Government bond market linkages: evidence from Europe

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1 Applied Financial Economics, 2005, 15, Government bond market linkages: evidence from Europe Jian Yang Department of Accounting, Finance & MIS, Prairie View A&M University, Prairie View, TX 77446, USA and Lingnan (University) College, Sun Yat-Sen University, Guangzhou, P.R. China This paper examines linkages among six major European government bond markets (Germany, France, Italy, UK, Belgium and the Netherlands) during There is weak evidence that a stable long-run relationship exists among the six markets during the sample period. Granger causal linkages are generally not pronounced between the markets, while the contemporaneous correlation is strong between bond market innovations. Allowing for both Granger causal relationships and contemporaneous correlation, forecast error variance decomposition suggests that European bond markets are generally interdependent without a distinctive leadership. There is also some evidence that the UK and Italy may be less integrated with other markets, possibly due to their nonparticipation in the European Monetary System during part of the sample period. I. Introduction The market capitalization of international bond markets is larger than that of international equity markets (Barr and Priestley, 2004, p. 91). However, compared to a large body of literature on international equity market linkages (see Bessler and Yang (2003) and references therein), only a few empirical works have investigated international bond market linkages (Smith, 2002; Barr and Priestley, 2004). The extent of international bond market linkages is indeed worthy of investigation, as it may carry important implications for the cost of financing fiscal deficit (Barr and Priestley, 2004), an independent monetary policymaking (Kirchgassner and Wolters, 1987), modelling and forecasting long-term interest rates (DeGennaro et al., 1994), and bond portfolio diversification (Clare et al., 1995). The theory, however, does not provide unambiguous prediction on the extent and the nature of international bond market linkages. As pointed out by Barassi et al. (2001), bond yields can be viewed either as analogous to other asset prices or as policy instruments. Hence, with voluminous capital flows across substantially deregulated international financial markets, bond yields as asset prices may be expected to move together to a certain extent, depending on the seriousness of the remaining barriers to market entry. On the other hand, the market-driven comovement of bond yields may be confounded by the degree of national monetary policy independence and/or fiscal budget constraints. Hence, the extent of international government bond market linkages is essentially a matter of empirical testing. This paper examines European government bond market linkages during European bond markets have grown significantly in recent years, particularly after the implementation of the European Monetary Union (EMU) in It is even projected Applied Financial Economics ISSN print/issn online # 2005 Taylor & Francis Group Ltd DOI: /

2 600 J. Yang that the government bond markets of the EMU members may be double the size of the US Treasury market in five to ten years (Holder, 1999, p. 29). Government bond issues generally make up more than 50% of the total EMU bond market value and represent the most important type of bond investment available to international investors in the EMU. 1 These markets are also considered highly efficient and liquid. This study contributes to the literature in several aspects. First, by extending previous studies focusing only on several major government bond markets in the world, this study is among the first to examine European government bond market linkages. Focusing on European markets can shed more light on the maximum level of integration currently attainable in international bond markets, because these markets are most likely to be integrated (at a regional level). The capital market integration has long been a major element of the European economic integration process. Although some studies have been conducted to address market integration in European equity markets (e.g., Yang et al., 2003), little research has been published on bond market integration in Europe. Harm (2001) is a notable exception. However, its focus is on European private sector bond markets. Second, various aspects of international bond market linkages are more thoroughly investigated in this study. While previous studies often focus on long-run cointegration relationships between bond yields (e.g., DeGennaro et al., 1994; Clare et al., 1995; Barassi et al., 2001; Smith, 2002), some studies also underscore other aspects of international bond linkages, including dynamic causal linkages between bond yield changes (Kirchgassner and Wolters, 1987), and contemporaneous correlations between bond yield innovations (Kirchgassner and Wolters, 1987; Sutton, 2000). This paper comprehensively examines long-run cointegration relationships between bond yields, dynamic causal linkages between bond yield changes and contemporaneous correlations between bond yield innovations. Few researchers have examined all these related, but distinctive perspectives, in an individual study. Toward this end, several relatively new techniques are employed to serve the purpose. In particular, a recursive cointegration technique (Hansen and Johansen, 1999) is applied to shed light on the controversy over the (non)existence of cointegration in international bond markets. For example, DeGennaro et al. (1994) and Clare et al. (1995) did not find any long-run linkages among international bond markets, while Barassi et al. (2001) and Smith (2002) reported positive evidence. A robust forecast error variance decomposition (Pesaran and Shin, 1998) is also employed to allow for both Granger causal relationships and contemporaneous correlation. As noted by Kirchgassner and Wolters (1987, p. 679), the instantaneous relations (among bond yield innovations) are probably much more important than the simple Granger causal relations (in international bond markets). 2 The method has only recently been applied in financial research (e.g., Ewing, 2002; Yang et al., 2003; Yang et al., 2005). The rest of this paper is organized as follows. Section II discusses econometric methodology. Section III describes the data. Section IV presents empirical results. Finally, Section V concludes the paper. II. Econometric Methodology Cointegration tests The empirical analysis is based on a vector autoregression (VAR) framework. The cointegration test in this study employs the procedure developed by Johansen (1991). Let X t denote a vector which includes the bond yield series ( p) for six government bond markets ( p ¼ 6) and the error correction model (ECM) representation is given by: X t ¼ X t 1 þ Xk i¼1 i X t i þ þ e t t ¼ 1,..., T ð1þ Equation 1 resembles a vector autoregression (VAR) model in first differences, except for the presence of the lagged level of X t 1. The parameter matrix,, contains information about the long-run (cointegration) relationships among p variables. The X t 1 term disappears when there is no cointegration. 1 As documented in Holder (1999), 58% of the EMU bond market consists of government bond issues in late 1990s, compared with 25% for the US market. By contrast, EMU does not have a liquid corporate bond market. Corporate bonds in the EMU market have only accounted for 3% of the total market value, compared with 20% in the USA. 2 Sutton (2000, p. 368) also argued that bond yields display excessive comovements in major government bond markets, which may be captured by contemporaneous correlations between bond yield innovations. Also see the discussion below on the argument of Swanson and Granger (1997) that contemporaneous correlations may actually result from unidirectional Granger causality in the presence of temporal aggregation. Also noteworthy, strong contemporaneous correlations between international stock market innovations have also been documented in the literature (e.g., Bessler and Yang, 2003).

