International bond market linkages: a structural VAR analysis

Int. Fin. Markets, Inst. and Money 15 (2005) 39–54

International bond market linkages: a structural VAR analysis Jian Yang∗ Department of Accounting, Finance and Information Systems, P.O. Box 638, Prairie View A&M University, Prairie View, TX 77446, USA Received 7 September 2003; accepted 12 February 2004 Available online 7 July 2004

Abstract This paper examines linkages between government bond markets of five industrialized countries (US, Japan, Germany, UK and Canada) during the period of January 1986 to December 2000. Recursive cointegration analysis clearly shows that no long-run relationship exists among the five major bond markets during the sample period. The contemporaneous causal pattern of the strong correlations between bond market innovations is uncovered, building on the recent advance in vector autoregression analysis. The identification of such a contemporaneous causal pattern further improves the investigation of the dynamic linkage pattern, which is based on data-determined forecast error variance decomposition. A number of new empirical regularities on international bond market linkages have been documented. © 2004 Elsevier B.V. All rights reserved. JEL classification: G15; C32 Keywords: International bond markets; Directed graphs; Forecast error variance decomposition

1. Introduction The integration of international bond markets has been perceived to increase dramatically in the last two decades since government-imposed barriers to the international flow of capital in major industrialized countries was substantially eliminated by the early 1980s. The extent and the nature of linkages in international bond markets carry important implications for an ∗

Tel.: +1 936 857 4011; fax: +1 936 857 2797. E-mail address: jian [email protected] (J. Yang).

1042-4431/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.intfin.2004.02.001

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independent monetary policymaking (e.g., Kirchgassner and Wolters, 1987; Sutton, 2000), modeling and forecasting long-term interest rates (e.g., DeGennaro et al., 1994), and bond portfolio diversification (e.g., Clare et al., 1995). The theory does not provide unambiguous prediction on the extent and the nature of international bond market linkages. Bond yields or long-term interest rates can be viewed either as analogous to other assets prices or as policy instruments (Barassi et al., 2001). With substantially deregulated international financial markets and voluminous capital flows across borders, bond yields in different markets may be expected to move together to a certain extent, depending on the seriousness of the remaining barriers to market entry. Furthermore, the market-driven comovement of bond yields may be confounded by the degree of monetary policy independence sought by national authorities. Hence, the extent of international bond market linkages is essentially a matter of empirical testing. Compared to a large body of literature on international stock market linkages (e.g., Eun and Shim, 1989; Arshanapalli and Doukas, 1993; Francis and Leachman, 1998; Bessler and Yang, 2003) and international money market linkages (e.g., Fung and Isberg, 1992; Fung and Lo, 1995), only very few empirical works have examined linkages in international bond markets. Applying a cointegration technique, DeGennaro et al. (1994) and Clare et al. (1995) did not find any long-run cointegration relationship among government bond markets of several major industrialized countries. By contrast, Barassi et al. (2001) and Smith (2002) reported existence of cointegration in these markets. Kirchgassner and Wolters (1987) found strong contemporaneous/instantaneous relationships and mild Granger causal linkages between US and two European government bond markets after 1980. Sutton (2000, p. 368) argued that bond yields display excessive comovements in major government bond markets, which may be captured by contemporaneous correlations between bond yield innovations. Obviously, the empirical findings are inconclusive and represent a number of different perspectives, thus calling for a more thorough analysis. This paper more comprehensively examines international bond market linkages, including long-run cointegration relationships between bond yields, dynamic causal linkages between bond yield changes and contemporaneous relationships between bond yield innovations. The study contributes to the literature in several aspects. First, to shed light on the controversy over the (non)existence of cointegration in international bond markets, the stability of the long-run relationship is investigated by applying a recursive cointegration technique (Hansen and Johansen, 1993) to test how the (non)cointegration relationship holds at each point of time during the sample period. Such a consideration is important, as Elyasiani and Kocagil (2001) recently found that possible structural breaks in the (non)cointegration relationship may occur due to some significant events. Second, the important contemporaneous causal pattern of the strong correlations between market innovations is explored building on recent advances in vector autoregression (VAR) analysis (Swanson and Granger, 1997; Bessler and Yang, 2003; Haigh and Bessler, 2004; Yang, 2003). Kirchgassner and Wolters (1987, p. 679) noted that “the instantaneous relations (among bond yield innovations) are probably much more important than the simple Granger causal relations (in international bond markets)”. Similarly, in Sutton’s (2000) model, excessive bond yield comovements are characterized by significant and positive correlations between bond yield innovations

