Cointegration of International Stock Market Indices

In this paper, we derive evidence on the integration of international stock markets from the cointegration properties of international stock market prices. Using the multivariate cointegration test of Johansen, we find that the set of six country stock price indices, including that of the United States, Canada, the United Kingdom, France, Germany, and Japan are cointegrated. The results suggest that there are long-run equilibrium relationships among the stock market prices. Subsample and subgroup analyses also indicate that the cointegration relationships have become stronger over time. This is consistent with greater stock market integration amid the increasing liberalization and globalization of capital markets.

Abstract

In this paper, we derive evidence on the integration of international stock markets from the cointegration properties of international stock market prices. Using the multivariate cointegration test of Johansen, we find that the set of six country stock price indices, including that of the United States, Canada, the United Kingdom, France, Germany, and Japan are cointegrated. The results suggest that there are long-run equilibrium relationships among the stock market prices. Subsample and subgroup analyses also indicate that the cointegration relationships have become stronger over time. This is consistent with greater stock market integration amid the increasing liberalization and globalization of capital markets.

I. Introduction

International capital market development in the past two decades has been marked by a series of policy changes under which many cross border investment restrictions, including exchange control and foreign participation restrictions, have been reduced or eliminated, and the market structures of many international exchanges were reformed. For example, in the United States, the regulation K which allows U.S. banks to deal in and underwrite equity securities outside of the United States was passed in 1979; foreign issuers were permitted by the NYSE, AMEX, and NASD in 1986, provided they comply with home country laws. In Canada, the Banking Act which lifts restrictions on the foreign share of Canadian banking activity was passed in 1984; a multi-jurisdictional disclosure system with the U.S. securities regulators was installed in 1991. In Germany, a regulation which allows foreign investors to buy five-year federal bonds in the primary market was passed in 1988. Furthermore, securities transfer tax was abolished in 1991. In Japan, Euro-yen CDs were introduced in 1984; foreign members were admitted to the Tokyo Stock Exchange in 1986; and Japanese financial institutions were allowed to trade in foreign futures markets starting in 1988. In the United Kingdom, foreign exchange control was abolished in 1979. In addition, the “Big Bang” which involves major changes in the trading mechanism and government regulations on securities markets was launched in 1986. In France, the government securities market was reformed in 1987; and almost all exchange controls were eliminated in 1990.

These market developments can alter the relationship between equity prices in different countries. The liberalization of capital markets can promote market integration, which has important investment and policy implications. For instance, the amount of benefit from international diversification would be different under internationally segmented markets than under integrated markets. The transmission of market turbulence from one country to another is also likely to be greater if international capital markets are integrated. Furthermore, the pricing of assets in segmented markets is different from that in integrated capital markets. It is therefore important to determine whether international stock markets have become more integrated. Previous works based on pre mid-1980s datasets tend to find that international capital markets were mildly segmented (see for examples, Errunza and Losq (1985) and Jorion and Schwartz (1986)). For an excellent survey and discussion on the integration of world capital markets, see Goldstein and Mussa (1993).

A traditional approach to ascertain changes in the degree of integration among international stock markets is to study changes in the correlations among international stock market prices over time. An increase in correlation is usually taken as evidence of an increase in the degree of market integration and a higher tendency that shocks in one country be transmitted to another. However, this approach might not be the most informative one, as correlations are determined by short-term trading noises as well as by long-run fundamental relationship among the markets. Such short-term variations in prices can obscure the picture of the long-run relationship among the markets caused by the growing globalization and liberalization of these markets. To solve this problem, we look directly at the long-run relationship among international stock markets based on the idea of cointegration introduced by Engle and Granger (1987).

Intuitively, if two random walk price series have a long-run equilibrium relationship, they cannot drift apart indefinitely. In other words, the deviation from their equilibrium relationship must be stationary with a zero mean. This can be translated into a testable implication that there is a combination of the two nonstationary series, which is itself stationary. In this case, following Engle and Granger (1987), the two price series are said to be cointegrated.

This idea can also be extended into a multivariate setting. Usually, an equilibrium relationship is multivariate in nature. As such, a deviation from the long-run relationship among the price variables can only be constructed from a combination of all the price series involved. While this might complicate the picture a little bit, the idea is essentially the same. If there is really a long-run relationship among the nonstationary price series, then there is a combination of the nonstationary price series which is stationary. This is called multivariate cointegration. It is important to note that if the equilibrium relationship is multivariate in nature, then incorrect inference can be drawn by looking at only two series at a time. In technical terms, not finding cointegration in a small system does not imply no cointegration in a larger system. In fact, the finding of cointegration in a larger system, but not in a smaller subsystem of prices, can be interpreted as indicating that the linkage among international stock markets is broader and hence the markets are more integrated.

