Spatial effects in the market for
sovereign bonds
M.P. van der Woerdt1
ABSTRACT
This paper examines to what extent the countries in the European Monetary Union (EMU) are interconnected in the assessment of risk in the form of the yield on 10-year sovereign bonds. The paper answers if there are spatial relations between EMU countries for risk indicators and if there is a flight-to-safety effect among the countries in the EMU. The study uses monthly data from January 1999 until December 2012 for 12 EMU countries. A distinction is made between country specific factors and common factors. The findings of this paper show that there are large spillover effects of risk indicators between EMU countries. Furthermore, there is some evidence of a flight-to-safety effect between high- and low-risk countries.
Keywords: Government Bonds, Euro Area, Sovereign Risk, Spatial Econometrics JEL classification: E430, G120, H630
Supervisors: Prof. dr. J.P. Elhorst Dr. L. Dam
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1
Introduction
This paper investigates the spatial relationship between the yields on sovereign bonds in the European Monetary Union (EMU) and if there is a flight towards safer investments during the recent financial crisis. To do that, this paper looks how the yields on sovereign bonds are described by country specific fundamental factors and common factors that measure investor preferences. A spatial relationship should indicate how much of country risk is determined by country specific factors and by how much it is influenced by risk factors from other members of the monetary union. The use common factors makes it possible to indicate whether there is a substitution between relatively risky and safe assets.
During the financial crisis most Western economies faced a great downturn of the economy with low growth rates, high unemployment and the need to safe financial institutions that were deemed too big to fail. Although, a great difference has been observed in how the financial markets reacted to the deterioration of the economy in different countries. From 2010, one speaks of a sovereign debt crisis in the Eurozone. However, when the debt rate of the entire Eurozone is compared to that of other western countries it shows that the debt rates are not significantly higher. For instance, Table 4 and Table 5 in appendix 9.2 illustrate that the US and UK had a debt to GDP ratio of respectively 106.3% and 103.9% compared to 99.1% in the Eurozone in 2012. The same applies for the deficit ratio, where the US and UK had a deficit respectively of -8.7% and -6.5% while the Eurozone as a whole had a deficit of -3.7% in 20122. Still, the financial markets seem to think that the debt crisis and the associated risk in the Eurozone is much more severe than in the US or UK, which is supported by credit rating agencies that give high ratings on sovereign debt of the US and UK. The crisis in the Eurozone focusses mostly on a few countries that became increasingly risky. Although these countries, like Greece, Ireland and Portugal, only constitute a small percentage of the total economy in the Eurozone.
Apparently, countries inside the European monetary union have an influence on each other and on the entire system to the extent that one can speak of an European debt crisis. It is argued that financial markets punish the Southern European countries more because of the higher risk that is caused by being a member of a monetary union. Membership of a monetary union does not only imply that a country gives up its currency but also that they are increasingly dependent on other economies in terms of trade and economic policy. One of the main fears of the European Central Bank (ECB) in the recent
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3 years was that the debt crisis in Greece would lead to insolvency of other European countries such as Portugal and even Italy.
Nevertheless, there is a large difference between economic spillover effects when looking at sovereign bond yields of different countries. The relatively risky Southern European countries seem to suffer a lot from the crisis and the poor economic situation on the financial market, while the relatively safe Northern European countries, in terms of debt and deficit, are paying a record low interest rate on their debt. This is in contrast with both the decreased economic conditions in these countries and the risk they bear from being in a monetary union with economically poor countries. The large differences are argued to be caused by a substitution between bonds in economically weak countries and more stable countries (Fontana and Scheicher, 2010).
The interconnection between countries and the spillovers that come along with it, is a research topic that is difficult to explain because it is hard to measure the actual spillover effects. In this paper spatial econometrics is used to estimate the relation between country specific risk factors. These give more insight in the real credit risk of a country, where a distinction is made between actual risk factors and the perceived risk by the market to be able to indicate if capital movements to safer countries are justified by increased risk.
For this study a panel dataset is used from the 12 first EMU members3 over the period from January 1999 to December 2012. Because of the relatively long period, most research only looks at data from 2006, it is possible to make better distinction between ‘normal’ and ‘extreme’ situations that occurred during the crisis.
This paper contributes to the existing literature in the discussion on which variables have an influence on sovereign bond yield. Existing research has used a wide variety of variables and this paper confirms the view that common factors have a large impact on the movement of sovereign bond yields. Furthermore, among the papers that have been published on yield spreads, research methods differ a lot. In this paper spatial econometric techniques are used to explain the spillovers in risk factors of individual countries. This method is, as far as the include literature study shows, not yet used for explaining the economic spillovers in a monetary union, despite the fact that spatial econometrics is a good instrument in explaining spillover effects and is intuitive to interpret.
Given the large financial support to the EMU countries that are in distress, it is important to understand how the economic spillovers in the EMU are determined. If there are indeed large spillover
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4 effects, there should be large investments in countries that are in distress in order to maintain the monetary system. Furthermore, the EMU should aim at decreasing any substitution of bonds between EMU countries. Although it decreases the yield on economically stable countries, it can harm these countries because of the spillover effects.
The structure of the paper is as follows. First, a theory on how the assessment of risk for counties in the EMU differs from a country that is not part of a monetary union is presented, followed by a testable hypothesis. Section 3 presents a literature review. Section 4 shows the methodology and section 5 discusses the data used. The results are presented in section 6 and a conclusion is given in section 7.
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Theory
The introduction of a common currency in the euro zone had an influence on the solvency of countries within the EMU. By giving up the individual currencies countries ensured no exchange rate risk which had to be the basis for increasing trade within the EMU area. However, having no individual currency decreases the possibilities of seigniorage and therefore the possibility to devaluate debt. Without this option the sustainability of government debt is much harder to keep and the risk to default on debt is increased. To prevent the insolvency of individual countries the stability and growth pact was introduced which limited the debt and deficit of countries and thereby limited the risk for both the nation and the Eurozone. Unfortunately, the stability and growth pact is not always well complied.
5 Figure 1: Yields on 10-year sovereign bond of EMU countries. The figure shows the development of yields on sovereign bonds
with a maturity of ten years. It shows monthly data from January 1995 until December 2012. Approaching the introduction of the Euro in 1999 the yields on sovereign bonds converge. Thereafter, with the exception of Luxembourg, the yields follow a similar path until September 2007 when Lehman Brothers filed for bankruptcy, which is generally marked as the beginning of the financial crisis. Thereafter the spreads between the yields increased. Source: Eurostat.
because markets anticipate fiscal support for EMU countries in distress; however, this declines with the size of the public debt relative to Germany.
