise in 10-year spreads of almost 240 basis points. A one standard deviation rise in growth (0.6 of a percentage point) causes spreads to fall by 90 basis points. A one standard deviation rise in oil prices leads to a 90 basis points rise in spreads. 10 The impact of a one standard deviation increase in the explanatory variables on 2-year spreads is much greater than their impact on 10-year spreads, reflecting the high levels to which 2-year spreads rose in the latter part of the sample.    R-squared without the ratings variable is 0.594 (see Appendix A); with the ratings variable the adjusted R-squared is 0.876. An implication of these findings is that ratings downgrades led to a self-perpetuating rise in spreads. Second, political uncer-tainty also appears to have contributed to the rise in spreadshigher stability reduces spreads. The decline in political sta-bility beginning in 2007 and continuing in 2011 raised spreads. Third, the SMP program appears to have reduced spreads during the short period during which it operated in Greece. In the case of the 10-year spread, SMP intervention reduced spreads by about 3% points. For the 2-year spread, SMP intervention reduced spreads by about 33% points. Fourth, the explanatory power of the equation for the 10-year spread is somewhat higher than the equation for the 2-year spread (0.916 for the former equation, 0.876 for the latter equation). Evidently, market psychology played a greater role in the evo-lution of the 2-year spread than the 10-year spread. As we indicated above, it may have been the case that rating agencies formulated their ratings of Greek sovereigns on the basis of both present and projected fundamentals. In that case, the residuals from a ratings regression involving both present and projected fundamentals would have been smaller than a regression based only on present fundamentals, and the impact of these residuals on spreads would (likely) have been smaller as well. Thus, to the extent that ratings were made on the basis of both present and projected fundamentals, our conjecture that ratings downgrades led to self-perpetuating rises in spreads needs to be tempered. Nevertheless, there are also several reasons to suppose that our empirical methodology does not fully capture the selfreinforcing impact of downgrades. First, we focused on the effects of sovereign downgrades. In fact, the developments during 2010-2012 were more complex. Sovereign downgrades led to downgrades of bonds issued by Greek banks, in part, since the banks held large amounts of Greek sovereigns in their portfolios. The downgrades of the banks affected their ability to provide liquidity to the economy, thus contributing to the contraction of real output, and to further sovereign downgrades. Our methodology does not fully capture such dynamics. Second, the actual pattern of down-grades was much more complex than what we assumed. Typically, each sovereign downgrade led to a rise in spreads. Each rise in spreads led to further downgradesof both sovereigns and banksin a chain of self-reinforcing moves. In our mea-sure of ratings, we include only the first downgrade in any chainthe first being what we identify to be a downgrade to a new lower level (e.g., BBB_ to BB+). After accounting for a downgrade of the sovereign to a specific rating, we do not account for subsequent downgrades of the sovereign by other rating agencies to the some rating level (another agency effectively downgrading from BBB_ to BB+). Yet these follow-on downgrades affected spreads in much the same way as the initial downgrade to the new lower level. These various feedback loops appear to have contributed to unfolding of events that in fact took place.
We now consider how precisely the effects of the fundamentals have changed over time. 11 To do so, we use the Kalman filter.
The specific Kalman filter model we use is a time-varying parameter model (see Cuthbertson et al., 1992) that provides consistent estimates of the underlying time-varying coefficients. It is set up in the form of a state space model consisting of a measurement equation and a set of state equations which govern the evolution of the parameters. Our measurement equation is exactly the same specification as the two estimated models above. The state equations, for the parameters, specify that they follow a simple random walk, thus allowing them considerable freedom to change over time.
The time-varying-parameter model, with the appropriate Kalman filter equations for the univariate case, following Har-vey (1987), is given by the following. Let be the measurement equation, where y t is a measured variable, z t is the state vector of unobserved variables, d is a vector of known parameters, which in this case are our explanatory variables, and e t _ NID(0, C t ). The state equation is then given as: where W are parameters and w _ NID(0, Q t ), Q t is sometimes referred to as the hyperparameters. The appropriate Kalman filter prediction equations are then given by defining z _ t as the best estimate of z t based on information up to t, and P t as the covariance matrix of the estimate z _ t , and stating: Once the current observation on y t becomes available, we can update these estimates using the following equations: and P t ¼ P t j t _ 1 _ P t j t _ 1 dd 0 P t j t _ 1 =ðd Eqs.