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41

(p. 368).1 Thus far, the existing literature concludes that “with respect to the (contemporaneous causal) direction of instantaneous relations nothing can be derived from the data alone” (Kirchgassner and Wolters, 1987, p. 679). Building on Sims (1986) and Swanson and Granger (1997), this study is able to provide a data-determined solution to the issue. In a sense, the way of identifying the contemporaneous causal pattern in this study is also more data-determined than Swanson and Granger (1997) and Haigh and Bessler (2004). After allowing for zero first-order conditional correlation constraints exhibited in the data (as proposed by Swanson and Granger (1997)), we further use Sims’(1986) likelihood ratio tests rather than some economic theory priors to help determine the contemporaneous causal pattern. Third, identifying the contemporaneous causal pattern among innovations enables us to conduct a data-determined structural decomposition of VAR residuals. The dynamic linkage patterns between financial markets are often inferred from forecast error variance decomposition (e.g., Eun and Shim, 1989). As vigorously argued in Swanson and Granger (1997), compared to the widely used forecast error variance decomposition of Sims (1980), data-determined forecast error variance decomposition should be superior. In this context, this study may produce a more accurate description of dynamic linkages between international bond markets, due to its improved modeling technique. The rest of this paper is organized as follows. Section 2 discusses econometric methodology. Section 3 describes the data. Section 4 presents empirical results. Finally, Section 5 concludes the paper.

2. Econometric methodology 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 Xt denote a vector which includes the bond yield series (p) for five government bond markets (p = 5) and the error correction model (ECM) representation is given by: Xt = ΠXt−1 +

k−1


Γi Xt−i + µ + et

(t = 1, . . . , T)

(1)

i=1

Eq. (1) resembles a VAR model in first differences, except for the presence of the lagged level of Xt−1 . The parameter matrix, Π, contains information about the long-run (cointegration) relationships among p variables. In the case where bond yields are found to be nonstationary, we can examine the international bond market linkage in the long run by determining the number of cointegrating vectors, r, as follows: H(r) : 1

Π = αβ

(2)

More generally, as pointed out by Swanson and Granger (1997, p. 358), 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. The argument particularly applies in the studies of international bond market linkages where the data of highest frequency available are monthly data. Strong correlations of market return innovations have also been documented in international stock markets (e.g., Eun and Shim, 1989; Bessler and Yang, 2003).

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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, we apply a recursive cointegration technique 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 (1993). Hansen and Johansen (1993) suggested that the rank constancy test can be done under two VAR representations of Eq. (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 Γ i are fixed to their full sample values and only the long-run parameters in Eq. (1) are reestimated. Hansen and Johansen (1993) also remarked that the results from the “R-representation” are more relevant in recursive analysis. In the case of no cointegration (which is applicable in this study), a first difference VAR should be estimated and used to summarize the dynamic influence that each market has on other markets. However, the adjustments that establish these dynamic relationships in response to various shocks from other markets and the strengths of these dynamic relationships remain unspecified. Because the individual coefficients of a VAR model are hard to interpret, we conduct forecast error variance decomposition to summarize short-run dynamic linkages among the five bond markets. As mentioned previously, critical to such a forecast error variance decomposition is how to specify an appropriate contemporaneous causal model based on the correlations of VAR innovations (Swanson and Granger, 1997). Also, modeling the causal (and independence) relationships of innovations in contemporaneous time is by itself interesting because it contains important information regarding transmission of new information from one market to another (Eun and Shim, p. 246). Following Bernanke (1986) and Sims (1986), the system of contemporaneous innovations can be generally modeled as Aet = vt :      v1t 1 a12 a13 a14 a15 e1t       a21 1 a23 a24 a25   e2t   v2t        a31 a32 1 a34 a35   e3t  =  v3t  (3)            a41 a42 a43 1 a45   e4t   v4t  a51 a52 a53 a54 1 e5t v5t where A is a 5 × 5 matrix, aij (i,j = 1–5) are parameters (to be estimated or a priori set equal to zero) which represents contemporaneous causal patterns among bond market yield innovations, e1t is the observed (nonorthogonalized) innovation in period t in the US bond yields, e2t the observed innovation in Japanese bond yields, e3t the observed innovation in German bond yields, e4t the observed innovation in the UK bond yields, e5t the observed innovation in Canadian bond yields, and vit (i = 1–5) are orthogonal shocks. It is common in the VAR analysis to rely on a Choleski factorization, which assumes the A matrix to be lower triangular to achieve a just-identified system in contemporaneous time. In other words, the Choleski factorization restricts Eq. (3) to be in the following