Concluding, the net effect on yields is ambiguous since on one hand, the inflation premium will go down and markets become more efficient while on the other hand, the default risk can increase. However, considering the low probability of default and the option of a bail out by other countries, EMU bond yields should go down and converge (Alesina et al., 1992; Codogno et al., 2003).
6 US state bonds in the 20th century. Two important differences have to be noted between the United States and the EMU. First, when an US state gets into distress the central government can easily intervene. In contrast, intervention by other EMU members is much harder so the conclusion of Bernoth et al. (2004) that the EMU decreases the possibility of default has its limitation. Second, US state bonds only play a minor role in the total bond market and are therefore not always a good substitute for treasury notes, whereas EMU sovereign bonds are very good substitutes for each other in terms of liquidity which has implications for the risk premium of EMU countries. In the light of the financial crisis of the last years it has become evident that EMU sovereign bonds are far from equal and indeed bare a significant amount of risk. Although initially, before the introduction of the EMU, bond yields converted, it is shown that while the financial crisis developed, the spread between bonds increased tremendously, see Figure 1.
Some papers (e.g. Fontana and Scheicher, 2010 and Sgherri and Zoli, 2009) argue that there has been a flight-to-safety amongst investors, meaning that they became more risk averse and substituted the lower rated bonds for high rated bonds. Because there is no exchange rate risk within the EMU the substitution between EMU country bonds is much easier and less risky than to invest large amounts of money in countries outside the euro-zone. Although there has been a clear effect on Switzerland where the yield on bonds also decreased and with it the Swiss Franc has appreciated.
Using spatial econometric techniques to model the flight-to-safety effect it is possible to explicitly model exogenous and endogenous variables of other countries. Furthermore, it is possible to see indirect effects to the yield on sovereign bonds. The flight-to-safety effect would suggest that if credit risk is very high in one country, investments will move from these countries to countries with a relatively low credit risk, as is indicated by a high rating. The advantage of using spatial econometrics is that it is easy to model the influence of risk factors in individual countries on neighboring countries.
7 From the theory about a monetary union the following testable hypothesis are formulated:
1. Substitution between sovereign debt increases for higher values of common risk factors. 2. There are spillover effects in risk factors that influence assessment of credit risk in a
monetary union.
3
Literature
A lot of has been written on risk and sovereign debt in the EMU. Earlier papers look at how the establishment of the EMU decreases risk for member countries, especially for countries with a record of high inflation. For example, Bernoth et al. (2004) show that the liquidity risk premium is reduced in the EMU because of higher financial market integration. On the other hand, some papers focus on the remaining spreads between government bonds in the EMU. Codogno et al. (2003) state that this is mostly due to different reactions to international risk factors. Also, Manganelli and Wolswijk (2007) found that the there are differences in spreads due to variables that do not necessarily reflect the underlying credit risk. Although they find that the distinction between good and bad credit is mostly due to the credit rating, the extent of the credit spread is largely determined by common factors and is best described by the level of short term interest rate.
However, a monetary union can also increase risk factors. De Grauwe (2011a,b) models how monetary unions increase the possibility of default on sovereign debt. Other examples of models describing default risk in the EMU include Gros (2011) and Corsetti and Dedola (2011).
8 papers use time dummy’s to account for a regime switch, e.g. De Grauwe en Ji (2013). By using time dummy’s De Grauwe and Ji (2013) argue that investors change their behavior and response to risk factors after an event.
Most research however, focused on Credit Default Swap (CDS) spreads (e.g. Fontana and Scheicher, 2010, Aizenman and Jinjarak, 2010, Calice et al., 2011). These papers found that during the crisis spreads are higher than fundamentals would suggest.
The use of CDS spreads has a couple of advantages and disadvantages. Some advantages of CDS data are that there is better country coverage, especially for developing countries. There is less difficulty in dealing with time to maturity and, opposed to yields on bonds, CDS do not embed inflation expectations and demand/supply conditions of credit (Aizenman et al., 2013). The largest disadvantage of CDS, however, is the data availability. Both Datastream, Datascope and Tickhistory do not provide data on CDS before 2004 while the full sample of EMU country data is available from October 2006, while Finland and Luxembourg are still excluded. The dataset stops in September 2010 when Thomson Reuters stops providing CDS data via these channels. Indeed, all paper that where found that used CDS data cover only the period 2006-2010. A disadvantage of using the small time period of available CDS spreads is that it does not take all moves during the crisis into account. This can be seen in Figure 1 where the yields on sovereign bonds increase steadily form the SWEAP countries until July 2011 after which some yields go down, e.g. Ireland and Spain, and some keep increasing until the overall high in June 2012. Using only data until September 2010 will not take into account the various fluctuations during the crisis. For some papers CDS are still the best choice because of the availability of daily data.
Another group of papers used the spread of yield on bonds over German Bonds (e.g. Bernoth et al., 2004, Sgherri and Zoli, 2009). It is justified by the fact that Germany historically had the lowest yield of all EMU countries. Before the start of the EMU it was mostly because of the strict inflation policy of the German central bank and after the introduction of the euro because Germany is the largest economy in the EMU and generally has the lowest bond yield4. However, only looking at spreads relative to Germany gives an incomplete view because you either assume the yield on German bonds to be stable over time or that it move with the world credit market that is to a large extent determined by US bonds. Moreover, these papers assume the yield on German bonds to be the risk free rate.
Aizenman et al. (2013) conclude that risk in the five South-West Eurozone Periphery Countries, or SWEAP group (Greece, Ireland, Italy, Portugal and Spain), is underpriced prior to the financial crisis
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9 and overpriced during the crisis. They argue that this might be caused by investors that look at the assessment of risk based on expected fundamentals because current fundamentals cannot fully explain current risk and investors might expect further deterioration of fundamentals during the crisis.
3.1.1 Flight-to-safety
Fontana and Scheicher (2010) have mentioned the ‘flight-to-safety effect’ in correlation to credit default swaps after 2008. When EMU government bonds are good substitutes for each other, it might lead to a higher default premium because it is easier to avoid higher risk. A large public debt or other risk factors are punished harder by the market and should give countries more incentives for strict fiscal policy that can lead to convergence of bond yields. Otherwise, if countries do not recognize the increased risk and do not decrease their country specific risk factors, country bond yields should divergence, especially in times of high uncertainty. On the other hand, due to market integration, the perceived ‘risk-free’ rate can decrease which benefits low-risk countries.