Given that the long-run relationship among the price series is indicated by their cointegration relationship, a change in the long-run relationship among international stock market prices can be studied by detecting changes in the cointegration relationship among the variables. We achieve this by comparing the cointegration relationship among the variables in different subsample periods. Our approach is similar to that of Taylor and Tonks (1989), except that their approach looks only at a bivariate cointegration relationship and is therefore limited in the sense that they cannot investigate the broader issue of the integration of multiple country stock markets. Furthermore, as we have discussed, bivariate cointegration results can be misleading, as the absence of a cointegration relationship between two stock market prices does not preclude the possibility that the two markets are integrated. It is possible that the two markets are related with other stock markets so that the equilibrium price relation must involve multiple stock market prices. The problem is analogous to the case of using a single variable regression when, in fact, the dependent variable is driven by more than one independent variable.

In the next section, we discuss in more detail our methodology. In Section III we present our results. Finally, in Section 4, we offer our interpretation of the findings and conclude the paper.

II. Methodology

Since our cointegration study depends crucially on the nonstationarity of the stock market prices under consideration, our empirical exercise is composed of two parts: (1) testing for a unit root in each price series, and (2) testing for the number of cointegrating vectors in the system of stock market prices, provided that we cannot reject the null hypothesis of a unit root for every stock market price series.

To test for a unit root in each price series, we employ the approach of Phillips and Perron (1988). This test method is preferred to the traditional approach of Dickey and Fuller, as it is robust with respect to the presence of heteroskedasticity.

Specifically, let sit be the logarithm of the stock market index of country i at time t. Two different forms of the Phillips-Perron test are considered. The first one does not allow for the presence of a deterministic time trend. It is based on the regression:

Δsit=μ+αsit-1+Σj=1mbjΔsit-j+eit

The null hypothesis is that α is equal to zero. The heteroskedasticity correction is based on the method of Newey and West (1987). The transformed test statistics proposed by Phillips and Perron has the same critical values as the traditional Dickey-Fuller test statistics.

The second unit root test allows for the existence of a deterministic trend. It is based on the following regression:

Δsit=μ+γt+αsit-1+Σj=1mbjΔsit-j+eit

For this regression, two null hypotheses are being considered. The first one is that α is equal to zero. The transformed test statistics proposed by Phillips and Perron again have the same critical values as the traditional Dickey-Fuller unit root test. The other null hypothesis is that γ = α = 0. This is constructed as an F-test of the joint significance of the two parameters. Again, the test statistics are the transformed test statistics introduced in Phillips and Perron (1988) and heteroskedasticity is accounted for using the Newey-West (1987) correction.

To test for cointegration among international stock market prices, we employ the approach of Johansen (1988) and Johansen and Juselius (1989). The approach has various advantages over the original two-step procedure of Engle and Granger (1987). In particular, the methodology of Johansen allows for the shortrun dynamics of the variables and provides estimates of all the cointegrating vectors within the system of nonstationary variables. Furthermore, the test statistics for the number of cointegrating vectors have an exact limiting distribution.

Let St be an Nx1 vector of the logarithm of international stock market prices, [s1t, S2t, .., sNt]’, where sit is the logarithm of the stock market index of country i. For the moment, we will assume that all N price variables are integrated of order 1, i.e. I(1). In the actual data analysis we will formally test this assumption. We will also assume that S has an AR(p) representation. That is,

St = A0 + A1St - 1 + A2St - 2 + … + ApSt - p + ϵt,

where Aj j=0,..,p are NxN matrices. Given that any AR(p) series can be written in terms of its first difference, p-1 lagged differences, and one lag level, the expression can be rewritten as:

ΔSt = B0 + B1ΔSt - 1 + B2ΔSt - 2 + . . + Bp - 1ΔSt - p+1 - CSt - p + ϵt,

where Bj, j=0,..,p-1, and C are NxN matrices dependent on Aj j=0,..,N. From this equation, we can see that if the C matrix is a matrix of zero, then any linear combination of St will be nonstationary. Alternatively, if C is full rank, then any linear combination of St is stationary. If C is of rank r where r is less than N, then there will only be r independent stationary linear combinations of St. That is, there are r cointegrating vectors.

Johansen’s procedure of testing for the number of cointegrating vector first involves concentrating out the short run dynamics by regressing ΔSt on ΔSt-1,.. ΔSt-p+1 and by regressing St-p on ΔSt-1,.. ΔSt-p+1. Let Udt and U1t be the residual vectors from the first and second regressions respectively, the procedure then computes the squares of the canonical correlations between Udt and U1t, which are arranged from the largest to the smallest as ρI2ρ22..ρN2.. The trace test statistics (a likelihood ratio test statistics) for the null hypothesis that there are r or fewer cointegrating vectors is then computed as:

-2lnQr= -TΣj=r+1Nln(1ρj2)2,

where T is the number of observations in the sample. The intuition behind the test statistic is rather simple. The canonical correlations measures the correlations between a linear combination w’St (after the removal of its short-term dynamics) and the stationary part of the process (after the removal of its short-term dynamics). If the linear combination is nonstationary, then the correlation will tend to zero. Thus, asymptotically, under the null hypothesis that there are r or fewer cointegrating vector, ρj=0 for j=r+1,..,N.