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form:



1   a21   a31    a41 a51

0

0

0

1

0

0

a32

1

0

a42

a43

1

a52

a53

a54

   v1t e1t     0   e2t   v2t          0   e3t  =  v3t      0   e4t   v4t  e5t v5t 1

0

43



(4)

The causal implication of the Choleski factorization (Eq. (4)) is that in the contemporaneous time the series 1 causes series 2 (a21 = 0), series 1 and 2 cause series 3 (a32 = 0 and a31 = 0), etc. The problems of implementing the Choleski factorization in the literature are well recognized and include an often unrealistic assumption of the existence of a recursive structure and failure to identify a recursive structure (if such exists) (Bernanke, 1986; Sims, 1986; Swanson and Granger, 1997). Bernanke (1986) and Sims (1986) proposed a structural decomposition of VAR residuals. The structural decomposition gives researchers a very general framework of modeling the contemporaneous causal structure of innovations and does not require a recursive structure. However, its use in the literature (e.g., Cody and Mills, 1991) is still generally reliant on subjective or theory-based information for specifying contemporaneous causal flow (Swanson and Granger, 1997). Swanson and Granger (1997) presented a recent advance in VAR analysis. Swanson and Granger (1997) proposed a data-determined method for modeling the contemporaneous causal pattern of VAR residuals. Specifically, Swanson and Granger (1997, p. 361) argued for identifying a contemporaneous causal structure which satisfies zero first-order conditional correlation constraints exhibited by the data and is also in accord with some set economic theory priors. Certain economic theory priors are still needed and used in their procedure because causal flows between some (or even many) variables may still be hard to direct based solely on zero first-order conditional correlation constraints in the data. The approach of Swanson and Granger (1997) has been applied and extended in Bessler and Yang (2003), Haigh and Bessler (2004), and Yang (2003), among others.2 In this study, we also employ the above structural decomposition as expressed in Eq. (3). Following Swanson and Granger (1997), we calculate all zero-order (i.e., unconditional) and first-order conditional correlations and test whether or not they may be equal to zero. Note that zero unconditional correlation constraints may be considered as a special case of zero first-order conditional correlation constraints (Fig. 2). As illustrated by Glymour and Spirtes (1988) and Swanson and Granger (1997), a linear causal modeling can also be conveniently represented as a directed graph. Thus, Eq. (3) is equivalent to a complete undirected graph (see Panel A in Fig. 2), where innovations from every market are connected with innovations from every other market through edges. The edge relationship characterizing each pair of variables may represent the contemporaneous causal relationship (or lack thereof) between 2

The procedure of Swanson and Granger (1997) is essentially a special case of more general directed graph algorithms as discussed in Spirtes, Glymour and Scheines (1993) (Swanson and Granger, 1997, p. 357). Recently, Bessler and Yang (2003) and Haigh and Bessler (2004) apply a popular directed graph algorithm (i.e., the PC algorithm) in their time series analysis. See the related discussion further.

