International bond markets: a cointegration study.

Kelly, G. Wayne ; Rogers, Kevin E. ; Van Rensselaer, Kristen N. 等

ABSTRACT

This study examines the relationships among government bond returns for the G-7 countries to identify possible diversification opportunities. Using cointegration and error correction models, there is evidence of common trends between these government bond returns. Recursive cointegration test results suggest that the stability of this relationship varies over time. The empirical evidence indicates that the available diversification benefits from investing across these markets are limited.

INTRODUCTION

With the increasing globalization of financial markets, investors face a greater opportunity set with which to address investment goals and strategies. The widening array of available investments extends investors' choices across assets that reflect firm, industry, and even economy wide characteristics. This study addresses one aspect of diversification opportunities across major international bond markets. Specifically, its objective is to determine whether government bond returns of the seven countries collectively known as the G-7 countries share long-run relationships using cointegration techniques.

A long-term relationship between the total returns of these bonds would provide insights into investment possibilities and tactical choices investors make among these securities. As barriers to capital flows erode, weak-form market efficiency would suggest increasing similarities in the behavior of bond returns in combined markets. Dissimilar long-term bond returns could indicate the existence of valuable international diversification opportunities for investors and fund managers who, by rule or choice, hold significant amounts of government securities in their portfolios.

The G-7 countries, Canada, United States (U.S.), United Kingdom (U.K.), France, Germany, Italy, and Japan have enjoyed relatively low capital barriers over a long period. If the lack of impediments to capital flows contributes to market efficiency, these countries can provide a good example of government bond markets across which returns follow similar patterns. That could further provide a preview of government bond markets on a greater scale in the face of the liberalization of capital flows that accompany increasingly global economic activity.

For the purpose of this study, another motivation for selecting this group of government bonds is that the bonds of the G-7 comprise more than ninety percent of the total of all outstanding sovereign debt. Their dominance of the market for sovereign debt instruments is longstanding and their high volume relative to other government bonds raises the likelihood that they are the most widely distributed and liquid of all such bonds. For the interval between 1990 and 1999, inclusive, U.S. Treasury securities made up an average of 47.8% of the total followed by Japanese bonds with an average share of 21.8%. The smallest average shares among these bonds over the same interval are those of U.K. (2.7%) and Canada (2.9%), each about double the largest share of non-G-7 nations.

For government bonds of different countries to provide effective diversification, the government bond market in one country should not share the same trends as the government bond market in another country. In other words, if two markets are cointegrated, then the markets share systematic risk. In addition, if two markets are cointegrated, profitable arbitrage opportunities may exist between them (Chan, Gup, & Pan, 1997). The absence of such similarities would indicate long-term diversification opportunities across government bond markets.

Numerous studies have explored the possibility of long-run relationships, using cointegration tests, for international interest rates and international stock market indexes. DeGennaro, Kunkel, & Lee (1994) find little evidence of cointegration between interest rates of Canada, Germany, Japan, and the United States. However, using the same data set of DeGennaro, et al., Hsueh & Pan (1998) find that interest rates among these five countries are fractionally cointegrated. Throop (1994) studies whether real interest rates of Canada, Germany, Japan, and U.K. are integrated with the U.S. More specifically, he tests for cointegration between short-term interest rates and long-term interest rates in the U.S. and each of the other four countries. Throop finds evidence of integration between short-term and long-term real interest rates in the U.S. and Japan and only long-term rates for U.S. and Germany.

Kanas (1998) investigates the potential for linkages between the U.S. stock market and the stock markets in U.K., Germany, France, Switzerland, Italy, and the Netherlands. Using pair-wise or bivariate cointegration tests, Kanas concludes that the U.S. does not share long-run relationships with any of these countries. Gerrits & Yuce (1999) find contrasting evidence to that of Kanas (1998). According to their study, the U.S. stock market is cointegrated with the stock markets in Germany, U.K., and the Netherlands and has a significant impact on the stock market movements in these three countries.