3 Government bond market linkages 601 In the case where bond yields are found to be nonstationary, the international bond market linkage in the long run can be examined by determining the number of cointegrating vectors, r, as follows: HðrÞ :¼ 0 A trace test (Johansen, 1991) is conducted to determine r. The null hypothesis for the trace test is that there are at most r(0 r<p) cointegrating vectors. To rigorously address the controversy over the existence of (non)cointegration in international bond markets, a recursive cointegration technique is applied to examine the stability of the identified (non)cointegration relationship over each data point during the sample period. This is accomplished by testing constancy of cointegration rank as described in Hansen and Johansen (1999). Hansen and Johansen (1999) suggested that the rank constancy test can be conducted under two VAR representations of Equation 1. In the Z-representation all the parameters of the ECM are reestimated during the recursive estimations. While under the R-representation the short-run parameters i are fixed to their full sample values and only the long-run parameters in Equation 1 are reestimated. Hansen and Johansen (1999) remarked that the results from the R-representation should be more relevant in recursive cointegration analysis. Mathematically, the R-representation can be derived as shown below (see Hansen and Johansen (1999) for more details). Let Z 0t ¼ X t, Z 1t ¼ X t 1, Z 2t ¼ Xt 1, 0..., Xt k 0. For the ease of the presentation, deterministic terms such as in Equation 1 can also be ignored. Equation 1 can thus be formulated as ð2þ Z 0t ¼ 0 Z 1t þ Z 2t þ " t t ¼ 1,..., T ð3þ Maximum likelihood estimation of Equation 3 based on all data consists of a reduced rank regression of Z 0t on Z 1t conditional on Z 2t. Define R ðtþ 0t andrðtþ 1t as residuals from the regression of Z 0t and Z 1t on Z 2t, respectively (where the superscript T denotes that estimation of short-run dynamics is based on full sample data). That is, where R ðtþ 0t R ðtþ 0t M t ij ¼ Xt h i 1Z2t ¼Z 0t M ðtþ 02 M ðtþ 22 h i 1Z2t ¼Z 1t M ðtþ 12 M ðtþ 22 s¼1 Z it Z 0 jt i, j ¼ 0, 1, 2 The remaining analysis can be based on the following regression equation where the parameter has been filtered out: R ðtþ 0t ¼ 0 R ðtþ 1t þ R ðtþ "t t ¼ 1,..., T ð4þ Equation 4 is termed the R-representation, and the cointegration rank as determined by the rank of ¼ 0 can be obtained recursively, as t increases each step by one data point until it reaches to the full sample size T. Noteworthy, the R-representation is constructed in such a way that any rejections of stability are due to changes in the long-run relationship, rather than due to shifts in short-run dynamics. Granger causality tests In the case of no cointegration, a first differenced VAR should be estimated and used to summarize the dynamic causal linkages between bond yield changes, which is applicable in this study. The study examines the dynamic causal relationship using two econometric methods. The first method is Granger causality tests. To illustrate, Granger causality running from X to Y can be tested based on the following specification: Y t ¼ 0 þ Xk i¼1 Y t ¼ 1 þ Xk i¼1 i Y t i þ " 0t i Y t i þ Xk j¼1 j X t j þ " 1t where " 0t and " 1t are white noise residuals. In this study, the same VAR lag k is used consistently in the context of Equations 5 and 6, and is chosen by the minimization of Akaike Information Criterion (AIC). The direct Granger causality test based on Equations 5 and 6 is equivalent to testing the following null hypothesis: 1 ¼ 2 ¼¼ k ¼ 0 ð7þ which can be conducted using the F-statistic F ¼ ðsse 1 SSE 2 Þ=k ð8þ SSE 1 =ðn 2k 1Þ where SSE 1 and SSE 2 are the sum of squared errors from least squares regressions on Equations 5 and 6 and n is the number of observations. However, as discussed in Engle (1982, p. 994), the existence of conditional heteroscedasticity may cause the conventional Granger causality tests to be not only inefficient but also inconsistent. The ordinary least squares estimator of coefficients is still consistent ð5þ ð6þ

4 602 J. Yang as long as independent variables are uncorrelated with the residual. However, if there are lagged dependent variables which are included as independent variables (which obviously applies to Granger causality tests), the standard errors as conventionally computed will not be consistent. This is because the squares of the disturbances will be correlated with squares of independent variables. As suggested in Engle (1982) and Swanson and Granger (1997), in the case where the conditional heteroscedasticity problem needs to be addressed, the appropriate heteroscedasticity and autocorrelation-consistent covariance matrix (Newey and West, 1987) can be applied to the estimation of Equations 5 and 6. This would give a consistent estimate of the leastsquares standard errors. In such a case, the appropriate 2 -statistic is used (instead of the F-statistic) to test the above null hypothesis in Equation 7. Forecast error variance decompositions The second method used in this study to gauge dynamic causal relationships is forecast error variance decomposition. As emphasized in the literature (Sims, 1980, p. 20; Abdullah and Rangazas, 1988, p. 682), it may be misleading to rely solely on the statistical significance of economic variables as determined by the Granger causality tests. Specifically, some variables may not be statistically significant in explaining a dependent variable for various reasons (e.g., instability) but may be economically significant (which may be captured by the magnitudes of coefficient estimates). These variables, which may be statistically insignificant but economically significant, should not be ignored in the model specification. Based on this very consideration, Sims (1980) recommended that forecast error variance decomposition (or impulse response analysis) should be used to model the relationship between economic variables, as it allows for economic significance of the selected variables. Thus, according to Sims (1980), forecast error variance decomposition may produce some insights beyond the Granger causality tests, such as the