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them. In the context of this study, no edge (X Y) indicates (conditional) independence between two variables, while an undirected edge (X–Y) signifies a covariance that is given no particular causal interpretation. A directed edge (Y → X) suggests that a variation in Y with all other variables held constant, causes a (linear) variation in X that is not mediated by any other variable in the system. A bi-directed edge (X ↔ Y) indicates the bi-direction of causal interpretation between the two variables. Zero first-order conditional correlation constraints (including zero unconditional correlation constraints) are used to remove connections (edges) between markets. Instead of using standard t statistics as done in Swanson and Granger (1997), following Glymour and Spirtes (1988) and Spirtes et al. (1993), we use a Fisher’s z statistic to test whether conditional correlations are significantly different from zero.3 Unfortunately, as mentioned previously, the contemporaneous causal pattern may not be fully identified using the above procedure and the causal flows for remaining connections (edges) between variables are often difficult to justify a priori. In this study, complementing the above procedure, we consider testing several possible combinations of zero restrictions on the aij which result in an overidentified A matrix, using the likelihood ratio test suggested by Sims (1986). The likelihood ratio test on the parameter restrictions relating observed innovations (et ) to orthogonal innovations (vt ) can be derived from the equation Aet = vt . Specifically, the test statistic is given as: 2[log(det(Ω)) − log(det(Σ))]T, where Ω is the variance–covariance matrix derived from the A matrix restrictions, Σ the variance–covariance matrix derived from the observed nonorthogonal innovations, T the number of observations used to estimate the model, log is the logarithmic transformation and det is the determinant operator. The test statistic is distributed χ2 with ((n(n − 1)/2) – m) degrees of freedom (n is the number of series in the VAR and m is the number of overidentifying restrictions). The null hypothesis is that the overidentifying restrictions are “true”.

3. Data The data for this study include 180 monthly observations, covering a 15-year period from January 1986 to December 2000. The five major government bond markets under study 3 The calculation and testing of zero-order (unconditional) and first-order conditional correlations are actually conducted using the PC algorithm as given in Spirtes et al. (1993). In this study, we follow Swanson and Granger (1997) to calculate only (up to) first order conditional correlations. Some differences between Swanson and Granger (1997) and the PC algorithm lie in that the PC algorithm calculates and tests up to k-2 order conditional correlations for k variables rather than only first-order conditional correlations and that the PC algorithm formally uses the notion of sepset to assign the direction of causal flow between variables which remain connected after all possible conditional correlations have been passed as nonzero. We also applied the PC algorithm, and were still unable to direct any remaining edges in this study and ended up with the same undirected graph. Our extension of Swanson and Granger (1997) (and Bessler and Yang (2003) and Haigh and Bessler (2004)) is that we seek using Sims’(1986) likelihood ratio tests to tackle the problem of assigning contemporaneous causal flows after removing some edges based on zero-order (unconditional) and first-order (or higher) conditional correlations. Readers are referred to Spirtes et al. (1993), Bessler and Yang (2003) and Haigh and Bessler (2004) for a more complete account of directed graphs.

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Table 1 Results of unit root tests Market

US Japan Germany UK Canada

Without trend

With trend

ADF

PP

ADF

PP

1.31 −1.09 −1.42 0.04 −0.40

0.71 −1.82 −2.25 −0.13 −0.53

−2.52 −2.51 −1.96 −2.22 −3.39

−8.85 −11.01 −7.51 −9.34 −20.35

The critical values of the ADF unit root tests without trend and with trend are −2.86 and −3.41 at the 5% level, respectively. The critical values of the PP unit root tests without trend and with trend are −14.1 and −21.7 at the 5% level, respectively.

are as follows: the United States (US), Japan (JP), Germany (GM), the United Kingdom (UK) and Canada (CA). Most previous studies (e.g., DeGennaro et al., 1994; Clare et al., 1995; Sutton, 2000; Smith, 2002) also used monthly observations and focused on these five countries because of their importance in international bond markets.4 Similar to Clare et al. (1995) and Smith (2002), we use J.P. Morgan total return government bond indexes as proxies of (realized) government bond yields in this study. These indexes represent the total return (including reinvested coupon payments) to investors from a representative portfolio of government bonds. The indexes are denominated in US dollars to reflect the possible benefits of international bond diversification to US investors. Though the creation of international bond market indexes is relatively new, the use of such bond indexes is becoming popular to international bond market investors. The J.P. Morgan and Salomon Brothers indexes are two most widely used international bond indexes. 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. Table 1 reports unit root results for five bond yield indexes. Similar to previous studies, we find that there is one unit root in each of the bond yield indexes under study, but no unit root in their first differences (available on request), at the 5% significance level.