In economic literature, a flight-to-safety effect is mostly mentioned in relation to developing and emerging economies as was observed during the Asian Crisis. An important difference, however, between capital flight in aforementioned examples and in the EMU is that in developing countries, the capital flight applies to a retraction of all kinds of assets in anticipation of a devaluation of the currency. In the EMU, a devaluation of the currency is only associated with the minimal chance of a country leaving the monetary union. Therefore, a flight-to-safety occurs mostly to avoid the risk of a default on government debt because this debt is not sustainable5. This phenomena mainly affects government debts and no other assets such as savings. Savings, however, can still be targeted in the case of a banking crisis as during the recent banking crisis in Cyprus.
Where other papers that examine the flight-to-safety effect look at the change in asset holdings in a country, the single currency of the EMU countries gives the opportunity to model the effect by looking at interest rate differences of sovereign bonds within the EMU. This is possible because of the high substitutability as a result of no exchange rate risk in the monetary union.
The interconnection amongst entities in economics has been modeled in various ways. One way to model the contagion between financial institutions is by estimating changes in the correlation coefficients after controlling for fundamental variables (e.g. Baig and Goldfajn, 1999; Hernández and Valdés, 2001; Fratzscher, 2003). A paper that tries to capture the interrelatedness of euro area countries is Caceres, Guzzo and Segoviano (2010). They used a spillover coefficient in order to measure if large
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10 fluctuations in sovereign spreads reflect changes in country-specific risk, via deteriorated fundamentals or contagion from other countries. To calculate the spillover coefficient a general measure for country distress is used. Another method is to use ARCH or GARCH techniques to estimates spillovers in volatility (e.g., Edwards and Susmel, 2000; Edwards and Susmel, 2001). A last approach, which is the most accurate, is to model the dependent variable of one institution to be conditional on the dependent variable of another institution in a system of equations. This model however, can only be used with a small number of dependent variables because the size of the model increases drastically with the number of institutions, known as the curse of dimensionality (e.g. Adams, Füss, and Gropp, 2010).
With the exemption of the last approach, all methods are inaccurate in describing all effects, whereas all methods have their own computational problems. Ultimately, the choice of which method to use depends on what to estimate. In this paper, spatial econometric techniques are used to estimate the interconnection in the sovereign bond market. As will be shown in section 4, this technique can overcome some problems of the models mentioned above and has great explanatory power.
3.1.2 Spatial econometrics
In the last decade, spatial econometrics has received increasing attention and has become more mainstream in econometric research (Anselin, 2006). Applications of spatial econometric models have also increased a lot, from the original applications in spatial science to the usage in social science and economics. With this increase in applications there has been a growing interest in the specification and estimation of models using panel data (Elhorst, 2010b). Furthermore, the use of different types of spatial models, with more than one spatial relation, has become more advocated by practitioners of spatial econometric (Elhorst, 2010a).
Although increasing, applications of spatial econometrics in finance are scarce. An example of spatial econometrics in finance is Fernandez (2011) who develops a spatial capital asset pricing model (S-CAPM) where the value at risk is derived from the spatial interaction model to improve risk management.
11 application in economics is by Kelejian, Tavlas, and Hondroyiannis (2006) who modeled how the instability of a foreign exchange market in an emerging economy affects other foreign exchange markets.
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Methodology
4.1 Spatial econometrics
The general consensus in economics is to model relations between variables with ordinary least square models which, in the case of panel data, are often extended with fixed effects. As described in the last section, to estimate a relation between dependent variables a few other techniques have been used although most can only give an approximation and are often hard to calculate and interpret. Incorrectly ignoring a spatial relation between variables where there is a spillover effect between the variables may however lead to biased and inconsistent estimates of the parameters (Anselin, 2006).
The basis spatial model, the spatial lag model, is set up as an OLS model where the dependent variable is partly determined by the dependent variable of other spatial units. In matrix algebra the equation becomes:
( 4.1 )
where the country index with , is an index for time with ; is a vector of dependent variables; is a matrix, being the number of independent variables; W is a positively defined by weight matrix with zeros on the diagonal measuring the extent of the spatial relation between the different spatial units so that the row elements of the weight matrix display the impact on one country by all other countries; is a scalar and are K-dimensional vector of constant coefficients; is an vector of error terms and is independent and identically distributed for and with zero mean and variance . Although intuitive, cannot be interpreted as a correlation coefficient between and . While does indicate the level of spatial spillovers it is not bound to and has in fact a maximum value of strictly less than one6 (LeSage and Pace, 2009).
Rewriting equation (4.1) gives the equilibrium value for
( 4.2 )
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12 The term , often called the spatial multiplier, determines the spatial relation followed by a shock in one of the independent variables to any . Such a shock has its effect the neighboring countries which will influence their neighbors, including the country where the shock originally originated. This process, the spatial autoregressive process, continues forever until it diminishes to zero and is described by the geometric series:
( 4.3 )
for . The higher order matrices , , … reflect both the spillover effect of second-order neighbors, neighbors of neighbors, on , including itself. Due to the two-way interaction among neighbors the autoregressive process induces simultaneity which is absent in the time domain so that every observation gives an equilibrium value among spatial units (LeSage and Pace, 2009; Durbin, 1998). The advantage of using a spatial econometric model is that it shows that the total effect is not necessarily equal to the sum of the parts. In the case of sovereign bond yields, if underlying variables influence the yield in two countries, it will effect both yields individually but also make the total monetary system more risky. A spatial econometrics model allows for a clear distinction between the direct effect, the same as in a normal OLS-regression, and the indirect effect due to higher order spillovers between countries.
In finance, the spatial econometric model turns out to have a very intuitive interpretation. Since is a measure for risk, Keiler and Eder (2013) show that a spatial econometric model gives a natural decomposition of total risk into systemic, systematic and idiosyncratic risk as shown in equation (4.4).
⏟ ⏟ ⏟ ( 4.4 )
The systemic risk component reflects the risk of shocks via the financial system. The systematic risk, or market risk, reflects the risk that effects the impact to aggregate risk factors such as broad market returns. Idiosyncratic risk reflects the risk factors to a specific institution. In contrast to systemic and systematic risk, idiosyncratic risk can be reduced or even fully eliminated in a well-diversified portfolio. Using this typology investors are able to make better allocation decisions. In the case of sovereign bonds, this means better diversification between countries in the world.