strength of a causal relationship between economic variables in addition to the direction of such a casual relationship. In addition, as it should be clear from further discussion on Equation 8, forecast error variance decomposition allows for both Granger causal relationships and contemporaneous correlations. More generally, unidirectional Granger causality in the presence of temporal aggregation can result in such contemporaneous correlations of residuals in a system that has contemporaneously uncorrelated residuals at the true time interval (Swanson and Granger, 1997, p. 358). In this sense, it is hard to distinguish between Granger causality and contemporaneous correlations, for which both should be allowed. Such an argument particularly applies in the studies of international bond market linkages where the data of highest frequency available are monthly data and contemporaneous correlations are far more pronounced than Granger causal relationships. In this study, a relatively new econometric technique, generalized forecast error variance decomposition (Pesaran and Shin, 1998), is employed to better explore interrelationships between economic variables. This decomposition is motivated by the existence of strong contemporaneous correlations between international bond markets (Kirchgassner and Wolters, 1987; Sutton, 2000). In such cases, it is well known that the traditional orthogonalized forecast error variance decomposition, based on the widely used Choleski decomposition, is sensitive to the ordering of the variables. By contrast, generalized forecast error variance decomposition is invariant to the ordering of the variables, and thus it is uniquely determined. Specifically, the above Equation 1 can be rewritten as an infinite moving average process: X t ¼ X1 i¼0 C i " t i t ¼ 1, 2,..., T ð9þ As demonstrated in Pesaran and Shin (1998), the generalized forecast error variance decomposition for the vector X t is given by ij ðnþ ¼ 1 ii P n l¼0 2 e0 ic l e j e0 i C lcl 0e i, j ¼ 1, 2,..., p i ð10þ P n l¼0 where jj is jjth element of the residual variancecovariance matrix of the vector X t, e j is a m 1 vector with unity at the jth row and zeros elsewhere, and n is the number of steps ahead. Note that the Granger causal relationship is allowed for (in the sense of economic significance) by the moving average coefficients C l (which are derived from the VAR coefficients in Equation 1), while the contemporaneous correlation is allowed for by the inclusion of. The generalized forecast error variance decomposition reveals to what extent variation of a certain economic variable can be explained by innovations from other economic variables in the system. It can be used to measure the relative importance of other economic variables in influencing a particular economic variable.

5 Government bond market linkages 603 III. Data The data for this study include 192 monthly observations, covering a 16-year period from January 1988 to December The six government bond markets under study are as follows: Germany (GM), France (FR), Italy (IT), the United Kingdom (UK), Belgium (BL) and the Netherlands (NL). These six markets represent all major government bond markets in Europe. Previous studies (e.g., DeGennaro et al., 1994; Clare et al., 1995; Sutton, 2000; Smith, 2002; Barr and Priestley, 2004) also typically used monthly observations. 4 Similar to Clare et al. (1995), Smith (2002) and Barr and Priestley (2004), J. P. Morgan total return government bond indexes are used in this study. These indexes represent the total return (including reinvested coupon payments) to investors from a representative portfolio of government bonds. They are constructed to include fixed-rate sovereign debt with maturities from one year to whatever maturity may be outstanding in the market in question. As pointed out by Smith (2002), compared to the data of a single maturity, such indexes are more likely to capture any long-run aggregate bond market relationships. As presented in Reilly and Brown (2003, p ), Solomon Smith Barney, J. P. Morgan, Lehman Brothers and Merrill Lynch compile four popular international government bond indexes, which are widely used as the benchmark for international bond portfolio management. These various indexes have several similar characteristics, such as measuring total return, using market-value weighting, and using trader pricing, although they differ in the number of countries included and the total sample size. As Merrill Lynch indexes do not cover some countries under study and Solomon Smith Barney indexes are unavailable, Lehman Brothers indexes are then used as an alternative to J. P. Morgan indexes. Lehman Brothers indexes start from January 1987 for all the six markets under study except the Netherlands, for which the data start from February Thus, as discussed below, analysis will be also repeated on the Lehman Brothers indexes from March 1990 to December The J. P. Morgan indexes are obtained both in local currency and US dollar terms. Following Barr and Priestley (2004), the central results are based on returns measured in local currencies. In general, the results in local currency terms are more relevant, if exchange rate risk is fully hedged in international investment (Barr and Priestley, 2004). By contrast, the results in US dollar terms reflect the possible benefits of international bond diversification to US investors (Smith, 2002). In this particular case, as five out of the six European markets share the same common currency (Euro) after 1999 and also had quasifixed exchange rates (against US dollars) before 1999, it should not be too surprising to find that the results in local currency and US dollar terms are qualitatively similar. Hence, the analysis is only reported hereafter based on the data in local currency terms. IV. Empirical Results Two standard procedures are applied to test the nonstationarity of each individual series. One is the augmented Dickey Fuller (ADF) test and the other is the Phillips Perron (PP) test. The null hypothesis for both procedures is that a unit root exists. Similar to most previous studies (e.g., DeGennaro et al., 1994; Clare et al., 1995; Smith, 