4. Empirical results We first select the optimal lag in Eq. (1) by minimizing the Akaike Information Criterion (AIC). The maximum lag is set at 12 months. The AIC suggests the optimal lag of k = 2 for the level VAR and k = 1 for the first difference VAR. The trace test of Johansen (1991) is conducted on the whole sample period to determine r. Based on the trace test results reported in Table 2, there is zero cointegrating vector(s) with a linear trend at the 5% significance level (and also at the 10% significance level). Additional specification tests show that residuals on the ECM estimation are reasonably well behaved. Lagrangian multiplier tests on fourth 4

The monthly data are the data of highest frequency available for the bond market indexes. The use of corporate bond market indexes is not an alternative here because few non-US countries have a corporate bond market.

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Table 2 Johansen trace test statistics for international bond markets H0

r=0 r=1 r=2 r=3 r=4

Without linear trend

With linear trend

T

C (5%)

T

C (5%)

87.82 47.57 29.29 15.52 3.60

76.07 53.12 34.91 19.96 9.24

61.03 33.86 17.30 4.74 1.07

68.52 47.21 29.68 15.41 3.76

r is the number of cointegrating vectors, T the trace test statistics, and C the trace test critical value.

order autocorrelation of the residuals cannot reject the null of white noise residuals at any conventional significance levels (P-value = 0.27). ARCH effects do not exist except for Canadian market innovations. To examine the stability of the above (non)cointegration relationship, we apply the recursive cointegration technique to test constancy of cointegration rank as described in Hansen and Johansen (1993). In Fig. 1, we show normalized trace tests calculated at each month over the period 1991:1 through 2000:12. The 5-year period in 1986–1990 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 we reject the null hypothesis at that data point). It is evident that no cointegration exists during most of the sample period, because the plots of trace test statistics under both representations are in most cases below the 1.0 line. This is most obvious in the “R-representation”, though we see a few very short peaks going beyond the line at 1.0 over the sample period in the “Z-representation”. In sum, the result of recursive cointegration analysis confirms the finding of no cointegration, which is consistent with DeGennaro et al. (1994) and Clare et al. (1995), but contradicts Barassi et al. (2001) and Smith (2002). As pointed out by Clare et al. (1995), lack of the long-run relationship may be due to existence of remaining barriers to market access in international bond markets, such as heterogeneous taxation and maturity structure, investment culture, and institutional arrangements. It may also be due to lack of sufficient macroeconomic (e.g., monetary) policy coordination among major industrialized countries. The result also suggests that the first difference VAR should be an appropriate specification. The first difference VAR with the lag of 1 is thus estimated and used to summarize dynamic interactions among five bond markets. The five-variable (first difference) VAR model results in the following innovation correlation matrix (lower triangular entries only are printed in the following order: x1, x2, x3 , x4 , x5 , where 1, US; 2, JP; 3, GM; 4, UK; 5, CA).   1   1  0.09     0.27 0.48 1 V = (5)     1  0.41 0.25 0.61  0.48 0.04 0.10 0.27 1

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47

The Trace tests Z(t)

1.2

1.0

0.8

0.6

0.4

0.2

0.0 1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

1996

1997

1998

1999

2000

R(t)

1.00

0.75

0.50

0.25

0.00 1991

1992

1993

1994

1995

1 is the 10% significance level

Fig. 1. Plots of trace test statistics at each month during 1991–2000.

The matrix provides the starting point for the analysis of the contemporaneous causal pattern. We begin with a complete undirected graph, which is given as Panel A in Fig. 2. Here we have an edge (line) connecting each variable with every other variable. Following Swanson and Granger (1997), we remove edges by considering the unconditional (zero-order conditioning) and conditional correlations (first-order conditioning) between variables. The resulting graph is Panel B in Fig. 2. The edges US–JP (P-value = 0.26), JP–CA (P-value = 0.64), GM–CA (P-value = 0.19) are removed at zero-order conditioning. Based on zero first-order conditional correlations, we further remove JP–UK (P-value = 0.47 conditioning on GM), US–GM (P-value = 0.71 conditioning on UK), and UK–CA (P-value = 0.20

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J. Yang / Int. Fin. Markets, Inst. and Money 15 (2005) 39–54 US

JP

GM

UK

CA

Panel A US

JP

UK

GM

CA

Panel B Fig. 2. Contemporaneous causal flow patterns. (Panel A) Complete undirected graph on innovations from Eq. (1). (Panel B) Final directed graph on the model based on the likelihood ratio tests.