4.2 Types of spatial regressions
13 The most interesting models are:
Spatial lag model:
Spatial error model: , Spatial Durbin model:
Manski model: ,
where is a scalars and is a K-dimensional vectors of constant coefficients. Since spatial econometrics started from geographical relations the spatial lag model is the most widely used model because of the easy use and interpretation. An example of a spatial relation involving distance given by LeSage and Pace (2009) is commuting time to a centre where the population density of the region closest to the centre can influence the travel times of commuters further away, but a higher population density in the outer regions also have effect on regions closer to the centre because of more traffic moving through the region. The spatial error model is often not motivated by economic theory but a way to deal with data problems. If there are issues with correlation in the data, not necessarily of a spatial nature, the spatial error model can overcome some of these problems and can therefore be used both in spatial and in non-spatial models (Anselin, 2006). The spatial Durbin model gives both the spatial spillovers of the dependent and the independent variables. Where the spatial lag model is a more broad model to define a spatial relation, the spatial Durbin model gives more detail in the spatial spillovers. Therefore, the set-up of a spatial Durbin model is derived from economic theory. Furthermore, LeSage and Pace (2009) show that the spatial error model is a special case of the spatial Durbin model.
4.3 Choosing the right model
14 (1993), the Manski model is inappropriate since the model is unidentified unless at least one of the interaction effects is excluded. On the other hand, if either the spatial lag or the spatial error model is used, the model is biased and inconsistent if one of the relevant explanatory variables is omitted (Greene, 2005). Omitting the spatial error, however, will only lead to a less efficient model. Furthermore, LeSage and Page (2009) show that the spatial error model is a special case of the spatial Durbin model and therefore the spatial Durbin model will always give correct estimates in terms of standard errors and t-values. Therefore the Durbin model is estimated and tested for simplification using a likelihood ratio (LR) test with the hypothesis and . If both of these hypothesis are rejected the spatial Durbin model must be used. If one of the two is not rejected use either the spatial lag or the spatial error model profited that the LM test on the OLS model also confirmed that model.
4.4 Robustness checks
The advantage of using panel data is that you can account for individual (country specific) effects. Testing for these effects however, makes the steps for determining the right model more extensive. First, the model is tested for fixed/random effects in the normal OLS regression before the test for spatial dependence. Thereafter, the test for fixed/random effects is repeated for the spatial Durbin model. Doing multiple tests for country specific effects makes sure that the right model is chosen because it cannot be assumed that country specific effects in the OLS model transfer directly to a spatial model because of the extra explanatory power of the spatial model. The LR-test is used to test for the significance of spatial fixed or random effects and a Hausman test is used to choose between fixed and random effects. Although the model is tested for both fixed and random effects the literature in spatial research actually has the prevailing view that it is controversial to apply the random effects model (Elhorst, 2010c).
The regressions will be executed in Matlab for which the Matlab routines written by Elhorst7 and Lesage8 will be used that are adapted for use with common variables.
4.5 Form of the regression equation
It is assumed in this paper that a flight-to-safety effect is only triggered in extreme situations and not necessarily by fundamentals because it is very hard to measure the point when debt becomes unsustainable. Also, as De Grauwe and Ji (2013) found, the changes in spreads are largely disassociated from fundamentals. Therefore it is assume that a flight-to-safety effect is triggered by investor
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See http://regroningen.nl/elhorst/software.shtml 8
15 sentiment as measured by the common factors that are the same for all countries in the EMU. Using the spatial Durbin model with both country-specific and common variables, in matrix notation, the model can be written as follows:
( 4.5 )
where is a K-dimensional vector of parameter that indicate the possible fixed or random effects. The common factors are indicated by the matrix of order , being the number of common variables and being a vector of the dimension . Since the diversion of yields will only occur in extreme cases, the matrix will include quadratic terms. To capture a flight-to-safety effect a difference needs to be made between the safe countries and the countries that are deemed risky. For this purpose the common factors multiplied by a rating dummy are also included. The advantage of using a form of investor sentiment on common factors is that it can account for large movements over short periods of time without the need for time dummy’s that indicate a regime switch. As common factors a measure for risk appetite and the risk free interest rate are used.
If the yields on sovereign bonds are determined by investor sentiment only in times of crisis than the linear terms and the quadratic terms of the common factors should have the same sign for countries with a good rating and they should have the opposite sign for countries with a bad credit rating. E.g. when risk aversion increases during normal times investors move more funds to sovereign bonds which are presumed to be relatively safe for all countries. In times of crisis risk, aversion increases a lot so investors move more funds to sovereign bonds who are presumed to be safe (AAA rating) while investors will decrease the amount of funds invested in countries with a bad rating. A reason can be that investors fear that the government cannot repay its debt. However, in case of a flight-to-safety the flows of funds can be a lot larger than would be expected from the fundamental values. Eventually, the substitution between relatively high and low risk countries can lead to increasingly high interest rates for high risk countries making these countries even more risky. While if possible risk spillover effects are taken into account, an increase of risk in one country in a monetary union should also increase risk in other countries of that monetary union making high rated sovereign bonds even more overpriced.
16 : high values of common variables, as measured by the squared value, have the same influence
on AAA rated countries as on lower rated counties.
The fundamentals variables on the other hand are used as a measure of the level of normal spreads between individual countries and how much risk spillover there is between countries. When there are spillovers in risk factors it means that and are larger than zero so the second null hypothesis is:
: and
4.6 Expectations
The variables representing country specific risk will be expected to have a positive effect on sovereign bond yields (higher rate), both for the own county as indirectly for neighboring countries because these variables represent the fundamental factors of risk in the economy.
If there is only a high substitution effect during times of crisis it would be expected that for small changes in the common variables have a negative effect on both the own country and indirectly the neighboring countries since these variables still represent risk factors. However, for extreme values of these variables, represented by a quadratic term, can influence the yield on sovereign debt both positively and negatively, depending on their relative risk. It is expected that high values of common factors have a negative effect on high rated countries, defined by the quadratic term multiplied by the rating dummy. For countries with relative high perceived risk it is expected that high values of the common factors to have a positive effect on sovereign bond yield.
Since a flight-to-safety effect would only occur in extreme situation it is expected that the linear values of the common variables are positive. So an increased risk in foreign countries is always bad to countries with a low credit rating.
4.7 Weight matrix
17 importance (Leenders, 2002). The traditional weight matrix is based on geographical characteristics, i.e. distance or neighbors, although Leenders (2002) argues that the specifications of W ideally follow from theory. For the interaction among bond markets and the underlying risk characteristics of countries a distance measure seems inappropriate since it will undervalue large distant countries and overvalue small, nearby countries, e.g. using this measure would make Luxembourg equally important to Belgium as Germany and France. In the case of highly liquid and international bond markets it seems that larger countries should have more influence to all other countries. On the other hand, for the risk characteristics of a country neighbors are of higher importance because of closer economic integration. In order to balance these two views, a country’s relative export flow as a percentage of export to all EMU countries is used to describe the economic dependence on other countries. The advantage of using this measure is that it naturally has a balance towards both neighbors and large countries. The export volume of one country to all other EMU countries will be normalized to 1 so the trade with another country is expressed as the percentage of trade relative to all trade with other EMU countries.