2002), there is one unit root in each of the bond yield indexes under study, but no unit root in their first differences at the 5% significance level (available on request). Further, as pointed out in Bessler and Yang (2003), simply including one stationary time series itself will give rise to one cointegrating vector in multivariate cointegration analysis. In this context, the finding of no cointegration below confirms nonstationarity of individual bond market return series. Hence, all the six series are modelled in a VAR representation as in Equation 1 to conduct cointegration analysis. The optimal lag is selected by minimizing the AIC. The maximum lag is set at 12 months. The AIC suggests the optimal lag of k ¼ 2 for the level VAR and k ¼ 1 for the first differenced VAR. The trace test of Johansen (1991) is conducted on the whole sample period to determine r. Additional specification tests also show that residuals on the ECM estimation are reasonably well-behaved. Lagrangian multiplier tests on first order autocorrelation of 3 The J. P. Morgan data are available beginning from January 1986 for all markets except Italy, which is only available from January 1988 for Italy. As the Italian government bond market is considered important in Europe, it should be included in the study. Further analysis shows that the basic findings of this study are qualitatively not affected (results are available on request), whether Italy is included or not. 4 Thus far, the monthly data are usually the data of highest frequency available for the bond market indexes. Beginning from September 2003, J. P. Morgan started providing daily data from international government bond markets. Hence, it may be interesting to conduct research using daily data in the future.

6 604 J. Yang the residuals cannot reject the null of white noise residuals at any conventional significance levels. However, ARCH effects exist for each market innovations under consideration (see the related discussion below). In Panel A of Table 1, the trace test statistics are reported on the number of cointegrating vectors among the six markets. The trace tests for both a constant within and outside the cointegrating vector(s) are presented. Determination of the cointegration rank depends on how enters into the ECM either as a restricted constant in the cointegrating vector or as a linear time trend in the model. To deal with this problem, Johansen (1992) proposed a sequential testing procedure with respect to the cointegration rank. If there is a linear trend in the model, this hypothesis is labelled H 1 (r) and it is an unrestricted constant case. If there is no linear trend in the model, the hypothesis is labelled H 1 (r)*, which is a restricted constant case. The sequential testing procedure suggests testing hypotheses in the following order: H 1 (0)*, H 1 (0), H 1 (1)*, H 1 (1),...,H 1 ( p)* and H 1 ( p). Testing is stopped and the associated null hypothesis is accepted at the first fail to reject in this sequence. Following the sequential testing procedure of Johansen (1992), the Panel A of Table 1 should be read from left to right and from top to bottom. The first fail to reject null hypothesis is the cointegration rank being equal to zero in the case of a linear trend. Thus, there is zero cointegrating vector(s) with a linear trend at the 5% significance level (as well as at the 10% significance level). The plot of the data also verifies existence of a linear trend in the data generating process. Nevertheless, there is some difference in these government bond ratings. Obviously, it would be desirable to examine cointegration only between the countries with same credit ratings/risk, as they are more comparable with each other. Specifically, government bonds of Germany, France, UK, and Netherlands have the rating of AAA, while those of Belgium and Italy have the rating of AA. Hence, cointegration tests are further conducted among Germany, France, UK, and Netherlands as one group and between Belgium and Italy as another group. The result confirms no long-run relationships among the four markets with the AAA rating (Panel B, Table 1) nor among the two markets with the AA rating (Panel C, Table 1). 5 To examine the stability of the above (non)cointegration relationship, the recursive cointegration Table 1. Johsensen cointegration tests for bond market indexes (01/ /2003) Without linear trend With linear trend H 0 : T C(5%) T C(5%) Panel A: The six markets (GM, FR, IT, UK, BL, NL) r ¼ r ¼ r ¼ r ¼ r ¼ r ¼ Panel B: The four markets with AAA credit ratings (GM, FR, UK, NL) r ¼ r ¼ r ¼ r ¼ Panel C: Two markets with AA credit ratings (IT, BL) r ¼ r ¼ Note: The lags are selected by the consideration of the minimization of the Akaike Information Criterion. The use of 10% critical values yields qualitatively the same conclusion. Countries are abbreviated as follows: GM (Germany), FR (France), IT (Italy), UK (the United Kingdom), BL (Belgium), and NL (Netherlands). technique is applied to test constancy of cointegration rank as described in Hansen and Johansen (1999). Figure 1 shows normalized trace tests calculated at each month over the period 1993 : 1 through 2003 : 12. The five-year period in is used as the base period. Statistics in the figure are normalized by the 10% critical values (figure entries greater than 1.0 indicate that the null hypothesis can be rejected at that data point). Based on the R-representation, it is evident that no cointegration exists during most of the sample period, because the plots of trace test statistics are in most cases below the 1.0 line. There are only a very few short peaks going beyond the line at 1.0 over the sample period, noticeably with one dated from late 1993 through early 1994 and the other from mid-2002 through early Hansen and Johansen (1999) also remarked that the results from the R-representation are more relevant in recursive cointegration analysis. However, the plot from the Z-representation provides somewhat stronger, but still limited evidence for cointegration. In particular, both representations show a downward 5 We thank the referee for suggesting such analysis, which is largely ignored in the literature.