conditioning on US). Obviously, the unconditional correlations and (first-order) conditional correlations for all these pairs of variables have a P-value higher than conventional 5 or 10% levels. We have the remaining edges undirected between four pairs of variables, i.e., US–UK, US–CA, JP–GM, and GM–UK. In the problem under investigation, contemporaneous causal flows for these edges are difficult to justify a priori. We apply the likelihood ratio test suggested by Sims (1986) to explore several possibilities of contemporaneous causal flow patterns which are equivalent to imposition of zero restrictions on some aij s. A plausible contemporaneous causal pattern is identified as depicted in Fig. 2, Panel B. That is, JP → GM (i.e., a23 = 0 but a32 = 0), GM → UK (i.e., a34 = 0 but a43 = 0), UK → US (i.e., a41 = 0 but a14 =0), and US → CA (i.e., a15 = 0 but a51 = 0). A likelihood ratio test shows that these restrictions can be jointly rejected at a P-value of 0.56, indicating rather strongly that the restrictions are reasonable. Eq. (6) summarizes the contemporaneous

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49

causal pattern of innovations (which is an equivalence to the directed graph in Fig. 2, Panel B).      1 0 0 −0.16 0 e1t v1t      1 0 0 0   e2t   v2t   0       0     −0.34 1 0 0 (6)    e3t  =  v3t       0 −0.73 1 0   e4t   v4t   0 −1.06 0 0 0 1 e5t v5t Here eit and vit (i = 1–5) are defined as in Eq. (3) and all nonzero numbers are statistically significant at any conventional levels. To examine the robustness of the above overidentifying restrictions, we also consider other alternative orderings. Specifically, we test reverse causal directions for each of the four edges. The reverse orderings of US → UK, CA → US, and UK → GM are rejected individually at very low levels of significance (0.01 or lower). However, we cannot reject the reverse ordering of GM → JP (with the P-value = 0.56) at conventional significance levels. Thus, it cannot be clearly distinguished between JP → GM and GM → JP, which could be due to instability of the concerned contemporaneous causal relationship in either direction. Below we present the forecast error variance decomposition result based on the orderings as summarized by Eq. (6). The result based on the alternative ordering of GM → JP (available on request) is also briefly discussed because it affects the inference on the dynamic relationship between JP and GM. As a preliminary analysis of short-run dynamic linkages, multivariate Granger causality tests are conducted and results are presented in Table 3. The results show that at the 10% significance level, no other market may influence the US and the UK; Canada may influence the Japanese market; the US and Japan may influence Germany; and the US may influence Canada. Hence, the result at the 10% level clearly suggests the dominance of the US market in the sense that it exerts causal influence on other markets (such as Canada and Germany) while it is isolated from the influence of all other major markets. At the 5% level, only the US is identified to influence the German market while all other markets are isolated from each other. Obviously, in contrast to the result at the 10% level, the evidence at the 5% level suggests generally weak causal linkages between the markets, and does not lend much support for the dominance of the US market. In general, the results Table 3 Multivariate Granger causality tests Dependent variable

US Japan Germany UK Canada

Test statistics (significance level) US

Japan

German

UK

Canada

8.81 (0.00) 1.99 (0.16) 7.91 (0.00) 0.63 (0.43) 3.22 (0.07)

2.15 (0.14) 0.02 (0.87) 3.25 (0.07) 0.01 (0.91) 0.01 (0.89)

2.20 (0.13) 1.02 (0.31) 3.91 (0.05) 0.95 (0.33) 0.05 (0.81)

0.37 (0.53) 1.13 (0.28) 1.20 (0.27) 0.24 (0.62) 0.42 (0.52)

2.65 (0.11) 2.99 (0.09) 0.00 (0.98) 2.26 (0.13) 2.51 (0.11)

The F-statistics are used. Numbers in parentheses are P-values.