One problem might be that the weight matrix should be exogenous. Whereas the absolute trading volume within the EMU and the trading volume with countries outside the EMU are changing a lot over time, mostly because trade with upcoming markets such as China and Brazil is increasing rapidly, the relative trade flows within the EMU are fairly constant over time, even during the financial crisis. Therefore, it is possible to use either a base year value or a long year average.
18 A Hausman test is performed to test if the weight matrix of relative trade flows or the weight matrix that is balanced towards country size give better estimates for the spatial relation between countries.
5
Data
The dataset consist of monthly panel data of EMU countries from January 1999 until December 2012. However, the countries that adopted the euro during the financial crisis (Slovenia, 2007; Cyprus and Malta, 2008; Slovakia, 2009; Estonia, 2011) are excluded because they lack data during ‘normal times’ making the comparison inaccurate. Excluding these countries will probably not have a large effect on the results since their weight in the European financial market is relatively small.
5.1 Dependent variable
The dependent variable that is used is the yield on sovereign bonds with a maturity of 10 years. The 10 year sovereign bonds are used because the long maturity better reflects the risk component of macro-economic variable since these have long run effects and it takes time for these variables to influence both the own economy and the economy of other countries. For Greece, only euro-denominated bonds where used for the period prior to the introduction of the euro in 2001.
Table 1 shows descriptive statistics of the of yields on 10-year bonds of the included countries over the sample period on a yearly base. It shows that the mean bond yield is rather stable over time with the highest mean value during the financial crisis not being significantly larger than the mean value in the first few years after the introduction of the euro. However, during the crisis there is a clear trend towards a higher standard deviation and an increasing spread between the minimum and maximum bond yield. These values already indicate an increasing difference in perceived risk between countries in the EMU.
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Table 1: Descriptive statistics for bond yields for all countries in the panel for the years 1999-2012.
The table shows the pooled statistics for all countries since the introduction of the Euro on a yearly bases. After 2008 the standard deviation increases significantly while the mean value does not change much. The increased spread between yields is an indication for a flight-to-safety effect. Source: Eurostat.
Mean Std. dev. Median Min Max
1999 4.82 0.73 4.90 3.70 7.03 2000 5.54 0.25 5.53 4.89 6.60 2001 5.05 0.24 5.06 4.29 5.54 2002 4.94 0.35 5.02 3.97 5.52 2003 4.09 0.31 4.18 2.85 4.51 2004 4.03 0.42 4.14 2.54 4.55 2005 3.34 0.34 3.39 2.12 3.92 2006 3.80 0.29 3.83 2.82 4.33 2007 4.35 0.22 4.35 3.83 4.85 2008 4.42 0.36 4.42 3.05 5.17 2009 4.11 0.62 3.96 3.02 5.87 2010 4.19 1.92 3.52 2.30 12.01 2011 5.74 4.06 3.82 1.83 21.14 2012 5.47 5.95 2.91 1.24 29.24 5.2 Independent variables
The following paragraphs contain an in-depth discussion of the independent variables. Two types of independent variables are used. The first group of variables are fundamental variables that explain default risk of individual countries and therefore the relative level of bond yields. The fundamental variables used are the debt to GDP ratio, the unemployment rate, inflation and a credit rating. The second group of variables are common factors that are the same for all countries and (partly) explain the business cycle in the economy. These variables consist of a measure for the risk free rate and a measure for investor risk appetite. It is expected that the common variables have the largest impact on the moves and volatility of bond yields.
20 the exact point when debt becomes unsustainable since this is dependent on a lot of factors, most of which can only be calculated when debt already became unsustainable. Therefore it is especially hard to calculate when this point arises. Furthermore, debt sustainability can very rapidly diminish when there is doubt about a government’s ability to repay debt. When investors fear that debt might not be repaid they can sell their bonds. This gives rise to a self-fulfilling prophesy because it raises interest rates and makes it more difficult to roll over existing debt. Appendix 9.1 gives a simple model for debt sustainability. In this simple model debt sustainability is a function of the government deficit, the GDP growth rate and the interest rate on debt. Solving for the interest rate gives:
( 5.1 )
where is the interest rate on debt, is the debt to GDP ratio, is the deficit to GDP ratio and is the GDP growth rate. Equation (5.1) gives the basis for the fundamental variables that determine the yield on sovereign bonds. Furthermore, using the Fisher equation ( ) it is clear that the interest rate level is also directly related to the inflation rate. However, the literature rarely uses these variables as a measure for bond risk. The GDP growth rate for example is not used, first, because only quarterly data is available on GDP growth and second, because it only influence the debt level through a change in taxes which and therefore does not add any new information compared to the deficit ratio. The following sections elaborate more on the individual variables and how they influence the bond yield. Appendix 9.2 show the descriptive statistics of all independent variables.
5.2.1 Debt to GDP
21 As a measure for monthly debt rates quarterly debt rates are cubically interpolated. Although probably not the best measure of monthly debt rates it will give a very good approximation of the real debt rates since the increase in debt often goes very smoothly as most expenses of the government are salaries of civil servants. Furthermore, cubic interpolation also encounters any seasonal pattern in government expenditure or tax income very well as it smooth out any frequent shocks. The quarterly data on debt rates are from Eurostat.
5.2.2 Unemployment rate
Equation (5.5) shows that one of the variables that influence the equilibrium value of debt, and therefore its sustainability, is the current account. However, only a few studies (e.g. Caceres et al., 2010, Kopf, 2011) actually take the deficit ratio into account. Reasons can be because the current account changes a lot from year to year and will therefore not give a good indication of the real sustainability of debt. Some authors have shown that a higher deficit has little effect on a countries interest rate. Evens (1985) looked at all periods with exceptional high inflation in the US since the nineteenth century and found no significant increase in interest rate on government bonds. Moreover, some data even indicate a decrease in the interest rate during periods of exceptional high deficit. Although others (e.g. Hoelscher (1985) find that although the effect on short term interest rates is tenues, there is a clear effect on long term interest rates. Another approach used by Aizenman and Jinjarak (2010) Aizenman et al. (2013) and De Grauwe and Ji (2013) is a measure for fiscal space which is defined as the ratio of deficit to total tax revenues and the ratio of debt to total tax revenues. It measures the tax-years it would take to repay the public debt. They argue that this is a better measure for the financial situation of the government than the current account because it better reflects the relationship to the public debt.
