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Changes in the international comovement of stock returns and asymmetric macroeconomic shocks
Available online at www.sciencedirect.com
Int. Fin. Markets, Inst. and Money 19 (2009) 289–305
Changes in the international comovement of stock returns and asymmetric macroeconomic shocks Renatas Kizys a,∗ , Christian Pierdzioch b a
Departamento de Econom´ıa, Instituto Tecnol´ogico y de Estudios Superiores de Monterrey, Monterrey 64849, Nuevo Le´on, Mexico b Department of Economics, Saarland University, P.O.B. 15 11 50, Saarbruecken, Germany Received 21 June 2007; accepted 5 January 2008 Available online 16 January 2008
Abstract We study whether asymmetric macroeconomic shocks help to explain changes in the international comovement of monthly stock returns in major industrialized countries over the period 1975–2004. Based on a time-varying parameter model, we trace out how the pattern of international comovement of stock returns changed over time. In order to identify asymmetric macroeconomic shocks, we estimate vector-autoregressive models. The results of estimating time-series regression models and panel-data models indicate that changes in the international comovement of stock returns are not systematically linked to macroeconomic shocks. © 2008 Elsevier B.V. All rights reserved. JEL classification: E32; F37; G15 Keywords: International comovement of stock returns; Asymmetric macroeconomic shocks; Time-varying parameter model; Time-series regression model; Panel-data model
1. Introduction According to modern portfolio theory, the international comovement of stock returns is of key importance for international investors who seek to invest in a well-diversified global portfolio. Identifying a well-diversified global portfolio is complicated by the stylized fact that
∗
Corresponding author. Tel.: +52 81 83582000x4305–7; fax: +52 81 83582000x4351. E-mail addresses: [email protected] (R. Kizys), [email protected] (C. Pierdzioch).
1042-4431/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.intfin.2008.01.002
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the international comovement of stock returns is not constant over time (Longin and Solnik, 1995). A natural question is whether macroeconomic variables help to explain changes in the international comovement of stock returns. Macroeconomic variables represent key state variables in widely used multifactor and intertemporal asset pricing models. It is, therefore, not surprising that many researchers have analyzed various aspects of the link between macroeconomic variables and the international comovement of stock returns (Bekaert and Harvey, 1995; Chinn and Forbes, 2004; Dumas et al., 2003 to name just a few). Despite the plentitude of empirical results reported in the relevant literature, no consensus has yet emerged as to whether macroeconomic variables help to explain changes in the international comovement of stock returns. While some authors have reported evidence of a link between macroeconomic variables and the international comovement of stock returns (Erb et al., 1994; Ragunathan et al., 1999), other authors have reported evidence that this link is rather weak (Verma and Ozuna, 2005; Kizys and Pierdzioch, 2006). Our contribution to this literature is frankly empirical and agnostic. In a comprehensive empirical study, we systematically analyze whether macroeconomic shocks that are asymmetric across countries help to explain changes in the international comovement of monthly stock returns in major industrialized countries over the period 1975–2004. Our main result is that changes in the international comovement of stock returns are not systematically linked to asymmetric macroeconomic shocks. Our research strategy is the following: • We estimate a time-varying parameter (TVP) model in order to trace out how the pattern of the international comovement of stock returns has changed over time. Our estimates reveal a tendency of the international comovement of stock returns to increase since the mid-1990s. This increase, however, has not been monotonic. • We estimate two vector-autoregressive (VAR) models in order to identify different types of asymmetric macroeconomic shocks. We estimate two different VAR models because it is potentially important to account for the nature of shocks. For example, a monetary shock may have a different impact on the international comovement of stock returns than a shock to aggregate supply. • We undertake a regression-based analysis in order to assess whether asymmetric macroeconomic shocks help to explain changes in the international comovement of stock returns. We estimate both time-series regression models and regression models for panel-data. Unlike Bracker and Koch (1999), who have used differences in the levels of macroeconomic variables, we focus on macroeconomic shocks rather than on macroeconomic variables per se because the international comovement of stock returns is likely to move in response to unexpected rather than to expected changes in macroeconomic variables and the stance of the business cycle. We focus on asymmetric macroeconomic shocks because the international comovement of stock returns should not respond to shocks that are common to the countries or the group of countries one studies. In this respect, our research complements recent research by Hess (2004), Nikkinen and Sahlstrom (2004), and Nikkinen et al. (2006). In Section 2, we describe our TVP model. In Section 3, we provide details concerning our VAR models. In Section 4, we summarize our empirical results. In Section 5, we offer some concluding remarks.