Few studies have focused on the potential long-run relationships between international bond markets. Clare, Maras, & Thomas (1995), CMT hereafter, used total return bond indexes for United Kingdom, United States, Germany, and Japan. The CMT perspective was that of the United Kingdom investor, since the indexes are sterling adjusted. During the 1978 to 1990 time period, CMT conclude that the returns in these bond markets move independently of one another thus providing potential diversification benefit to the U.K. investor.

This study differs from the CMT study in several ways. The present study includes three additional countries for a later period of similar length, testing for cointegration within the entire group and pair-wise between the U.S. and each of the 6 remaining countries. Recursive cointegration tests are also applied to the data to see if the integration of these bond markets increased over time.

DATA

The data are Merrill Lynch government bond total return indexes obtained from Bloomberg. The total return indexes reflect interest income plus price appreciation for government bonds with maturities greater than one year. The total return index is expressed in U.S. dollars and in local currencies. This allows the comparison of relationships for investors that hedge currency risk and for those that do not. The emphasis of the analysis will be placed on the U.S. investor where the return is expressed in U.S. dollars, implying that the total return index for Canada, France, Germany, Italy, Japan, and the United Kingdom also considers the return investors would receive from currency fluctuation. For more details on the Merrill Lynch indexes, see the Merrill Lynch Indexes: Rules and Definitions (1997). The weekly data spans the period from October 1, 1993 to December 29, 2000. The availability of weekly data for Italy begins on October 1, 1993. The other countries, except for the U.S., have weekly data available beginning January 5, 1990. The weekly availability of the US index began November 6, 1987. All of the indexes were converted to natural logs.

Table 1 displays average weekly returns, standard deviations, and coefficients of variation for each country in both local currencies and the U.S. dollar. Returns were calculated by differencing the natural log of the indexes. Perhaps the most surprising aspect of these statistics is the apparent poor risk-return trade-off that exists with international bond investments. Comparing the bond returns and risk denominated in local currency, the Italian bond market offered the most favorable risk-return trade-off. Comparing the U.S. dollar denominated returns and risk, the U.S. government bond market returns appear to dominate the other government bond returns. Of these seven countries, the U.S. has the lowest and Japan has the highest risk per unit of return. From a stand-alone investment perspective, U.S. investors that do not hedge currency risk would have been wise to select the U.S. government bonds over this time period. Of course, this pair-wise comparison ignores any diversification potential.

Table 2 reports correlation coefficients between the weekly returns. From the perspective of short-term relationships, the U.S. has the strongest relationship with Canada and weak relationships with the remaining countries. Considering the close economic and geographic ties shared between these two countries, a higher correlation between returns would be expected. For the U.S., the weakest relationship is with Japan, suggesting that U.S. investors would benefit the most by including Japanese government bonds in their portfolio. The bond returns in Japan are more highly correlated with the European countries than with U.S. and Canada. All of the European countries share a high correlation between monthly returns. This is not surprising given the strong ties between these countries. It is important to remember that the correlation coefficients shown in Table 2 are measuring the contemporaneous short-term relationships in weekly returns and do not detect long-run relationships between total returns in different markets.

METHODOLOGY

The methodology for this study consists of three steps. First, the data are tested for nonstationarity using standard techniques as described by Dickey & Fuller (1979, 1981) and Phillips & Perron (1988). After establishing that each series is integrated of order one or I(1), cointegration tests are used to determine whether long-run relationships exist between the returns in the U.S. government bond market and any of the other G-7 government bond markets. In addition to pairwise cointegration tests, multivariate cointegration tests are conducted on the entire G-7 group, using the procedures outlined by Johansen (1988) and Johansen & Juselius (1990). Last, if evidence of cointegration is found, error correction models will be developed to explore the short-term nature of the relationship.