7 Government bond market linkages The Trace tests Z(t) R(t) is the 10% significance level Fig. 1. Plots of trace test statistics at each month during trend to move below the 1.0 line when it is near the end of 2003, which strongly suggests lack of a (stable) cointegration relationship during the sample period. In sum, the result of recursive cointegration analysis confirms the finding of no cointegration. While the Johensen cointegration test is commonly used in previous international bond market studies, the Engel Granger (1987) cointegration test is further conducted as one more robustness check. The test is based on testing the (non)stationarity of the residuals from a cointegrating regression, i.e., a bond market index regressed on all other five market indexes in this case (see, e.g., Engle and Granger, 1987; Enders, 2004). Hall (1989) discussed some well-known problems of the residual-based cointegration tests when they are applied to multiple variables. Nevertheless, the Engle Granger test is suitable for testing the null of no cointegration against the alternative of cointegration, which is the major interest in this case. The cointegrating regression is conducted with and without a time trend, and with each market as a dependent variable in such regression to allow for possible sensitivity. As shown in Table 2, the null of no cointegration cannot be rejected in any case for the whole sample period at the 5% (or 10%) significance level. The finding of no cointegration is consistent with DeGennaro et al. (1994) and Clare et al. (1995), but contradicts Barassi et al. (2001) and Smith (2002). 6 Lack of the long-run relationship may be due to 6 The different findings on cointegration between this study and previous studies might also be due to the difference in sample periods, different sets of markets under consideration, and different proxies for bond markets. For example, Barassi et al. (2001) used 10-year government bond rates rather than bond market indexes.

8 606 J. Yang Table 2. Engle Granger cointegration tests for bond market indexes (01/ /2003) Dependent variable Without linear trend With linear trend T C(5%) T C(5%) GM FR IT UK BL NL Note: The results are based on the ADF test with two lags, but have little change from 0 to 6 lags. The critical values are interpolated using the response surface in MacKinnon (1991). Using the 5% critical value for the specification without linear trend up to five variables from Enders (2004) ( 4.49), the inference remains unchanged. the existence of many barriers to market access in international bond markets such as heterogeneous taxation and maturity structure, investment culture, and institutional arrangements (Clare et al., 1995). It may also suggest insufficient macroeconomic (e.g., monetary and fiscal) policy coordination among major European countries during the sample period. As pointed out in Barassi et al. (2001, p. 128), even though the European Monetary System (EMS) (effective during the period in this study) aims to produce policy coordination, it is possible for national monetary authorities to pursue an independent long-term interest rate policy agenda over long periods. The recursive analysis also shows more clearly that the establishment of the EMU does not appear to improve the long-run relationship between European bond markets. The finding might be not too surprising, in the light of the argument that the policies of the European Central Bank may not necessarily be as stable or credible as those previously adopted by the German authorities, because smaller countries will also have an influence on monetary policy (Barassi et al., 2001, p. 128). Further, Harm (2001) argued that the stickiness in the regime shift to increasing integration cannot be solely attributable to regulatory issues. Instead, other factors such as reputational customer ties are partly responsible for the slow transition to an integrated European financial marketplace. Given lack of a stable cointegration relationship, a first differenced VAR should be an appropriate specification. The first differenced VAR with one lag is thus estimated and used to summarize dynamic interactions among the six bond markets. As a preliminary analysis of short-run dynamic linkages, Table 3. Multivariate Granger causality tests (01/ /2003) Variables GM FR UK IT NL BL Panel A: Granger causality tests (w/o adjustments for conditional heteroscedasticity) GM FR UK * IT NL * BL Panel B: Granger causality tests (w/adjustments for conditional heteroscedasticity) GM ** FR ** UK ** IT NL ** BL * Note: Each of the variables in the first column is the dependent variable in the relevant Granger causality regression where the variables in the first row are all included as independent variables. ** and * denote statistical significance at the 5% and 10% levels, respectively. F-tests are conducted for Panel A and 2 tests for Panel B. Numbers reported are p-values for these statistics. multivariate Granger causality tests are conducted and results are presented in Table 3. The results based on least square regressions without adjustment for conditional heteroscedasticity (Panel A) show that there are no causal linkages between any of these markets at either the 5% or the 10% significance level. The only exceptions are causality from France to both UK and Netherlands at the 10% level. However, as mentioned previously, the diagnostic tests show that each of bond yield changes exhibits ARCH effects. In particular, the Lagrange Multiplier statistics based ARCH(12) tests show very strong evidence for conditional heteroscedasticity. The p-values are as follows: (GM), (FR), (UK), (IT), 0.023(NL), (BL). The existence of conditional heteroscedasticity for bond yields at monthly frequency has not been reported in the literature, with the only exception of Barr and Priestley (2004). The finding here also extends Barr and Priestley (2004) in that ARCH effects are documented for all major European bond markets. To address the conditional heteroscedasticity problem, the least square regression is employed with the heteroscedasticity and autocorrelationconsistent covariance matrix (Newey and West, 1987). As reported in Panel B of Table 3, there are more