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2. Measuring the international comovement of stock returns We analyze the international comovement of continuously compounded (U.S. dollar) returns on the MSCI stock indexes for Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States. The data are at a monthly frequency and cover the sample period 1975–2004. The data are from Thompson Financial Datastream.1 Because the international comovement of stock returns may have changed over time, we use a TVP model to measure changes in the international comovement of stock returns (for a similar model, see Rockinger and Urga, 2001). We use the Kalman-filter model to estimate the TVP model (Harvey, 1992; Kim and Nelson, 2000). We use the following TVP model: Rt,i = β0,t,i + β1,t,i Rt−1,i + β2,t,i Rt,j + ut,i ,
(1)
βm,t,i = βm,t−1,i + vm,t,i ,
(2)
m = 0, 1, 2
where Rt,i denotes the stock returns in country i = / j, Rt,j denotes the stock returns in a benchmark country, and t denotes a time index. The disturbance terms, ut,i and vt,i , are independently normally distributed and are mutually uncorrelated. Eq. (1) stipulates that the returns in a domestic country are equal to a time-varying intercept term, the lagged own returns, the returns in a foreign benchmark country, and a disturbance term. The lagged own returns control for the effects of potential market inefficiencies, irrational behavior of investors, and other effects that may give rise to autocorrelation in stock returns. Fratzscher (2002) has stressed the importance of controlling for such effects in analyses of international financial linkages. The coefficients have a time index and, thus, can change over time. According to Eq. (2), the time-varying coefficients follow a random walk process. In terms of the International Capital Asset Pricing Model, one can interpret the time-varying coefficients as time-varying betas. In order to estimate the TVP model, two steps have to be taken. The computations that have to be carried out in order to take these two steps are summarized at the end of the paper (Appendix A).2 1. Prediction: At the beginning of period t, an optimal predictor of returns is determined on the basis of all information available up to period t − 1. 2. Updating: Once returns have been observed at the end of period t, the prediction error can be used to update the estimates of the coefficients. Our TVP model implies that we can use either filtered or smoothed estimates of the coefficient β2,t,i to estimate the time-varying international comovement of stock returns. The difference between the filtered and the smoothed estimates lies in the information one uses to compute these estimates (Kim and Nelson, 2000).3 The filtered estimates refer to an estimate of the coefficients based on information available up to time t. In contrast, the smoothed estimates refer to an estimate of the coefficients based on all available information in the entire sample period. We use 1 Results similar to those we report in this paper obtain when we use stock returns measured in local currency rather than in U.S. dollars. The results are also robust to using quarterly rather than monthly data. The results based on local stock returns and on quarterly data are available from the authors upon request. 2 We used a maximum likelihood estimator to estimate the Kalman-filter model. We implemented the maximum likelihood estimator in Matlab (release R2007b). 3 The variances of the disturbance terms in Eqs. (1) and (2) are estimated based on the full sample of data.