Cointegration tests determine whether a linear combination of the nonstationary variables results in a stationary error term. The Johansen (1988) and Johansen & Juselius (1990) multivariate cointegration test will be used to detect possible cointegration

Two additional tests will be conducted to examine the long-run relationships between these return series. Recursive cointegration tests will indicate if the G-7 government bond markets have become more integrated over time. Exclusion tests will indicate if all seven of the government bond markets are important in the long-run relationships.

If evidence of cointegration is found, then error correction models (ECM) will be estimated. If returns in two markets are cointegrated, this means the returns share the same common trend or risk factor. When the returns depart from the long-run relationship, one or both of the returns must adjust to the departure to sustain the long-run relationship. ECMs indicate how the long-run relationship is maintained in the short-run and can specify which market corrects to divergences in the long-run relationship. To estimate error correction models, the first difference of each variable is regressed upon the error correction term and lagged values of the first difference of each variable. If evidence of cointegration is not found, then the G-7 government bond markets do not share a long-run relationship. Investors would be able to achieve diversification benefits by investing in these markets.

Error correction models also allow for the testing of Granger causality. In a cointegrated system, to say that the first variable "Granger causes" the second variable two conditions must be met. The error correction term must be statistically insignificant in the first variable's ECM but statistically significant in the second variable's ECM. This means that the first variable does not react to errors in the long-run relationship and the second variable does the "correcting" to deviations in the relationship. Second, the lagged values of the first variable must be statistically significant in the ECM for the second variable. The second condition requires that the second variable react to past changes in the first variable. If both conditions are satisfied it can be said that the first variable Granger causes the second variable (Enders, 1995).

EMPIRICAL RESULTS

Table 3 gives the results for the Augmented Dickey-Fuller (ADF) and the Phillips-Perron (PP) unit root tests. Lag lengths were selected by starting with a twelve-period lag and paring down the lag lengths until a significant length was found using the Akaike Information Criterion (AIC). The ADF and PP test confirm one another when the lag length is other than zero. This allows greater confidence in the results. The outcomes of the unit root tests were insensitive to the choice of lag length. The model used for the tests includes a time trend and drift and was selected after visual inspection of the graphs of each series. It is common to include a trend and drift term when working with index data. However, the conclusion of the test was not affected by excluding the time trend or constant from the model. For each of the series, it can be concluded that the series are nonstationary or integrated of order one or higher at the five-percent level. To determine if the order of integration of each series is greater than one, the data is first differenced and the unit root tests are conducted again. While the results are not reported here, each of the series was found to be stationary after first differencing.

Table 4 reports the results of the pair-wise Johansen Cointegration test. The lag lengths were determined by selecting the lag length that minimized the AIC for each of the bivariate vector autoregressions. The model chosen for the cointegration test allows for a deterministic trend in the data and a constant in the cointegration equation. The test statistic reported is the Trace test statistic (see Johansen, 1988 and Johansen & Juselius, 1990). The null hypothesis for the Trace test in a bivariate relationship is no cointegration or no common trends among the variables.

The null hypothesis of no cointegration cannot be rejected at the five-percent level for any of the countries, whether the returns are given in local currency or denominated in U.S. dollars. At the ten percent level of significance, the null hypothesis of no cointegration can be rejected for the returns for the U.S. and Japan government bond markets. The inability to reject the null hypothesis indicates that the returns between the U.S. and the other six countries of the G-7 do not share a long-run relationship or risk factor on a pair-wise basis. This result suggests that U.S. investors can achieve diversification benefits by forming a portfolio of U.S. government bonds with bonds of any one of the other six countries in the G-7.

Bivariate cointegration tests can overlook more complex relationships between these countries. To provide a more comprehensive test for the possibility of long run relationships, the G-7 is tested as a group. Table 5 shows the results for the multivariate cointegration test. The null hypothesis of no cointegration (none) is rejected at the five percent critical value, indicating that the bond markets of the G-7 share a long-run relationship. Given that only one long-run relationship appears to exist among these seven countries, the relationship is not very stable.