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Table 4 Forecast error variance decomposition results (percentage) Month US 1 2 3 12 Japan 1 2 3 12 Germany 1 2 3 12 UK 1 2 3 12 Canada 1 2 3 12

US

Japan

Germany

UK

Canada

83.0 80.4 80.1 80.0

1.5 1.6 1.7 1.7

4.9 6.6 6.7 6.7

10.7 10.0 9.9 9.9

0.0 1.4 1.6 1.6

0.0 3.1 3.4 3.4

100.0 94.6 94.0 94.0

0.0 0.6 0.8 0.8

0.0 0.0 0.0 0.0

0.0 1.6 1.8 1.8

0.0 4.9 5.1 5.1

23.1 21.5 21.5 21.5

76.9 73.6 73.0 73.0

0.0 0.0 0.0 0.0

0.0 0.0 0.4 0.4

0.0 1.5 1.6 1.6

8.6 8.4 8.4 8.4

28.6 28.4 28.4 28.4

62.8 60.5 60.3 60.2

0.0 1.3 1.4 1.4

19.3 19.3 19.4 19.4

0.3 0.6 0.6 0.6

1.1 1.7 1.7 1.7

2.5 3.0 3.1 3.1

76.7 75.3 75.2 75.2

The variance decomposition is based on the directed graph on innovations given in Fig. 2. The month 1 is the contemporaneous period.

are similar to Kirchgassner and Wolters (1987) in that the Granger causal relations are not pronounced. However, the multivariate Granger causality test results should be viewed as preliminary for two reasons. First, the (strong) instantaneous correlations between market innovations (as shown in Eq. (5)) are not yet taken into consideration. Second, the Granger causality test only allows for the statistical significance of economic variables (Sims, 1972, p. 545; Sims, 1980, p. 20; Abdullah and Rangazas, 1988, p. 682). By contrast, the forecast error variance decomposition may provide additional insights because it allows for the economic significance of economic variables (Sims, 1980; Abdullah and Rangazas, 1988). Under the orderings of innovations as indicated by the directed graph (Fig. 2, Panel B), 12-month forecast error variance decomposition results are given in Table 4. The results at the horizons of 2–12 months are largely consistent with but also appear more informative than the multivariate Granger causality test results. Specifically, the UK (about 10%) and Germany (about 7%) have the ability to noticeably influence the US, which is not captured by the Granger causality test results. This may reflect the role of London as an international financial center and the influence of more integrated European economies on the US. By contrast, Japan is the most exogenous market, and other markets including the US and

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Canada only have a trivial impact on this market. This may be an indication of the fact that the Japanese financial markets are the least open to international investors among the five major industrialized economies (Francis and Leachman, 1998). Japan (about 21%) and the US (about 5%) can substantially explain the movements of the German market over time, which is consistent with the causality test results. This could be a reflection of the following facts. Japan has become one of the biggest net capital exporters, particularly since the late 1980s when bubbles in its economy and the stock market burst. On the other hand, Germany has been in great need of huge amounts of foreign capitals after its reunification in 1990. Thus, it seems plausible that bond yields offered by Germany are particularly sensitive to changes in the bond investment opportunities in Japan available to Japanese investors. However, the evidence for the significant influence of Japan on Germany might be somewhat fragile, as such evidence is not robust against the alternative ordering of GM → JP (to be discussed below). As shown previously, the possibility of such an alternative ordering cannot be completely ruled out based on the data alone. Germany (about 28%) and Japan (about 8%) have substantial influence on the UK over time, which is not captured by the Granger causality test results. As discussed shortly, the influence of Japan on the UK, however, is also somewhat fragile. Obviously, the evidence is generally in line with the well-known hypothesis of German dominance in Europe (e.g., Uctum, 1999). Finally, consistent with the causality test results, the US (about 19%) is the only market which can significantly impact the Canadian market. This is an indication that the US economy and macroeconomic policies can exert much influence on its neighboring market of Canada. The similar relationship between two countries’ stock markets is also well documented in the literature (Eun and Shim, 1989; Bessler and Yang, 2003). Finally, some of the above results may be critically dependent on the ordering JP → GM. Using the alternative ordering of GM → JP, the result (available on request) shows that the influence of Japan on Germany and the UK disappears. Instead, Germany would be the most exogenous market and significantly influence the Japan market. The findings on other markets are qualitatively the same. In sum, it is still hard to tell which ordering between JP and GM is more likely to be true. However, the ordering of JP → GM yields the dynamic linkage pattern which is more consistent with the Granger causality test results (at the 10% significance level) and (in our judgement) more sensible. Thus, we presume that this particular ordering is more likely to hold.