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the filtered estimates because our aim is to study the international comovement of stock returns from the perspective of an international investor. 3. Measuring asymmetric macroeconomic shocks We use two different VAR models to identify macroeconomic shocks.4 The first VAR model (VAR 1) contains an equation for the short-term interest rate, an equation for the inflation rate (measured in terms of changes in the logarithm of national consumer price indexes), and an equation for the month-to-month growth rate of industrial production (Rotemberg and Woodford, 1997). These three equations represent the three basic building blocs of many modern macroeconomic models: an interest rate rule that describes monetary policy, a Phillips curve equation, and an aggregate demand equation. The second VAR model (VAR 2) is an open-economy VAR model (Clarida and Gali, 1994). The VAR model features three equations. The first equation describes the dynamics of changes in the logarithm of the ratio of the industrial production of a pair of countries. The second equation describes changes in the logarithm of the real exchange rate of a pair of countries. The third equation describes the dynamics of changes in the logarithm of relative price levels defined as the ratio of the consumer price indexes of a pair of countries. We use four lags of the endogenous variables in order to estimate our VAR models. The average lag length of 4 for the VAR 1 is dictated by the Akaike information criterion. The average lag length for the VAR 2 dictated by the Akaike information criterion is three, but using four lags ensures that any autocorrelation in the residuals of the VAR is eliminated. In order to identify the structural macroeconomic shocks that drive our first VAR model, we invoke a specific ordering of the three endogenous variables to compute a unique Choleski decomposition of the residuals of the reduced-form VAR (Sims, 1980).5 The ordering scheme we use implies that the variables are ordered as follows: inflation rate, growth rate of industrial production, short-term interest rate.6 We then compute the cross-country difference of the structural macroeconomic shocks obtained from the VAR model to measure asymmetric shocks to the Phillips curve equation, asymmetric aggregate demand shocks, and asymmetric monetary policy shocks. In order to identify the structural macroeconomic shocks that drive our second VAR, we use three long-run identifying restrictions along the lines of Blanchard and Quah (1989). The three restrictions serve to identify a supply shock, a real demand shock, and a money market shock.7
4 Data are from Thompson Financial Datastream. In order to measure the short-term interest rate, we use the 1-month Treasury bill rate. In the case of Germany, we use a 3-month money market rate due to data availability problems. In the case of Japan, we use a 2-month Treasury bill rate. The Japanese data are from the homepage of the Bank of Japan. We use the 1-month Treasury bill rate taken from Thompson Financial Datastream to fill some gaps in the Japanese series. In the case of Italy, the data on the money market rate are from the IFS CD-ROM published by the IMF. We use the Census X-12 method to seasonally adjusting the data. 5 The ordering implies that a shock to a variable placed in a lower position of this ordering exerts no contemporaneous effect on the variables placed in a relatively higher position of the ordering. In contrast, a shock to a variable placed in a higher position of this ordering scheme exerts a contemporaneous effect on the variables placed in a relatively lower position of the ordering. 6 Because the correlations between the reduced-form residuals of our VAR model are small, changes in the ordering of the variables do not matter much for the computation of the structural residuals. 7 The first two restrictions imply that money market shocks do not affect industrial production and the real exchange rate in the long run. These restrictions imply that monetary neutrality holds in the long run. The third restriction implies that demand shocks do not affect relative output in the long run.