It is possible that the nature of the relationship has changed over the time period under study. It is commonly argued that with increased globalization and technological improvements, financial markets will become more integrated over time. Bremnes, Gjerde, & Saettem (1997) find in their study of currency yields on U.S. dollars, U.K. pounds, German marks, French francs, and Japanese yen that the number of cointegrating vectors increases over time.

As the number of cointegrating vectors increase, the cointegrated system is considered more stable or integrated. As in Dickey, Jansen, & Thornton (1991), cointegrating vectors reflect economic constraints imposed on the movements of variables in the system in the long run. As a result, a system is more stable when it has a greater number of cointegrating vectors.

While only one cointegrating vector was found using both local currency and U.S. dollar denominated return indexes, it is possible to determine if there have been periods of increased stability in the relationship among the G-7 government bond markets using recursive cointegration tests. Employing the methodology for recursive cointegration tests outlined by Bremnes, Gjerde, & Saettem (1997), as many as three cointegrating vectors were found. While it is possible with seven variables to have as many as six cointegrating vectors, there is no evidence of more than three cointegrating vectors. The results indicate that the G-7 government bond markets have experienced periods of increased integration but there is no evidence of progressive integration. The results of the recursive cointegration tests can be found in Figures 1 through 4 in Appendix A.

The evidence of cointegration implies that long-run trends exist between at least some of the countries. The cointegration detected for these seven countries could be a shared relationship between any subset of two or more countries. It is possible to determine which countries "belong" in the cointegrating equation via formal testing through parameter restrictions. The parameter exclusion test is a likelihood ratio test and is discussed in Johansen & Juselius (1990). The test statistic is distributed chi-squared with one degree of freedom since only one parameter is being restricted. Table 6 reports the results of the restriction tests. The null hypothesis for the test is that the selected variable can be restricted to zero, implying that the variable does not belong in the cointegrating vector. Rejection of the null means that the restriction is not binding and that the variable is statistically significant in the cointegrating equation. For the returns denominated in local currencies, the null hypothesis not rejected for Italy and U.K. According to this evidence, all the countries belong in the cointegrating equation except for Italy and the U.K. Looking at the U.S. dollar denominated return indexes, these results indicate that Canada, Japan, and the U.K. are not significant in the cointegrating equation. This implies a long-term relationship between the government bond returns for France, Germany, Italy, and the U.S

To investigate the short-run dynamics involved with the long-run relationships, Tables 7 and 8 show the results of the ECM for the returns in local currency and U.S. dollar respectively. In Table 7, the error correction term is significant for France and the U.S. In Table 8, the error correction term is significant only for Italy.

Turning to the lagged relationships, it is interesting to see that regardless of the currency, there are no significant lagged relationships between the weekly returns for the countries. This means that past returns in these markets do not influence current returns in other countries. The absence of significant lagged relationships is evidence of weak-form efficiency for these bond markets.

CONCLUSIONS

The object of this study is an examination of total returns to government bonds of the G-7 countries in light of long-term relationships. The results of the pair-wise tests provide preliminary results that can be interpreted as diversification opportunities for U.S. investors with government securities of the G-7. The only country that stands in exception is Japan. Further investigating the G-7 as a group reveals that the group shares a long-run relationship regardless of whether the returns are denominated in local currency or U.S. Dollars. This evidence diminishes the potential for diversification benefits to U.S. bond investors considering these markets for their bond portfolios.

Using cointegration tests, the possibility of comovements or long-run relationships between the U.S. government bond market and the remaining G-7 government bond markets was explored. The bivariate cointegration tests indicate that the U.S. government bond market does not share common risk factors or comovements with any of the other government bond markets in the G-7 countries with perhaps Japan being an exception. Further cointegration testing was conducted to determine whether the G-7 government bond markets share a more complex relationship. Cointegration tests, along with exclusion tests, indicated that Canada, France, Germany, Japan, and the U.S. bond markets share a common trend when local currencies are considered. For the U.S. investor that is exposed to currency risk, the nature of the relationship changes. In this case, the U.S. government bond market shares a long-run relationship with France, Germany, and Italy. The ECM revealed the complexity of the relationship among these bond markets.