5. Conclusions This paper examines linkages on government bond markets of five industrialized countries (US, Japan, Germany, UK and Canada) during the period of January 1986 to December 2000. Recursive cointegration analysis clearly shows that no long-run relationship exists among the five bond markets during the sample period. The finding supports DeGennaro et al. (1994) and Clare et al. (1995), but contradicts more recent studies of Barassi et al. (2001) and Smith (2002). Also, as found in Kirchgassner and Wolters (1987), there exist strong correlations between bond yield innovations. The causal pattern of such strong instantaneous relationships is uncovered, building on the recent advance in VAR analysis. We first document in the literature the following data-determined causal patterns between

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bond yield innovations: the contemporaneous causality running from Japan to Germany, from Germany to the UK, from the UK to the US, from the US to Canada. However, the causality running from Japan to Germany might be more or less tenuous, as the data cannot rule out the reverse direction of causality. We presume the direction from Japan to Germany because further forecast error variance decomposition result based on this ordering appears more sensible and more consistent with the multivariate Granger causality test results than based on the reverse ordering. The identification of the contemporaneous causal pattern further improves our investigation of the dynamic linkage pattern that is based on data-determined forecast error variance decomposition. Such a dynamic linkage pattern in international bond markets has not yet been seriously explored in the literature, with the possible exception of Kirchgassner and Wolters (1987). In general, the results in this study show that international bond markets are not completely segmented but instead are partially segmented in the short run and there is no distinctive leadership role. Specifically, we find that only the UK and Germany have some noticeable influence on the US over time. Consistent with the finding on international stock markets (Eun and Shim, 1989; Francis and Leachman, 1998; Bessler and Yang, 2003), Japan is the most exogenous market and other countries have little influence on this market. Only Japan and the US have noticeable influence on the German market over time. Only Germany can significantly influence the UK over time, which supports the well-known hypothesis of German dominance (e.g., Uctum, 1999). The US is the only market that can significantly influence the Canadian market over time, which is similar to their stock market relationship (Eun and Shim, 1989; Bessler and Yang, 2003). Noteworthy, however, is the relative influences of Japan and Germany on each other and their exogeneity may be reversed if the presumed contemporaneous causal direction from Japan to Germany is reversed. This sensitivity also underscores the importance of correctly modeling the contemporaneous causal relationships of VAR innovations, which has been well recognized theoretically but not often carefully addressed in empirical works due to lack of a satisfying technique. In this sense, the recent advance in VAR analysis as presented by Swanson and Granger (1997) should deserve more attention in future research. Finally, the findings of this study have some important implications for policymakers and investors. In particular, our ability of exploring international bond market linkage patterns at different time horizons may provide rich information to policymakers and investors with different decision horizons. First, in general, for national policymakers, an independent monetary policy with respect to long-term interest rates appears possible in the long run. In the short term (e.g., time periods up to a year), effectiveness of a country’s monetary policy may be substantially affected by policies of one or two other countries, which policymakers should take precaution against. Second, for investors with long investment horizons and passive portfolio management strategies, international diversification benefits can be exploited on their bond investments, as recommended by Levy and Lerman (1988) and Filatov et al. (1991). Investors can diversify their bond portfolios into any of other four major foreign bond markets, with little difference in terms of risk reduction. Investors who have shorter investment horizons or who are in favor of active bond portfolio management strategies, however, may use the identified contemporaneous causal pattern or short-run dynamic causal linkage pattern in the international bond markets to time different market movements. They may also diversify their bond portfolios into other markets which have

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little dynamic interaction with their own country market. For example, Canadian investors would be better off by diversifying into foreign bond markets other than the US market. Finally, the results suggest that although modeling and forecasting a country’s bond yields should be largely based on domestic macroeconomic variables, inclusion of one or two other countries’ macroeconomic variables may improve short-term forecasts of the country’s bond yields.

Acknowledgements This study was supported by the College of Business summer research grant at Prairie View A&M University. I gratefully acknowledge helpful comments from David A. Bessler, Bradley T. Ewing, Cheng Hsiao, Qi Li, and particularly an anonymous referee. I also thank Edwina Garcia for her editorial assistance.

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