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Unlike in the first VAR, the structural macroeconomic shocks obtained from the second VAR are asymmetric macroeconomic shocks. 4. Empirical results We proceed in three steps. In a first step, we present our estimates of the time-varying international comovement of stock returns. In a second step, we present results derived from time-series regression models that show how asymmetric macroeconomic shocks affect the international comovement of stock returns. In a third step, we present results derived from panel-data models. 4.1. International comovement of stock returns Fig. 1 depicts how the international comovement of stock returns has changed over time. For completeness, the figure shows both the filtered and the smoothed estimates.8 It is interesting to note that, in many cases, the strength of the international comovement of stock returns has not increased monotonically during our sample period. However, apart from a few exceptions, the international comovement of stock returns tends to show a tendency to increase since the mid-1990s. A stronger international comovement of stock returns implies that the diversification benefits from investing in a portfolio of international stocks will tend to decline (Kearney and Lucey, 2004). As indicated by the smoothed estimates, the comovement of stock returns was relatively stable over time in the cases of the country pairs U.S./Canada, U.S./UK, Germany/France and Germany/UK. When interpreting the smoothed estimates, however, one should take into account that the maximum likelihood estimator of the variance of a coefficient in a TVP model has a large point mass at zero when coefficient variation is small (Stock and Watson, 1998). Thus, the variance may be readily mistaken for zero. Moreover, we are mainly interested in analyzing the comovement of stock returns from an investors’ perspective. The smoothed estimates, however, are based on information on the full sample of data. We, therefore, focus in the remainder of this paper on the filtered estimates. The explanations for the recent increase in the international comovement of stock returns are numerous. One explanation is that the importance of country effects documented by Heston and Rouwenhorst (1995) has declined in recent years. According to this explanation, global industry factors have grown in importance (Baca et al., 2000), and even may have surpassed countryspecific effects in importance (Cavaglia et al., 2000). Another explanation is that the increase in the international comovement of stock returns is closely linked to the stock market bubble of the late 1990s (Brooks and Del Negro, 2004). One could also imagine that the comovement of stock returns is affected by the recent upsurge in cross-border financial flows. Cross-border financial flows in equities have significantly increased since the mid-1990s (Eichengreen and Fishlow, 1998). International equity flows may affect stock returns through momentum trading of foreign investors, price-pressure and liquidity effects, a potential broadening in the investor base, and changes in the cost of capital (see Stulz, 1999, for a survey). Finally, the increased international
8 In order to account for the introduction of the Euro, the estimation results for the intra-European comovements of stock returns are based on a sample period containing data up to and including 1998:12. The results of estimating the TVP model are similar if the sample period for the intra-European comovements of stock returns is extended to 2004:12. The results for the extended sample period are available from the authors upon request.
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Fig. 1. Kalman-filter estimates of time-varying international comovement of stock returns. This figure shows Kalman-filter estimates of the time-varying parameters (Kalman-filter estimates are depicted as continuous lines and Kalman-smoother estimates are depicted as dashed lines), β2,t,i . Coefficients for the intra-European comovements of stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States.
comovement of stock returns has been attributed to an increase in equity market integration in the nineties (Ayuso and Blanco, 2001) and an increase in bilateral trade flows (Pretorius, 2002). 4.2. Time-series regression models We estimate the following time-series regression model in order to analyze whether changes in the international comovement of stock returns are systematically linked to asymmetric macroeconomic shocks: β2,t,i = δ1 asy1,t,i + δ2 asy2,t,i + δ3 asy3,t,i + et,i ,
(3)
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Fig. 2. International comovement of stock returns and macroeconomic shocks, VAR 1, 1975:1–2004:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
where denotes the first difference operator, et,i denotes a disturbance term, and asyj,t,i , j = 1, 2, 3 denote the three asymmetric macroeconomic shocks implied by our first and second VAR model, respectively. Our time-series regression model answers the question whether macroeconomic shocks help to explain the stochastic changes in the international comovement of stock returns, β2,t,i = v2,t,i , modeled in Eq. (2). Similar to Barberis et al. (2005), we focus on the differenced “beta” coefficient, β2,t,i , as a measure of changes in the comovement of stock returns. Fig. 2 summarizes the results based on the asymmetric macroeconomic shocks implied by our first VAR model. Fig. 3 summarizes the results based on the asymmetric macroeconomic shocks from our second VAR model. The general picture that emerges from Figs. 2 and 3 is that changes in the international comovement of stock returns are not systematically linked to asymmetric macroeconomic shocks. This picture corroborates the results reported by Connolly and Wang (2003), who found that the comovement
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Fig. 3. International comovement of stock returns and macroeconomic shocks, VAR 2, 1975:1–2004:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 2 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the ratio of industrial production. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the real exchange rate. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the ratio of consumer price indexes.