9 Government bond market linkages 607 statistically significant test statistics with such adjustment. In particular, the causal influence of France on Germany, UK and Netherlands is now significant at the 5% level and its influence on Belgium is significant at the 10% level. The only two markets that France does not exert causal influence are UK and Italy. Coincidently, these two markets were the only two countries which withdrew from the European Rate Mechanism in September Nevertheless, it is somewhat surprising to see that there also exists statistically significant influence of Italy on the French market. There are no other causal relationships between these markets. Hence, consistent with Kirchgassner and Wolters (1987), the overall result suggests the Granger causal relationships are not pronounced and that France plays an important role in causal linkages between European bond markets. To the best of the author knowledge, such an informational role of France has not yet been reported in the literature. However, as discussed above, the multivariate Granger causality test results should be viewed as preliminary for the following reasons. First, strong contemporaneous correlations between market innovations are not yet taken into consideration. The six-variable VAR model results in the following innovation correlation matrix (lower triangular entries only are printed in the following order: x 1, x 2, x 3, x 4, x 5, x 6, where 1 GM, 2 FR, 3 UK, 4 IT, 5 NL, 6 BL) :93 1 0:80 0:79 1 V ¼ 0:98 0:94 0: :93 0:93 0:78 0: :76 0:82 0:72 0:79 0:79 1 ð11þ The significance test is also conducted on whether each pairwise correlation is significantly different from zero and confirms the statistical significance even at the 1% level. The pattern observed from the residual correlation matrix (11) is also consistent with the return correlation matrix between major world government bond markets reported in Smith (2002, p. 209). That is, the correlation between European markets is typically higher than that between any other markets outside the Europe, which indicates a higher degree of integration between European markets than between other non-european markets. Second, the Granger causality test only allows for the statistical significance of economic variables (Sims, 1980; Abdullah and Rangazas, 1988). By contrast, the forecast error variance decomposition may provide additional insights because it allows for the economic significance of economic variables. Various factors such as instability may cause statistical insignificance of economic variables. Such a point may apply in this study, as the sample period covers the prolonged progress of European economic integration. Some possible instability on the model specification is also already reflected on the instability of the cointegration relationship (or lack of it) in the above recursive cointegration analysis. 7 As mentioned previously, the strong contemporaneous correlation also implies sensitivity of traditional orthogonalized forecast error variance decomposition to the ordering of economic variables. To explicitly examine such sensitivity, orthogonalized forecast error variance decomposition is conducted based on Choleski factorization with two particular orderings. The analysis is done up to a 12-month horizon. As the results at other horizons yield similar inference, only the result at the 3-month horizon is reported in Table 4. The first ordering (Germany, France, Italy, UK, Belgium, Netherlands) is suggested roughly by the relative size (or importance) of individual bond markets. Specifically, the weights (in October 2001) for each market in the global government bond market as proxied by the J. P. Morgan global index are as follows: Germany (9.26%), France (8.75%), Italy (8.18%), UK (5.24%), Belgium (3.02%) and Netherlands (2.34%). The result for this particular ordering (Table 4) clearly suggests dominance of Germany in European government bond markets. Specifically, Germany is not influenced by any other markets under consideration, but greatly explains the movement on all other markets (50 60% on UK and Italy, 80 90% on France, Belgium, Netherlands). It also shows that the UK and Italy are less integrated with Germany than France, Belgium, and the Netherlands, which is 7 In addition, based on the first differenced VAR model as applied in the Granger causality test below, the CUSUM test does not show any sign of structural breaks, but the CUSUMSQ test suggests that two structural breaks might have occurred, one in 1990 (possibly related to the German reunification) and another in 2001 (possibly related to the establishment of the EMU). However, further analysis shows that the basic inference of this study should be robust. Recursive estimation is conducted on the VAR model. The inference on the statistical significance for each coefficient remains the same throughout the sample period (results are available on request). In addition, it is well known that the deterministic change would not affect the result on the forecast error variance decomposition.