Three overall implications are suggested by the above results for investors in G-7 country bonds, particularly those who hold U.S. bonds. First, pair-wise results suggest that there are possible diversification benefits for holders of U.S. bonds. Second, investors seeking diversification benefits by investing in both U.S. government bonds and multiple government bonds of the G-7 countries should use caution since the cointegration of these bond markets implies a shared risk factor. Third, there is little evidence that these markets have become more integrated over time.

Appendix A: Results of Recursive Cointegration Tests

[FIGURE 1 OMITTED]

Figure 1 shows the Trace Test Statistic for zero cointegrating vectors for the government bond market returns denominated in U.S. dollars. The figure indicates that the null hypothesis of zero (no cointegration) cointegrating vectors can be rejected for all periods. There is at least one cointegrating vector for the returns in the G-7 government bond markets.

[FIGURE 2 OMITTED]

Figure 2 shows the Trace Test Statistic for one cointegrating vector for the government bond market returns denominated in U.S. dollars. The figure shows that the null hypothesis of one cointegrating vector is rejected for most periods, indicating the existence of at least two cointegrating vectors.

[FIGURE 3 OMITTED]

Figure 3 shows the Trace Test Statistic for two cointegrating vectors for the government bond market returns denominated in U.S. dollars. The figure shows that the null hypothesis of two cointegrating vectors is rejected for some periods, indicating the existence of at least three cointegrating vectors.

[FIGURE 4 OMITTED]

Figure 4 shows the Trace Test Statistic for three cointegrating vectors for the government bond market returns denominated in U.S. dollars. The figure indicates that the null hypothesis of three cointegrating vectors cannot be rejected over any period periods. There are never more than three cointegrating vectors over the period under study.

REFERENCES

Akaike, H., (1974). A new look at statistical model identification. IEEE Transactions on Automatic Control 19, 716-723.

Bremnes, H., Gjerde, O., and Saettem, F., (1997). A multivariate cointegration analysis of interest rates in the Eurocurrency market, Journal of International Money and Finance, 16, 767-778.

Chan, K., Gup B., and M. Pan, (1997). International stock market efficiency and integration: a study of eighteen nations, Journal of Business, Finance, and Accounting 24, 803-814.

Clare, A., Maras, M., and Thomas, S., (1995). The integration and efficiency of international bond markets, Journal of Business, Finance, and Accounting 22, 313-322.

DeGennaro, R., Kunkel, R., and Lee, J., (1994). Modeling international long-term interest rates, Financial Review 29, 577-597.

Dickey, D. and Fuller, W., (1979). Distribution of the estimates for autoregressive time series with a unit root, Journal of the American Statistical Association 78, 427-437.

Dickey, D. and Fuller, W., (1981). Likelihood ratio statistics for autoregressive time series with a unit root, Econometrica 49, 1057-1072.

Dickey, D., Jansen, W., and Thornton, D., (1991), A primer on cointegration with and application to money and income, Federal Reserve Bank of St. Louis, 58-78.

Enders, W., (1995). Applied Econometric Time Series New York: Wiley Publishing.

Engle, R. and Granger C., (1987). Cointegration and error-correction: representation, estimation, and testing, Econometrica 55, 251-276.

Gerrits, R., and Yuce, A., (1999). Short- and long-term links among European and us stock markets, Applied Financial Economics 9, 91-9.

Hseuh, L., and Pan, M., (1998). Integration of international long-term interest rates: a fractional cointegration analysis, Financial Review 33, 213-224.

Johansen, S., (1988). Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control 12, 231-254.

Johansen, S. and Juselius, K., (1990). Maximum likelihood estimation and inference on cointegration with applications to the demand for money, Oxford Bulletin of Economics and Statistics 52, 169-209.