22 how the unemployment rate has a large effect on the bond yield of a country, the sovereign debt in Spain will not be influenced as much by debt as in Greece, Italy and even Belgium; however, with one of the highest unemployment rates in de EMU it will have a higher risk on which is shows in the bond yield of Spain. Lastly, a change in the unemployment rate can give a good long term view of the economic conditions because it signals a change in production and consumption expectations. This is also true for other EMU countries because over 66% of trade in Europe is intra-regional (WTO, 2013).
5.2.3 Inflation
Although in theory inflation is a monetary phenomenon and inflation rates in the EMU should be equal in the long run, this is certainly not the case in the short run. Investors will take account of the short run inflation differences because high inflation in one country might indicate higher future inflation in all countries and inflation is also an indicator of the economic conditions and competitive position of a country. Sgherri and Zoli (2009) even find that over the long run, inflation, together with wholesale money market developments, account for more than half of the changes in the common component of euro area sovereign spreads.
5.2.4 Credit Rating
In a model that includes all information about the economy the rating of creditworthiness of a country should not add any new information because it reflects exactly the same as the yield on sovereign bonds, namely credit risk. However, in reality this is not the case. First, a model can only give an approximation of the risk in an economy and therefore the rating functions as an instrument for omitted variables.
23 A disadvantage of using only two classes of ratings is that there is not a lot of variation in the ratings. Of the AAA-rated countries, only Ireland and Spain lose their high AAA credit rating during the financial crisis, where Spain has received the AAA-rating at the beginning of 2004. Of the countries that initially had a credit rating of AA- or higher, Ireland, Italy, Portugal and Spain all had a decline in credit rating to a value below AA-. Furthermore, Greece did not have a credit rating of AA- or higher during the complete sample period. Since there is slightly more variation for the AA- dummy and because this variation has an impact on all SWEAP countries, it is expected that the AA- dummy can better explain the sovereign bond yields.
5.2.5 Risk free rate
The first common variable that can influence is the bond yield is the risk free interest rate because it defines the rate on alternative investments. Rajan (2006) argues that investors’ attitude towards risk is influenced by the interest rate and that investors get more risk loving when interest rates are low and more risk averse during periods of high interest rates. Moreover, the risk-free rate influences the present value on future cash flows of investments. Manganelli and Wolswijk (2007) find that the spreads between sovereign bonds are mainly driven by the level of short-term interest rates. This is because, as they show, the short term interest rate determines a large part of investment choices and they find a similar effect on both the corporate bond spreads as the spreads between sovereign and corporate bonds. As a Euro-wide homogeneous measure for the short-term risk free rate the three-month Euribor short rate is used.
5.2.6 Risk appetite
24 As a measure for risk appetite this paper follow the approach Fontana and Scheicher (2010) who calculate a proxy for risk appetite to estimate the relation between CDS spreads and the underlying sovereign bond. They use the VIX index of implied S&P volatility and deduct a GARCH-based estimate of volatility from that index. It represents the risk premium that investors in equity option require as a compensation for equity market risk. Pan and Singleton (2007) have shown that the VIX index itself also is a significant determinant for sovereign credit risk.
6
Results
6.1 OLS regression
The results are discussed in the same order as the model comparison scheme proposed by Elhorst (2010). First, the results of the basic OLS regressions are examined and test statistics are shown to see if the model can be improved by including spatial spillover effects. Thereafter, the results of the spatial Durbin model are shown, followed by robustness check of this model to see if the model can be improved by using the spatial lag or spatial error model instead of the spatial Durbin model. Both models are described using all variables discussed and with a selection of variables in order to get an impression of how some variables impact other variables in the equation. Finally, LR-tests of model simplification to the spatial lag and error model are presented.
Table 2 shows the results for the OLS regression. This model is uses the same variables as the proposed model in equation (4.5) only without the spatial autoregressive terms.
( 6.1 )
Table 2 shows the OLS model with all variables and two regressions using a limited number of variables. The basic equation (a) excludes the credit rating dummy and all quadratic terms of the common variables. Next, the rating dummy is added in (b) and finally in column (c) the model with all variables is shown.
25 all variables except for the constant term are significant at the 1% level. Column (b) shows an OLS regression including the credit rating dummy. The dummy has a large negative effect on bond yields as is expected because a better distinction is made between high- and low-rated countries. In this model, however, the inflation rate is negative and insignificant. In the last column, (c), the regression with all variables is presented. The inflation rate is again the only insignificant variable. The largest surprise is that the rating dummy has a positive value in this model which can be explained by the inclusion of the common variables that are multiplied by rating dummy.
In model (a) and (b) the inflation rate is not in line with the theory that higher inflation leads to more risk on bonds. When looking at the data however, it shows that during the financial crisis there where large changes in both inflation and bond yields. Whereas the sovereign bond yields increased, the inflation rate showed the largest decrease over the sample period. Between 2008 and 2009 the average inflation rate declined from 3.46% to 0.22%. The large decline is not extraordinary as companies dismissed a lot of workers and the unemployment rate went up with 2 percentage points in the same period. Moreover, the decrease in inflation was especially large for countries like Greece, Portugal and Spain for which the bond yield also increased the most.
Furthermore, only some of the common variables have the expected signs. The quadratic effect of the risk free rate for high-rated countries is still positive while the quadratic effect for low-rated countries turns negative. This means that for normal values of the risk free rate an increase (decrease) of the risk free rate lead to a higher (lower) value of bond yields. For extreme values of the risk free rate however, a higher (lower) value of the risk free rate leads to a decrease (increase) in bond yields whereas for high rated countries this effect is almost completely cancelled by the variable so that the effect of the quadratic term is very small. An increase (decrease) in the risk free rate will, for the sample values, always have a positive (negative) effect on bond yields of high-rated countries.
26
Table 2: Regression of sovereign bond yields by OLS: 01/1999 – 12/2012
This table describes the OLS regression for monthly sovereign bond yields of countries, where the countries are the first 12 EMU countries (see footnote 3). The regression is given by:
where is the country specific bond yield; are the country specific independent variables; are the common independent variables and is an i.i.d. error term is a vector of constant coefficients and is a vector of possible fixed effects.
Debt/GDP is the ratio of government debt over GDP. Unemployment is the unemployment rate. Inflation is the inflation rate.
represents a dummy variable that is 1 for countries with a credit rating of or higher and is 0 otherwise. These
variables are measured at a country level. RF is the risk free rate for which the 3-month Euribor rate is used. RA is the risk appetite which is measured by the VIX index minus a GARCH based estimate. RF and RA are the same for each country. All variables are measured on a monthly bases. Sources: Eurostat, Datastream.