(1)-(6) then represent jointly the Kalman filter equations. 11 We tested the above models for stability using recursive estimation and found that both equations are highly unstable. Recursive estimation does not, however, provide consistent estimates of the underlying parameters if there is instability, as each recursion is based on the assumption of constant parameters. If we then define the one-step-ahead prediction errors as, then the concentrated log likelihood function can be shown to be proportional to where k is the number of periods needed to derive estimates of the state vector; that is, the likelihood function can be expressed as a function of the one-step-ahead prediction errors, suitably weighted.
We now turn to the results of the Kalman filter exercise. Did markets continuously focus on the same fundamentals throughout the sample period? Was the sensitivity of spreads to those fundamentals stable? In Figs. 7 and 8, we plot the coefficients from Kalman filter estimates of the regressions for the 10-year spread and the 2-years spread, respectively from 2006 onwards. Looking first at the 10-year spread, several conclusions can be drawn. First, for the period before the inter-national financial crisis, markets largely ignored all fundamentals in pricing spreads. Specifically, the coefficients on most of the variables are near zero until 2008-2009. Second, for those variables which were correctly signed and significant (debt, fiscal news, growth, oil prices and political stability in our above static regression), there is evidence that markets began to price developments into yields and spreads as early as 2008, and more strongly from 2009. Third, the time-varying coeffi-cients on those variables (the current account, the deficitto-GDP ratio and, to a lesser extent, relative prices), that had incor-rect signs (in our static regressions), move much laterin 2010 and 2011reflecting the large volatility of spreads which characterizes the latter part of the sample period. Fourth, the influence of political stability kicks in from early 2009 and then more strongly in 2011, as would be expected. Finally, the residuals from the ratings equations show a sharp increase from early 2011, reflecting the large number of downgrades that occurred along with the fact that they were multiple notch downgradesin early 2011 Greece was BB+; by the end of the sample, she had been downgraded to selective default.
In the case of 2-year spreads ( Fig. 8), the coefficients are more unstable than they are for the 10-year spreads. The current account actually has the correct sign (negative) until the latter part of the sample; the same pertains to the fiscal deficit. Nevertheless, as in the case of the 10-year spread, the coefficients on the fundamentals are again close to zero until 2008-2009. There is again evidence that the markets slowly woke up to the fundamentals after the surprise news about Greece's fiscal situation in late 2009.

Conclusions
The main conclusions of this paper are as follows. First, the time-varying results indicate that the coefficients on most, if not all, of the variables were near zero until 2008-2009. In other words, prior to 2008-2009, financial markets paid little attention to the deteriorating Greek economic fundamentals in pricing spreads. Effectively, the markets treated Greek sovereigns almost on a par with German sovereigns. Thus, the markets failed to incorporate credit risk in the price of Greek sovereigns, presumably because the markets expected that Greek sovereigns would be protected by the core euro-area countries should the need arise. Second, sovereign downgrades and political uncertainly appear to have been drivers of the sharp rises in Greek sovereign spreads from 2008 to 2009 onwards, over-and-above the impact of the economic funda-mentals. An implication of our finding of a separate effect on spreads from the credit downgrades is the following; negative feedback loops between spreads, real economic activity, debt sustainability and credit ratings, perpetuating and deepening the financial crisis. Third, the Eurosystem's SMP program had a pronounced effect on reducing spreads whilst the program was in place. Fourth, our time-varying results provide support for the view that once markets reassessed their pricing of Greek credit risk, the change in the influence of the fundamentals came swiftly and abruptly, exhibiting overshooting char-acteristics, thus suggesting that market psychology played an independent role in the pricing of spreads.
These conclusions suggest that markets were not rational during the sample period considered in this paper. While the above evidence is consistent with the self-reinforcing-feedback-loop hypothesis, a fuller analysis would require that ratings and spreads be modeled as a simultaneous system. Such a system could be used to quantify the degree of overshooting of spreads from the fundamentals. We leave this idea as a suggestion for future research.