10 608 J. Yang Table 4. Forecast error variance decomposition results (percentage, three-month horizon) Type GM FR IT UK BL NL Variation of GM explained by shocks to the six markets C C G Variation of FR explained by shocks to the six markets C C G Variation of IT explained by shocks to the six markets C C G Variation of UK explained by shocks to the six markets C C G Variation of BL explained by shocks to the six markets C C G Variation of NL explained by shocks to the six markets C C G Note: Forecast error variance decomposition has been standardized for each explained market so that the sum is 100%. C1 denotes orthogonalized forecast error variance decomposition based on the Choleski factorization with the particular ordering (GM, FR, IT, UK, BL, NL), C2 denotes that with the particular ordering (FR, GM, UK, IT, NL, BL), and G denotes generalized forecast error variance decomposition robust against any particular ordering. largely consistent with the generalized forecast error variance decomposition result below. Nevertheless, the ordering based on the market size might not be the only possible ordering, and the second ordering (France, Germany, UK, Italy, Netherlands, Belgium) is meant for such sensitivity analysis. In particular, the orderings are switched between Germany and France, Italy and the UK, and Belgium and the Netherlands. The forecast error variance decomposition result in Table 4 clearly suggests great sensitivity to the switch in the ordering between France and Germany, but little or none to the switch in the other two pairs of orderings. Based on the second ordering, France takes the place of Germany to be dominant in Europe, while less influence of France on the UK and Italy than on other markets is still evident. Generalized forecast error variance decomposition is further conducted for up to a 12-month horizon, and the result at the three-month horizon is also given in Table 4. As noted previously, forecast error variance decompositions may be more informative than the multivariate Granger causality test results. Specifically, in addition to France (17%), all the other markets, including Netherlands (20%), Belgium (18%), and to a lesser extent, UK (13%) and Italy (12%), have the ability to noticeably influence Germany, which is not captured by the Granger causality test results. This may reflect a relatively high degree of interdependence between European government bond markets in the short run. Nevertheless, it also hints at lack of a leadership role by Germany in European government bond markets. As shown below, Germany does not exert a dominant influence on any other markets, either. The finding might be due to the fact that the German government has been in a great need of foreign capital after its reunification in Thus, it seems plausible that bond yields offered by Germany are also sensitive to changes in the bond yields in other European markets. Consistent with the finding here, Uctum (1999) reported that a structural break occurred and the dominant influence of German short-term interest rates on other EMS member interest rates disappeared after the German reunification in Also different from the Granger causality test results, all the other markets (Germany (18%), Netherlands (18%), Belgium (18%), and to a lesser extent, UK (13%) and Italy (12%)) can substantially explain the movements of the French market. While the evidence here does not strongly suggest the leadership role of France in European government bond markets, it clearly dismisses the possibility of its being a passive follower. According to Bessler and Yang (2003), however, France is among the least exogenous stock markets in the sense that information from other major stock markets is most prevalent in explaining its stock price movement, compared to other major European countries such as Germany and the UK. It is also interesting to note that although the UK and Italian markets are larger among the six markets under consideration, these markets seem to be less integrated with the other four markets. Specifically, their market exogeneity as indicated by the percentage of self-explained variation (25% for both markets) is higher than other markets (20 21%). On the other hand, the percentage of price variations on other European markets, explained by any of these two markets (12 13%), is lower than by other four markets (15 19% for Germany, 15 18% for France, 15 20% for Netherlands, and15 18% for Belgium).

11 Government bond market linkages 609 Such a finding may be accounted for by the nonparticipation of these two countries in the EMS during part of the sample period. In particular, both the UK and Italy withdrew their currencies from the EMS in September Since then, the British pound has been floating freely against other European Union country currencies, while Italy rejoined the EMS in November However, Italian government bonds are still considered to be of lower creditworthiness than other major European markets. As mentioned earlier, Italy has a credit rating of AA, while France, Germany and the Netherlands have a rating of AAA. Germany and France, and to a lesser extent, the UK and Italy, have noticeable influence on both Netherlands and Belgium, which is again not captured by the Granger causality test results. Consistent with Yang et al. (2003), the influence of the Netherlands is comparable to Germany and France and the three markets are substantially integrated in the short run. It is also found that Belgium is substantially integrated with other major markets, including Germany, France and the Netherlands. Finally, Lehman Brothers indexes are used as an alternative dataset to check the sensitivity of the findings to the data source used. The above analysis is repeated on this dataset during the sample period from March 1990 to December 2003, when Lehman Brothers indexes exist for all the six markets. To conserve the space, only Johensen cointegration test results are reported in Table 5, as such analysis has been a focus of previous studies. Following Johansen s (1992) sequential testing procedure, the first fail to reject null hypothesis is the cointegration rank being equal to zero with no linear trend for all the three cases considered at the 5% significance level. Nevertheless, there might be some evidence for one cointegrating vector (with no linear trend) in the cases of all the six markets and the two AA markets at the 10% significance level. In sum, the basic results (complete results available on request) are qualitatively unchanged. Such similarity should not be too surprising, in the light of the fact that J. P. Morgan and Lehman Brother indexes are highly correlated. Simple correlation between two indexes for the same market is typically between 0.6 and 0.7 (for example, 0.73 for France and 0.72 for UK). V. Conclusions This paper examines linkages on six major European government bond markets (Germany, France, UK, Italy, Netherlands and Belgium) during the period of January 1988 to December Conventional cointegration analysis suggests and recursive Table 5. Johsensen cointegration tests for alternative bond indexes (03/ /2003) Without linear trend With