The (robust) LR-test for spatial lag and spatial error indicate if the model can be improved by including respectively a spatially lagged dependent variable or a spatial dependent error term. Form the (robust) LR-test it can be concluded that the OLS model, whichever variable are used, can be improved by adding a spatially lagged dependent variable or a spatial error term.
t-values are in parentheses. *, ** and *** indicate the significance at respectively the 10%, 5% and 1% level.
OLS (a) (b) (c) Debt/GDP 0.015*** 0.007*** 0.013*** (10.924) (4.725) (7.570) Unemployment 0.251*** 0.196*** 0.196*** (21.327) (16.539) (17.135) Inflation 0.099*** -0.044 -0.012 (3.035) (-1.351) (-0.391) - -2.085*** 0.237** - (-14.183) (2.254) 0.313*** 0.341*** 0.766*** (9.967) (11.385) (6.532) 0.048*** 0.050*** 0.178*** (6.931) (7.463) (6.876) - - -0.266*** - - (-10.703) - - 0.005*** - - (4.948) - - 0.214*** - - (15.608) - - -0.011*** - - (-21.136) Constant -0.288** 2.780*** -0.980*** (-1.537) (9.908) (-2.777) No. Obs. 2016 2016 2016 0.339 0.399 0.471 Adj. 0.338 0.398 0.468
LR-test for spatial lag 12.822*** 14.878*** 12.660*** Robust LR-test for spatial lag 39.625*** 113.274*** 156.557***
LR-test for spatial error 8.231*** 8.415*** 5.381***
27 Concluding, most variables behave in the way that is expected by theory. Furthermore, the risk free rate indicates a safety effect whereas the risk appetite does not indicate any flight-to-safety effect.
Finally, the values of the (robust) LM-tests for inclusion of a spatial lag or a spatial error term are shown. For all models, both the regular and robust LM tests indicate that the model can be improved with a spatial lag or spatial error term.
6.2 Spatial panel regression
Table 3 shows the regressions for the spatial Durbin model. Again, multiple regressions are shown to give a good impression of how the variables behave in different models. The first model in column (d) is a model with all variables but without fixed or random effects. Essentially, this model is the same as model (c) of the OLS regression with this inclusion of spatial spillover effects. The second model in column (e) includes fixed effects and excludes the quadratic terms of the common variables. Next, in column (f), again, the full model is shown including fixed effects. Finally, in column (g) the full model with random effects is presented.
The first regression (d) is without fixed or random effects including all variables. In this regression all variables have the same sign as in the OLS regression (c) that includes all variables. New in this model is the distinction between direct and indirect effect. The direct effect shows the same as the coefficient for the variables, however, since the spatial effects are obtained by creating random changes in the variables to measure the direct and indirect effects, the direct effect and the coefficient are not necessarily the same. For all variables the direct effect and the coefficient are close to each other and all have the same sign, only for the debt to GDP ratio the difference is relatively large, although, the difference is only small compared to the indirect effect. The indirect effect, as explained in section 4.1, measures the effect of the spatial autoregressive term which is the rebound effect of a change in one of the variables so that the variable influences the variables of other countries that again have an (indirect) effect on the first country. For the fundamental variables, except for the rating dummy, the indirect effects are all much larger than the direct effect. This means that a change of a variable has a relatively small effect on the risk of one country although the effect on the system as a whole is relatively large and therefore the total effect is increased a lot. The high values of the indirect effect are an indication of high systemic risk in the EMU, which is the risk of a collapse of the monetary system.
28 where all independent variables are negatively defined. The fact that the unemployment rate is negative indicates a flight-to-safety effect because, although risk increases by an increase in the fundamental variables of one country, the bond yields of other countries decrease. The rating dummy on the other hand, indicates a normal effect. If one country gets a higher rating, the bond yield of other countries decrease. Lastly, the variable indicate that the bond yields of all countries move largely together which is especially the case during the years before the financial crisis. It should be noted that the coefficients of the variables multiplied by do not give a one-to-one relation as the matrix consist of values strictly smaller than 1.
Furthermore, in the full spatial Durbin model without fixed effects the inflation rate is still negative which can be explained by the same reason as in the OLS model.
Column (e) shows the spatial Durbin model without the quadratic terms of the common variables and includes fixed effects. This model shows a few different outcomes compared to model (d). First, the inflation rate is positive as well as the credit rating dummy. For the inflation rate, this means that the coefficient is according to the theory, however, it is not clear why it is positive in this model and negative in the other models. The negative sign of the credit rating dummy might be explained by the relatively large effect of . Lastly, the effect of the variables of other countries on the bond yield are all
insignificant except for the rating dummy and the dependent variable so there is no flight-to-safety effect observed in this model.
Regression (f) shows the spatial Durbin model with fixed effects. Again, all variables have the same sign as in both the OLS model with all variables and the spatial Durbin model without fixed effects. What is interesting is that in the fixed effect model the direct effect of inflation is not significant while the indirect effect is significant. This indicates that the inflation rate has an insignificant effect on the own bond yield, however, an change in inflation has an significant indirect effect. Therefore, it can be concluded that inflation mostly affects systemic risk. The rating dummy in this model has a positive and significant value meaning that countries with a high rating pay, ceteris paribus, a higher rate on their debt than low rated countries. Again, this might be due to the large negative value of
.Moreover, the term is positive and significant meaning that an increase in the debt ratio of
other countries in the EMU do lead to higher bond yield. However, the effect of the risk free rate and investor risk appetite have a larger effect on high rated countries which can cancel the effect of a high rating.
29 more risk aversion. However, low-risk countries are affected by extreme values which indicate that they do profit from a rebalance of investor portfolios so there is a flight to safety effect from other securities towards low-risk sovereign bonds. The risk free rate clearly indicate a flight-to-safety effect. For small changes in the risk free rate the effect is positive while the effect is negative for extreme values of the risk free rate. For high-rated countries however, this effect is much smaller. Since the term is
smaller than it cannot be concluded that there is a direct flight-to-safety effect from high-risk countries to low-risk countries. However, investor portfolios have rebalanced more towards high-rated bonds than to low-rated bond in the financial crisis during which the risk free rate had a very low value. Finally, the LR-test for fixed effects indicate that fixed effects are significant.
The regression with random effects is shown in column (d). the LR-test for random effects show that the random effects are preferred to a model without random effects. Although the coefficients in both the fixed and random effect models are almost similar in value and have the same sign, a Hausman test shows that the model with fixed effect is preferred to the model with random effects. This is in line with the prevailing view that it is controversial to apply the random effects model (Elhorst, 2010c).