of international stock returns is unrelated to public information about economic fundamentals, and by Verma and Ozuna (2005), who found that stock market movements in Latin America cannot be attributed to movements in cross-country macroeconomic variables. One could argue that the link between changes in the international comovement of stock returns and asymmetric macroeconomic shocks may have changed over time. Specifically, the globalization of the world’s economy and the ensuing international financial integration has been largely a phenomenon of the 1990s. Furthermore, the Maastricht Treaty establishing the European Union came into force in November 1993, which may have affected the intra-European comovement of stock returns. Therefore, we present in Fig. 4 results for a first subsample period, 1975:1–1993:12, and in Fig. 5 results for a second subsample period, 1994:1–2004:12. The results are based on the
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Fig. 4. International comovement of stock returns and macroeconomic shocks, VAR 1, 1975:1–1993:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
asymmetric macroeconomic shocks implied by our first VAR.9 As in the case of the full sample, the results for the two subsample periods do not reveal any clear-cut systematic link between changes in the international comovement of stock returns and asymmetric macroeconomic shocks. Because Ammer and Mei (1996) have suggested the existence of lags in the transmission of economic shocks, we analyze a time-series regression model that also allows for lagged asymmetric shocks to affect the international comovement of stock returns. We use the following time-series regression model: β2,t,i =
n l=0
9
δ1,l asy1,i,t−l +
n l=0
δ2,l asy2,i,t−l +
n
δ3,l asy3,i,t−l + et,i ,
l=0
The results for our second VAR are similar. (The results are available upon request).
(4)
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Fig. 5. International comovement of stock returns and macroeconomic shocks, VAR 1, 1994:1–2004:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
where n denotes the number of lagged asymmetric macroeconomic shocks included in the regression model. We set n = 2, implying that asymmetric macroeconomic shocks lagged once and twice are included in addition to contemporaneous macroeconomic shocks. We use likelihood ratio tests for each of the three types of asymmetric macroeconomic shocks to check whether their lagged values can be dropped from the list of regressors. The results shown in Fig. 6 suggest that using lagged asymmetric macroeconomic shocks does not systematically strengthen the explanatory power of asymmetric macroeconomic shocks for changes in the international comovement of stock returns. Some likelihood ratio tests yield significant results, but the significance in general is sensitive to the specification of the VAR model.10
10 The results are based on the asymmetric macroeconomic shocks implied by our first VAR model. The results for the second VAR model are similar.
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Fig. 6. International comovement of stock returns and contemporaneous and lagged macroeconomic shocks, VAR 1, 1975:1–2004:12. This figure shows p-values of likelihood ratio tests of the hypothesis that in Eq. (4) the coefficients are δ1,2 = δ1,3 = 0 (Graph 1), δ2,2 = δ2,3 = 0 (Graph 2), and δ3,2 = δ3,3 = 0 (Graph 3). Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
4.3. Panel-data models As a further robustness check, we use techniques developed for the estimation of panel-data models to estimate Eq. (3). An advantage of panel-data models is that they use a larger information set and, thus, yield more efficient estimates of the coefficients. Another advantage is that paneldata models render it possible to control for cross-sectional and group heterogeneity. We use the panel-EGLS (estimated generalized least squares) estimator to estimate the link between the international comovement of stock returns and asymmetric macroeconomic shocks because of the presence of cross-sectional correlation among the disturbance terms, et,i . We use our panel-data models to address two different questions. The first question is whether the observed international comovement of stock returns is country-specific. In order to answer the first question, we estimate a panel-data model with fixed effects. The second question is
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Fig. 7. International comovement of stock returns and macroeconomic shocks in a panel-data model. This figure shows p-values of t-tests for significance of macroeconomic shocks in a panel-data model with fixed effects estimated by means of the panel-EGLS estimator. Graph 1 depicts the results based on VAR 1, where CHOL 1, CHOL 2, and CHOL 3 denote the three asymmetric shocks derived from VAR 1 by means of a Choleski decomposition. Graph 2 depicts the results based on VAR 2, where CG 1, CG 2, and CG 3 denote the three asymmetric shocks derived from VAR 2 by means of long-run identifying restrictions. The full sample period is 1975:1–2004:12, the first subsample period is 1975:1–1993:12, and the second subsample period is 1994:1–2004:12. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro.