Various quintiles for the test statistics are reported by Johansen (1988) for r = 1,…5. Baillie and Bollerslev (1989) and Dickey and Rossana (1990), show that the test distribution can be well approximated by c times a Chi-square f, where f is set equal to 2 times the square of N-r, and the constant c is set equal to 0.85 - 0.58/f. The critical values on which our inferences are based are from this calculation.

III. Empirical Results

The empirical work in this paper is based on weekly data of the stock market indices of the United States, the United Kingdom, Japan, France, Germany, and Canada. The data were obtained from the Federal Reserve Board of Governors and the sample period is July 1976 to December 1989. There is a total of 700 weekly observations. Corresponding exchange rate data were obtained from the same source. These are used to transform the price series in local currency into prices denominated in U.S. dollars. Our analysis is based on the logarithm of the local stock price series and the logarithm of the stock price series in U.S. dollars.

We first test for unit root in each price series based on the Phillips Perron test discussed in the previous section. The lag length for the augmented terms is specified as 5. An inspection of the autocorrelation and partial autocorrelation functions of the first difference of the log price series suggests that five lags are sufficient to capture the short-run price dynamics. The test results are reported in Table 1 for both cases using the local currency (Panel A) and the U.S. dollar (Panel B). The null hypothesis of a unit root can in no case be rejected at the 5 percent level. In other words, all 12 stock indices (6 in local currency and 6 in U.S. dollar) are nonstationary.

Table 1.

Univariate Unit Root Tests (Phillips-Perron)

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* The lag length of the augmented terms is 5. The reported numbers for the null hypothesis that α=0 are the Phillips-Perron t test statistics. The 5 percent asymptotic critical value under the no trend model is -2.86. The 5 percent asymptotic critical value under the model with a deterministic time trend is -3.41. The numbers reported for the null hypothesis that α=γ=0 are F test statistics. The 10 percent asymptotic critical value is 6.25.

Given that we cannot reject the null hypothesis that the stock market index of each country is nonstationary, we can now continue to test the possibility that there are long-term equilibrium relationships among the stock market indices based on the idea of cointegration. That is, we test whether there are some stationary linear combinations of the series. The test employed is Johansen’s trace test discussed in the previous section.

To get a better understanding of the cointegration relationships, we apply the cointegration test on the set of all six stock market indices and on some smaller subsets of indices. Specifically, we consider explicitly the long-run relationship between the two countries in North American (the NAm group), the United States and Canada, which share a free trade agreement. We consider the cointegration relationship among the three European countries (the Euro group): the United Kingdom, France, and Germany, which are members of the European Community. We also consider the so-called Pacific (Pac) group which includes the United States, Canada, and Japan, and the Western group (West), which includes the North American group and the European group excluding Japan. The cointegration test results are reported in Table 2. The tests are based on the logarithm of the stock indices. Test results are reported for the local currency case (Panel A) and for the U.S. dollar case (Panel B).

Table 2.

Multivariate Cointegration Test

(Number of cointegrating vectors: r)

July 1976 - December 1987

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(**) indicates significance at the 5 percent level. (*) indicates significance at the 10 percent level. (+) indicates significance at the 20 percent level

For the local currency case, the null hypothesis of no cointegration is not rejected for the North American group. However, it is rejected at the 5 percent significance level for the Euro group, the Pac group, and for the set of all series. For the Euro group, there is mild rejection (at the 10 percent significance level) of the null hypothesis that there is one or less cointegrating vector, indicating that there might be a second cointegrating vector among the United Kingdom, Germany, and France. However, the test statistic for the same null for the Pac group is not rejected. Furthermore, at the 20 percent significance level, for the set of all countries, the nulls of one or fewer and two or fewer cointegrating vector are rejected. 2/ In other words, the evidence points to the existence of one to three cointegrating vectors in the system. Combining this result with the subgroup test results, the general picture is that there is a cointegration relationship between the United States, Canada, and Japan. There is also a sort of European cointegrating vector linking the three European countries.