Because of all spatial Durbin models the model with fixed effects best describes the spatial spillover effects some robustness checks are performed with this model. First, a robustness check executed on the weight matrix of the spatal Durbin model. For this test the model is compared to a model that uses a weight matrix that consists only of relative trade flows and is not balanced towards country size by GDP. The comparison is made by a Hausman test. The Hausman test indicates that the model with a weight matrix that is balanced towards GDP is better in explaining the spatial effect between bond yields, however, only at a ten percent significance level. The low significance level is no surprise since the relative weights to other countries are almost unchanged, only a higher absolute weight is assigned to larger countries.
Next, the model is compared with a regression which is similar in all aspects to model (f) except for the rating dummy. Instead of a dummy that is 1 for a rating of AA- or higher a rating dummy that is 1 for countries with a rating of AAA is used. Again, a Hausman test is used to compare both models. The test shows that the rating dummy with rating AA- or higher is significantly better in explaining bond yields.
Table 3: Regression of sovereign bond yields with Spatial Durbin Model: 01/1999 – 12/2012
This table describes the Spatial Durbin regression for monthly sovereign bond yields of countries, where the countries are the first 12 EMU countries (see footnote 3). The regression is given by: where is the country specific bond yield; are the country specific independent variables; are the common independent variables and is an i.i.d. error term; is a row-normalized weight matrix; is a scalar indicating the spatial lag effect of the dependent variable; and are vectors of constant coefficients and is a vector of possible fixed effects. Debt/GDP is the ratio of government debt over GDP. Unemployment is the unemployment rate. Inflation is the inflation rate.
represents a dummy variable that is 1 for countries with a credit rating of or higher and is 0 otherwise. These
variables are measured at a country level. RF is the risk free rate for which the 3-month Euribor rate is used. RA is the risk appetite which is measured by the VIX index minus a GARCH based estimate. RF and RA are the same for each country. is the spatial lag effect of the dependent variable which indicate the effect of bond yields of the countries on the yield of country where . The variables , , and indicate the effect
of a change of the fundamental variables of country on country , . All variables are measured on a monthly bases. Sources: Eurostat, Datastream.
The LR-test for spatial lag and spatial error indicate if the model can be improved by using respectively a spatially lagged dependent variable or a spatial dependent error model instead of the spatial Durbin model. Form the LR-test it can be concluded that the spatial Durbin model best describes the spatial relationship in explaining sovereign bond yields.
The Hausman test for is a test to see if the weight matrix can be replaced by a better weight matrix. The original is adjusted for GDP whereas the alternative is not. The Hausman statistic indicates that the original weight matrix indeed best describes the spatial spillovers.
The Hausman test for AAA is a test to see if the rating dummy has better explanatory power by using a rating of AA- and higher or a AAA rating. The Hausman statistic indicates that the rating dummy AA- and higher significantly better describes bond yields.
t-values are in parentheses. *, ** and *** indicate the significance at respectively the 10%, 5% and 1% level.
Spatial Durbin Model
(d) (e) (f) (g)
Coefficient Coefficient Coefficient Coefficient
31 (-10.039) (2.110) (-9.611) -2.859*** 0.350* 0.524** 0.456* (-11.482) (1.516) (1.987) (1.737) Direct effect -2.882*** 0.354* 0.535* (-11.393) (1.505) (1.939) Indirect effect -1.076*** 0.283* 0.279* (-6.801) (1.655) (1.889) Total effect -3.958*** 0.638* 0.814* (-10.639) (1.610) (1.930) RF 1.015*** 0.456*** 1.737*** 1.732*** (6.695) (8.589) (10.770) (10.768) RA 0.137*** 0.023*** 0.124*** 0.125*** (5.560) (3.576) (5.751) (5.788) -0.365*** -0.430*** -0.430*** (-13.068) (-16.284) (-16.314) 0.001 0.000 0.000 (0.696) (0.397) (0.396) 0.262*** 0.256*** 0.256*** (18.698) (18.644) (18.761) -0.005*** -0.004*** -0.004*** (-6.652) (-6.788) (-6.816) -0.005 -0.008 0.048*** 0.048*** (-0.544) (-0.841) (4.610) (4.671) -0.112** 0.050 -0.006 -0.007 (-2.277) (0.979) (-0.117) (-0.158) -0.010 -0.034 -0.038 -0.039 (-0.157) (-0.544) (-0.665) (-0.673) -6.106*** -4.224*** -4.550*** -4.588*** (-7.511) (-5.926) (-6.738) (-6.785) 0.279*** 0.378*** 0.355*** 0.355*** (11.331) (17.157) (15.777) (15.788) Constant 9.079*** -4.929*** (5.900) (-3.207) No. Obs. 2016 2016 2016 2016
Fixed/Random effects no fixed fixed random
LR-test fixed/random
effects 609.7*** 535.6***
0.535 0.584 0.659 0.657
Log Likelihood -3629 -3528 -3324 -3263
LR-test spatial lag 625.425*** 43.136*** 93.626*** LR-test spatial error 625.425*** 64.245*** 93.626***
Hausman test for 23.497*
Hausman test for
32 including a spatial error term, this test essentially is a test to see if the spatial Durbin model can be replaced by the spatial error model. For all models the LR-test indicate that the null hypothesis that the spatial lag or error model better describes sovereign bond yields is rejected.
It can be concluded that the spatial Durbin model with fixed effects best describes the relationship between sovereign bond yields. This model indicates a clear spillover effect of the fundamental variables as well as for the dependent variable. Furthermore, the common variables have a large effect on sovereign bond yields. Also there is evidence of a flight-to-safety effect. However, the flight-to-safety effect is not only a direct substitution between low- and high-rated bonds. Some of the flight-to-safety comes from other securities and the investor preference to invest in high-rated sovereign bonds.
7
Conclusion
This paper has investigated the spatial relationship between the yields on sovereign bonds in the European Monetary Union (EMU) and whether there is a flight towards safer investments during the recent financial crisis. Using monthly data on 10-year sovereign bond yields of EMU countries between January 1999 and December 2012 it is examined if there are spatial spillovers between risk indicators.
The paper has looked how the yields on sovereign bonds are described by country specific fundamental factors and common factors that measure investor preferences. A spatial relationship should indicate how much of country risk is determined by country specific factors and by how much it is influenced by risk factors from other members of the monetary union. The Use of common factors makes it possible to indicate if there is a substitution between relative risky and safe assets.
In line with the literature on bond pricing, this study shows that common variables that explain general investor behaviour play a large role in describing the yields on sovereign bonds. However, when accounting for the indirect spatial effect of fundamental variables, the fundamental variables do have an important impact on risk assessment that is underestimated when only direct effect are examined. The indirect effect indicates a systemic risk factor that should be taken into account when to decide for support of weak countries in the EMU.