whether the international comovement of stock returns is group-specific. In order to answer the second question, we divide our cross-section of country pairs into two groups. The first group (“Europe”) contains the intra-European country pairs. This group is defined by means of a dummy variable that assumes the value one if the international comovement of stock returns is intra-European, and zero otherwise. The second group (“US”) contains the country pairs involving the United States and one of the other countries. This group is identified by means of a dummy variable that assumes the value one if the comovement of returns is measured with reference to the United States, and zero otherwise. Our two groups are designed to capture in a stylized manner region effects in international stock returns (Brooks and Del Negro, 2005).
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Fig. 8. International comovement of stock returns and macroeconomic shocks in a panel-data model including dummy variables. This figure shows p-values of t-tests for significance of macroeconomic shocks in a panel-data model with fixed effects estimated by means of the panel-EGLS estimator. Graph 1 depicts the results based on VAR 1, where CHOL 1, CHOL 2, and CHOL 3 denote the three asymmetric shocks derived from VAR 1 by means of a Choleski decomposition. Graph 2 depicts the results based on VAR 2, where CG 1, CG 2, and CG 3 denote the three asymmetric shocks derived from VAR 2 by means of long-run identifying restrictions. DUMMY EU (DUMMY US) is a dummy variable that is one for intra-European country pairs (country pairs including the United States), and zero otherwise. The full sample period is 1975:1–2004:12, the first subsample period is 1975:1–1993:12, and the second subsample period is 1994:1–2004:12. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro.
In economic terms, one could think of different observed and unobserved factors that account for differences between the two groups. One factor could be the physical distance between financial markets that might have an effect on the international comovement of stock returns (Griffin and Karolyi, 1998; Portes and Rey, 2005). Another factor could be the intra-European harmonization of macroeconomic and fiscal policies brought about by the establishment of the European Economic Community, the European Union, and the Euro Area (Rezayat and Yavas, 2006). We estimate four different specifications of our panel-data model. In the first specification, we explain the international comovement of stock returns in terms of the asymmetric macroeconomic shocks only. The second specification features, in addition to the asymmet-
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Fig. 9. Results of Wald tests for significance of differences between interaction terms. This figure shows p-values of Wald tests for significant differences between interaction terms in a panel-data model. The interaction terms capture potential differences between the effects of the asymmetric macroeconomic shocks on the intra-European comovement of stock returns and on the international comovement of the stock returns in the United States with the other countries in our sample. The interaction terms are computed by multiplying asymmetric macroeconomic shocks with the “Europe” or the “US” dummy. The panel-data model is estimated by means of the panel-EGLS estimator. CHOL denotes the results for the asymmetric shocks derived from VAR 1 by means of a Choleski decomposition. CG denotes the results for the asymmetric shocks derived from VAR 2 by means of long-run identifying restrictions. The full sample period is 1975:1–2004:12, the first subsample period is 1975:1–1993:12, and the second subsample period is 1994:1–2004:12. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro.