linear trend H 0 : T C(5%) T C(5%) Panel A: the six markets (GM, FR, IT, UK, BL, NL) r ¼ r ¼ r ¼ r ¼ r ¼ r ¼ Panel B: the four markets with AAA credit ratings (GM, FR, UK, NL) r ¼ r ¼ r ¼ r ¼ Panel C: two markets with AA credit ratings (IT, BL) r ¼ r ¼ Note: The lags are selected by the consideration of the minimization of the Akaike Information Criterion. cointegration analysis confirms that no stable longrun relationship exists among the six bond markets during the sample period, which is consistent with some earlier studies (DeGennaro et al., 1994; Clare et al., 1995), but contradictory to more recent studies (Barassi et al., 2001; Smith, 2002). Further, as found in Kirchgassner and Wolters (1987), there exist strong contemporaneous correlations between bond yield innovations, while causal linkages are generally not pronounced. Allowance for conditional heteroscedasticity is found to be important to detect any statistically significant causal relationships. A robust forecast error variance decomposition, combining both Granger causal relationships and contemporaneous correlation, suggests that European markets are generally interdependent. In general, consistent with previous studies of Harm (2001) and Barr and Priestley (2004), the results in this study show that European government bond markets are partially integrated in the short run. In addition, there is no evidence for a distinctive leadership role. In particular, consistent with the recent literature (e.g., Uctum, 1999), the result does not support the well-known German dominance hypothesis. Finally, the findings of this study carry some important implications. First, for investors with long investment horizons and passive portfolio management strategies, each of European bond markets can still provide its own substantial diversification

12 610 J. Yang potentials, even during the accelerated process of European economic integration. Long-term international investors should diversify their bond portfolios into each of these six major European bond markets to fully exploit risk reduction. Investors who have shorter investment horizons, however, may have much more limited diversification potentials from individual European markets, as all these markets tend to be much more closely linked in the short run. Second, the results suggest that short-term forecasts of bond yields for a major European market should be based on both domestic and other European markets macroeconomic variables. Finally, as the markets are only partially integrated in the short run and not integrated in the long run, governments in EMU member countries are currently paying too high a rate for their deficit funding. Nevertheless, as pointed out in Barr and Priestley (2004, p. 94), governments might be willing to continue to pay unnecessarily high funding costs in order to escape the discipline that would be exerted by a fully integrated world bond market. Acknowledgement The author would like to thank an anonymous referee of the Applied Financial Economics for many helpful comments, which substantially improve the paper. The author acknowledges financial support in the form of the College of Business summer research grant at Prairie View A&M University. References Abdullah, D. A. and Rangazas, P. C. (1988) Money and the business cycle: another look, Review of Economics and Statistics, 70, Barassi, M. R., Caporale, G. M. and Hall, S. G. (2001) Irreducibility and structural cointegrating relations: an application to the G-7 long-term interest rates, International Journal of Finance and Economics, 6, Barr, D. G. and Priestley, R. (2004) Expected returns, risk and the integration of international bond markets, Journal of International Money and Finance, 23, Bessler, D. A. and Yang, J. (2003) The structure of interdependence in international stock markets, Journal of International Money and Finance, 22, Clare, A., Maras, M. and Thomas, S. (1995) The integration and efficiency of international bond markets, Journal of Business Finance and Accounting, 22, DeGennaro, R., Kunkel, R. and Lee, J. (1994) Modeling international long-term interest rates, Financial Review, 29, Enders, W. (2004) Applied Econometric Time Series, 2nd edn, John Wiley & Sons, New York. Engle, R. F. (1982) Autoregressive conditional heteroscedasticity with estimates of the variance of UK inflation, Econometrica, 50, Engle, R. F. and Granger, C. W. J. (1987) Cointegration and error correction: representation, estimation and testing, Econometrica, 55, Ewing, B. T. (2002) The transmission of shocks among S&P indexes, Applied Financial Economics, 12, Hall, S. G. (1989) Maximum likelihood estimation of cointegration vectors: an example of the Johansen procedure, Oxford Bulletin of Economics and Statistics, 51, Hansen, H. and Johansen, S. (1999) Some tests for parameter constancy in cointegrated VAR models, Econometrics Journal, 2, Harm, C. (2001) European financial market integration: the case of private sector bonds and syndicate loans, Journal of International Financial Markets, Institutions & Money, 11, Holder, M. (1999) The Euro impact on European financial markets, Managerial Finance, 25(11), Johansen, S. (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models, Econometrica, 59, Johansen, S. (1992) Determination of cointegration rank in the presence of a linear trend, Oxford Bulletin of Economics and Statistics, 54, Kirchgassner, G. and Wolters, J. (1987) US European interest rate linkages: a time series analysis for West Germany, Switzerland, and the United States, Review of Economics and Statistics, 69, MacKinnon, J. G. (1991) Critical values for cointegration tests, in Long-run Economic Relationships: Readings in Cointegration (Eds) R. F. Engle and C. W. J. Granger, Oxford University Press, Oxford. Newey, W. and West, K. (1987) A simple positive semidefinite heteroscedasticity and autocorrelation consistent covariance matrix, Econometrica, 55, Pesaran, M. H. and Shin, Y. (1998) Generalized impulse response analysis in linear multivariate models, Economics Letters, 58, Reilly, F. K. and Brown, K. C. (2003) Investment Analysis and Portfolio Management, 7th edn, Thomson/South- Western, OH. Sims, C. (1980) Macroeconomics and reality, Econometrica, 48, Smith, K. L. (2002) Government bond market seasonality, diversification, and cointegration: international evidence, Journal of Financial Research, 25, Sutton, G. (2000) Is there excess comovement of bond yields between countries?, Journal of International Money and Finance, 19, Swanson, N. R. and Granger, C. W. J. (1997) Impulse response functions based on a causal approach to residual orthogonalization in vector autoregressions, Journal of the American Statistical Association, 92, Uctum, M. (1999) European integration and asymmetry in the EMS, Journal of International Money and Finance, 18, Yang, J., Balyeat, R. B., and Leatham, D. J. (2005) Futures trading activity and commodity cash price volatility, Journal of Business Finance and Accounting, 32, Yang, J., Min, I. and Li, Q. (2003) European stock market integration: does EMU matter?, Journal of Business Finance and Accounting, 30,

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