The message from the U.S. dollar case analysis is similar. However, the null hypothesis of no cointegrating vector in the Pac group, and that of one or fewer conintegrating vector in the Euro group, are only rejected at the 20 percent significance level. For the West group, the null of no cointegration is rejected at the 10 percent level but the null of one or fewer cointegrating vector is not rejected. This indicates that there is one cointegrating vector for the United States, Canada, the United Kingdom, Germany, and France. For the entire set of countries, the null of one or fewer cointegrating vector is rejected at the 20 percent significance level. However, the null of two or fewer cointegrating vector is not rejected. Combining this evidence with the subgroup results, there seem to be two cointegrating vectors, with one of them more closely linked to the European countries.

Given the market development towards globalization and liberalization and its potential effects on the integration of international stock markets, it is interesting to see if the cointegration results have changed over time. Since the trend towards globalization is marked by a large number of policy changes occurring in different times, it is particularly difficult to identify an exact regime shift day. To look for changes in cointegration as such, we simply break our sample of 700 weekly observations down into two subsamples of equal size (350 observations). The first subsample is from July 1976 to March 1983. The second subsample is from April 1983 to December 1989. The subsample analysis, while not precise, should be able to pick up a significant change in the long-run relationship between the stock market price series, should there be one. The Johansen cointegration test results are reported in Table 3. As in Table 2, the first panel (A) is for the local currency case, and the second panel (B) is for the U.S. dollar case.

Table 3.

Multivariate cointegration tests: Subsample analysis

(Number of cointegrating vectors: r)

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(**) indicates significance at the 5 percent level. (*) indicates significance at the 10 percent level. (+) indicates significance at the 20 percent level.

In the local currency case, there is strong evidence that the cointegration relationship among the international stock price series has changed over time. In the first subsample, the null hypothesis of no cointegrating vector is not rejected for the North American group, and the Pac group. This null is rejected for the Euro group (at 5 percent). For larger systems the cointegration evidence is weaker. The null of no cointegration for the West five and for the set of all six countries are rejected only at the 20 percent level. The analysis points to the existence of one cointegrating vector in the entire system. Furthermore, this cointegrating vector is more related to the European countries. In the second subsample, we found much stronger evidence of cointegration. The null hypothesis of no cointegration between the United States and Canada is now rejected. The same hypothesis is also rejected for the Pac group. In fact, the null hypothesis of one or fewer cointegrating vectors between the United States, Canada, and Japan is also rejected at the 20 percent level. It is particularly interesting to see that the null hypothesis of no cointegration is not rejected for the Euro group but is rejected for the West group. The interpretation of this evidence is not that the three European countries are not related to each other, but that they are somewhat absorbed into a larger system including also the United States and Canada. This can be taken as evidence for less segmentation between the European countries and the North American ones. The test of cointegration applied to the entire set of all six countries indicates that there are one to three cointegrating vectors as the null hypothesis of no, one or fewer, and two or fewer cointegrating vectors are rejected respectively at the 5 percent, 10 percent and 20 percent levels. The result indicates that two of the cointegrating vectors are for the group of Western countries and that there is a cointegrating relationship between the United States, Canada, and Japan.

In the U.S. dollar case, the message is about the same. There is stronger and broader linkage of international stock markets in the second subsample period than in the first subsample. The null of no cointegration for the Euro group of countries is rejected in the first subsample period but not in the second subsample period. The null of no cointegration for the entire set of Western countries is marginally (at the 20 percent level) rejected in both the first subsample period and the second subsample period. These two pieces of evidence taken together imply that the three European stock markets are more integrated with the North American stock markets as the cointegration relationship involves both North American and European price series. Furthermore, the Japanese stock market price is not cointegrated with the United States and the Canadian stock market prices in the first subsample, but is cointegrated with these prices in the second subsample at the 20 percent level. This evidence, together with the finding of a more cointegrating vector in the entire set of countries, indicate that the Japanese stock market has become more integrated with the other international stock markets.

IV. Conclusion

In this paper, we derive evidence on the integration of international stock markets from the cointegration properties of international stock market prices. Using the multivariate cointegration test of Johansen, we find that there are one to three cointegrating vectors in the set of six country stock price indices, including that of the United States, Canada, the United Kingdom, France, Germany, and Japan. The results suggest that there are long-run equilibrium relationships among the stock market prices. Using subsets of countries, we find that the stock market prices of the three European countries are cointegrated. Furthermore, the stock market prices of the United States, Canada, and Japan are cointegrated.

Subsample analysis also indicates that the cointegration relationships have become stronger over time. Specifically, we find evidence that the European country stock markets have become more related to the United States and Canadian stock markets. Furthermore, the Japanese stock market has become more integrated with the other stock markets. The strengthening of international stock market integration is consistent with the increasing liberalization and globalization of capital markets.

Cointegration of International Stock Market Indices
Author: Mr. Ray Yeu-Tien Chou, Mr. Victor Ng, and Lynn K. Pi