ric macroeconomic shocks, the “Europe” dummy. In the third specification, we replace the “Europe” dummy with the “US” dummy. Finally, in the fourth specification, we include both the “Europe” and the “US” dummies. Because the second and third specification yield results similar to the results for the fourth specification, we only report results for the first specification (Fig. 7) and fourth specification (Fig. 8). We report results for the full sample period, 1975:1–2004:12, for the first subsample period, 1975:1–1993:12, and for the second subsample period, 1994:1–2004:12. As a rule, we find that the international comovement of stock returns does not systematically respond to asymmetric macroeconomic shocks. Across the various specifications of the panel-data model that we analyze, there are exceptions from this rule, but they do not follow any systematic pattern. Noteworthy, there are no significant cases in the second subsample period. The group-specific dummies are not significant in the full sample period and in the first subsample period. The dummy “US” is insignificant in all specifications. In contrast, the “Europe” dummy becomes significant (at the 10% significance level) in the second subsample. This significance suggests that the international comovement of stock returns among the European countries has become stronger than the comovement of stock returns vis-`a-vis the United States. The significance of the “Europe” dummy is robust to including the “US” dummy in the panel-data model, and it suggests that either the geographical distance between two countries or the integration efforts made by the European countries may have played a role for the international comovement of stock returns. The group-specific dummies “Europe” and “US” allow the question whether the estimated international comovement of stock returns varies across the two groups to be answered. The groupspecific dummies, however, do not answer the question whether the link between the comovement
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of stock returns and the asymmetric macroeconomic shocks is different between the two groups. In order to address this question, we interact, in a yet different specification of our panel-data model, the group-specific dummies with the asymmetric macroeconomic shocks. The interaction terms capture potential differences between the effects of the asymmetric macroeconomic shocks on the intra-European comovement of stock returns and on the international comovement of the stock returns in the United States with the other countries in our sample. We use Wald tests to analyze whether there are significant differences between the interaction terms that are based on the dummies “Europe” and “US”. The significance of the test results is stronger in the full sample period and in the first subsample period, but loses significance in the second subsample period. Fig. 9 summarizes the test results. The results of the Wald tests, even if they are insignificant, do not imply that all differences between the interaction terms are insignificant. In fact, some of the differences between the interaction terms are significant. (Results are not reported, but are available upon request.) The cases of significant differences between the interaction terms, however, depend on the VAR model being used to identify asymmetric shocks and on the subsample period being studied. 5. Concluding remarks The general result that emerges from our empirical results is that the international comovement of stock returns has changed over time, but that asymmetric macroeconomic shocks do not help much to explain these changes. This result does not imply that the international comovement of stock returns is per se decoupled from macroeconomic fundamentals at all times and in all countries, or that it does not reflect trends in the degree of international financial integration. Likewise, our result should also not be interpreted to indicate that country or regional effects caused by, for example, differences in institutions or differences in openness to trade are unimportant for international portfolio diversification strategies. Rather, our result suggests that in general monitoring asymmetric macroeconomic shocks in a cross-section of major industrialized countries should be of little systematic help for international investors who seek to choose, based on changes in the comovement of international stock returns, a portfolio on the efficient mean-variance world-wide portfolio frontier. We deem this to be an interesting result because international investors can choose among a large set of variables to model changes in the international comovement of stock returns. Given the plentitude of variables available to an international investor, it is important to sort out those variables that are not particularly useful for modeling the changes in the international comovement of stock returns. Acknowledgment We thank an anonymous referee and Ike Mathur (the editor) for very helpful comments. The usual disclaimer applies. Part of this paper was written during a research visit of Renatas Kizys at Saarland University. Appendix A We use the following six equations to implement the TVP model (the notation follows Kim and Nelson, 2000):
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A.1. Prediction: βt|t−1,i = Fi βt−1|t−1,i ,
(A1)
Pt|t−1,i = Fi Pt−1|t−1,i Fi + Qi ,
(A2)
ηt|t−1,i = Rt,i − Rt|t−1,i ,
(A3)
2 ωt|t−1,i = xt,i Pt|t−1,i xt,i + σu,i ,
(A4)
A.2. Updating: βt|t,i = βt|t−1,i + Kt,i ηt|t−1,i ,
(A5)
Pt|t,i = Pt|t−1,i + Kt,i xt,i Pt|t−1 ,
(A6)
ω−1 where i is a country index and Kt,i = Pt|t−1,i xt,i t|t−1,i is the so-called Kalman gain, which determines the weight assigned to new information about βt,i contained in the prediction error. We use / j, Fi = (3 × 3) denotes the following notation: βt,i = (β0,t,i β1,t,i β2,t,i ) , xt,i = (1 Rt−1,i Rt,j ) with i = 2 σ 2 σ 2 ). Furthermore, β an identity matrix, and Qi = diag(σv,1,i t|t−1,i denotes expectation of v,2,i v,3,i βt,i conditional on information up to period t − 1, Pt|t−1,i denotes the covariance matrix of βt,i conditional on information up to period t − 1, βt|t,i denotes the expectation (estimate) of βt,i conditional on information up to period t, and Pt|t,i denotes the covariance matrix of βt,i conditional on information up to period t. The term Rt|t−1,i denotes the forecast of Rt,i given information up to period t − 1, ηt|t−1,i = Rt,i − Rt|t−1,i denotes the prediction error, and ωt|t−1,i denotes the conditional variance of the prediction error. The smoothed estimates implied by the TVP model can be computed using the following recursive equations, where T denotes the sample size: −1 βt|T,i = βt|t,i + Pt|t,i Fi Pt+1|t,i (βt+1|T,i − Fi βt|t,i )
(A7) −1
−1 Pt|T,i = Pt|t,i + Pt|t,i Fi Pt+1|t,i (Pt+1|T,i − Pt+1|t,i )P t+1|t,i FPt|t,i .