Kanas, A., (1998). Linkages between the U.S. and European equity markets: further evidence from cointegration tests, Applied Financial Economics 8, 607-614.

MacKinnon, J., (1991).Critical values for cointegration tests, Long-Run Economic Relationships: Readings in Cointegration, (Oxford University Press, Oxford).

Merrill Lynch Indexes: Rules and Definitions. (n.d.) Retrieved 1997, from http://www.research.ml.com/Marketing/index04.htm

Osterwald-Lenum, M., (1992). A note with quintiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics, Oxford Bulletin of Economics and Statistics 54, 461-471.

Phillips, P. and Perron P., (1988). Testing for a unit root in time series regression, Biometrica 57, 1361-1401.

Schwarz, G., (1978). Estimating the dimension of a model, Annals of Statistics 6, 461-464.

Throop, A., (1994). International financial market integration and linkages of national interest rates, Economic Review (Federal Reserve Bank of San Francisco) 3, 3-18.

G. Wayne Kelly, Mississippi State University

Kevin E. Rogers, Mississippi State University

Kristen N. Van Rensselaer, University of North Alabama

Table 1: Weekly returns, standard deviations, and coefficient of
variation (CV)

 Local Currencies U.S. Dollar

 Weekly Standard CV Weekly Standard CV
 Return Deviation Return Deviation

Canada 0.16% 0.72% 4.50 0.12% 1.14% 9.50
France 0.13% 0.55% 4.23 0.08% 1.45% 18.13
Germany 0.12% 0.45% 3.75 0.06% 1.49% 24.83
Italy 0.18% 0.66% 3.67 0.11% 1.53% 13.91
Japan 0.09% 0.54% 6.00 0.07% 1.89% 27.00
U.K. 0.17% 0.81% 4.76 0.17% 1.34% 7.88
U.S. 0.12% 0.63% 5.25 0.12% 0.63% 5.25

Table 2: Correlation coefficients for weekly returns: October 1993
through December 2000

Panel A: Local Currency

 Canada France Germany Italy Japan U.K.

Canada 1.00
France 0.49 1.00
Germany 0.52 0.87 1.00
Italy 0.38 0.69 0.61 1.00
Japan 0.14 0.19 0.23 0.05 1.00
U.K. 0.53 0.72 0.74 0.53 0.11 1.00
U.S. 0.76 0.56 0.58 0.35 0.18 0.59

Panel B: U.S. Dollars

 Canada France Germany Italy Japan U.K.

Canada 1.00
France 0.06 1.00
Germany 0.04 0.94 1.00
Italy 0.15 0.67 0.62 1.00
Japan -0.02 0.32 0.37 0.14 1.00
U.K. 0.21 0.56 0.53 0.41 0.10 1.00
U.S. 0.48 0.23 0.21 0.18 -0.07 0.41

Table 3: Results of unit root tests

 Local Currency U.S. Dollar

Variable Lag ADF PP Lag ADF PP
Canada 0 -1.51 -1.51 0 -2.02 -2.02
France 3 -1.39 -1.11 0 -1.50 -1.50
Germany 0 -1.20 1.20 0 -1.73 -1.73
Italy 0 -0.48 -0.48 0 -1.04 -1.04
Japan 2 -1.70 -1.45 0 -2.66 -2.66
U.K. 3 -2.48 -2.16 1 -1.62 -1.68
U.S. 0 -2.57 -2.57 3 -2.66 -2.55

The MacKinnon (1991) critical value rejecting the null hypothesis of a
unit root or nonstationarity is -3.45 at the five- percent level of
significance.

Table 4: Results of the Johansen cointegration test

 Local Currencies U.S. Dollar

 Trace Test Trace Test
 Lag Statistic Lag Statistic

U.S. and Canada 2 4.28 2 4.56
U.S. and France 4 7.01 2 5.97
U.S. and Germany 2 9.56 1 6.59
U.S. and Italy 1 4.00 4 6.89
U.S. and Japan 1 14.35 2 4.70
U.S. and U.K. 2 11.67 2 4.12

The null hypothesis is no cointegration and the 5% critical value is
15.41 (Osterwald-Lenum, 1992).

Table 5: Results of the multivariate Johansen cointegration test for
G-7 countries

 Local Currency U.S. Dollar

Hypothesized Number Trace Test Trace Test Critical
of Cointegrating Vectors Statistic Statistic Value (5%)

None 132.88 * 124.56 * 124.24
One 90.81 82.51 94.15
Two 58.55 56.50 68.52
Three 38.53 36.82 47.21
Four 20.09 19.42 29.68
Five 7.35 6.39 15.41
Six 1.27 0.29 3.76

* Indicates statistical significance at the 0.05 level.

Table 6: Tests for exclusion of variables in the cointegrating vector

 Local Currency U.S. Dollar

 Test Statistic Test Statistic

Canada 8.44 * 2.30
France 7.58 * 15.70 *
Germany 8.42 * 16.33 *
Italy 3.71 13.99 *
Japan 4.72 * 3.34
U.K. 1.30 0.41
U.S. 10.08 * 4.28 *

* Indicates significance at the 0.05 percent level

Table 7: Results of the error correction model for Canada, France,
Germany, Italy, and U.S. (Local Currency)

Regressor Regressand

 Canada France Germany

Error -0.024 -0.037 -0.017

Correction (-1.760) (-3.592) * (-1.943)

Constant 0.001 0.001 0.001
 (3.584) * (4.729) * (5.245) *

[Canada 0.075 -0.071 -0.028
.sub.-1] (0.933) (-1.157) (-0.535)

[France 0.163 -0.101 0.023
.sub.-1] (1.181) (-0.965) (0.258)

[Germany -0.128 0.124 -0.064
.sub.-1] (-0.746) (0.954) (-0.584)

[Japan 0.122 -0.048 -0.013
.sub.-1 (1.704) (-0.892) (-0.290)

[U.S. -0.156 0.048 0.018
.sub.-1 (-1.593) (0.650) (0.295)

Adj.
[R.sup.2] 0.01 0.025 -0.003

Regressor Regressand

 Japan U.S.

Error -0.015 -0.049

Correction (-1.416) (-4.204) *

Constant 0.001 0.001
 (3.130) * (3.744) *

[Canada -0.024 0.058
.sub.-1] (-0.400) (0.842)

[France -0.125 -0.024
.sub.-1] (-1.195) (-0.119)

[Germany 0.152 0.085
.sub.-1] (1.169) (0.574)

[Japan 0.074 0.037
.sub.-1] (1.370) (0.609)

[U.S. -0.041 -0.223
.sub.-1] (-0.546) (-2.647) *

Adj.
[R.sup.2] 0.003 0.051

* Indicates statistical significance at the 0.05 level.
The t-statistics are given in parenthesis.

Table 8: Results of the error correction model for France, Germany,
Italy, and U.S. (U.S. Dollar)

 France Germany Italy U.S.

Error 0.003 0.002 -0.007 0.002

Correction (1.305) (0.581) (-2.687) * (1.710)

Constant 0.001 0.000 0.001 0.001
 (0.839) (0.524) (1.243) (3.990) *

[France -0.172 -0.010 -0.072 0.058
.sub.-1] (-0.979) (-0.056) (-0.392) (0.759)

[Germany 0.165 0.013 0.161 -0.029
.sub.-1] (1.040) (0.078) (0.969) (-0.424)

[Italy -0.040 -0.053 -0.084 -0.023
.sub.-1] (-0.587) (-0.743) (-1.163) (-0.776)

[U.S. 0.141 0.121 0.146 -0.124
.sub.-1] (1.143) (0.949) (1.129) (-2.305)

Adj. [R.sup.2] 0.004 -0.008 0.015 0.008

* Indicates statistical significance at the 0.05 level. The
t-statistics are given in parenthesis.