(A8)
References Ammer, J., Mei, J., 1996. Measuring international economic linkages with stock market data. Journal of Finance 51, 1743–1763. Ayuso, J., Blanco, R., 2001. Has financial market integration increased during the nineties? Journal of International Financial Markets, Institutions and Money 11, 265–287. Baca, S., Garbe, B., Weiss, R., 2000. The rise of sector effects in major equity markets. Financial Analysts Journal (September/October), 34–40. Barberis, N., Shleifer, A., Wurgler, J., 2005. Comovement. Journal of Financial Economics 75, 283–317. Bekaert, G., Harvey, C.R., 1995. Time-varying world market integration. Journal of Finance 50, 403–444. Blanchard, O., Quah, D., 1989. The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79, 655–673. Bracker, K., Koch, P.D., 1999. Economic determinants of the correlation structure across international equity markets. Journal of Economics and Business 51, 443–471. Brooks, R., Del Negro, M., 2004. The rise in comovement across national stock markets: market integration or IT bubble? Journal of Empirical Finance 11, 659–680. Brooks, R., Del Negro, M., 2005. Country versus region effects in international stock returns. Journal of Portfolio Management 31, 67–72.
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Cavaglia, S., Brightman, C., Aked, M., 2000. The increasing importance of industry factors. Financial Analysts Journal (September/October), 41–54. Chinn, M.D., Forbes, K.J., 2004. A decomposition of global linkages in financial markets over time. Review of Economics and Statistics 86, 705–722. Clarida, R., Gali, J., 1994. Sources of real-exchange rate fluctuations: how important are nominal shocks? Carnegie Rochester Conference Series on Public Policy 41, 1–56. Connolly, R.A., Wang, F.A., 2003. International equity market comovements: economic fundamentals or contagion? Pacific-Basin Finance Journal 11, 23–43. Dumas, B., Campbell, R.H., Ruiz, P., 2003. Are correlations of stock returns justified by subsequent changes in national outputs? Journal of International Money and Finance 22, 777–811. Eichengreen, B.J., Fishlow, A., 1998. Contending with capital flows: what is different about the 1990s? In: Kahler, M. (Ed.), Capital Flows and Financial Crises. Manchester University Press, Manchester, pp. 23–68. Erb, C., Campbell, H., Viskanta, T., 1994. Forecasting international equity correlations. Financial Analysts Journal (November/December), 32–45. Fratzscher, M., 2002. Financial market integration in Europe: on the effects of EMU on stock markets. International Journal of Finance and Economics 7, 165–193. Griffin, J.M., Karolyi, A., 1998. Another look at the role of the industrial structure of markets for international diversification strategies. Journal of Financial Economics 50, 351–373. Harvey, A.C., 1992. Forecasting, Structural Time Series Models and the Kalman Filter. Press Syndicate of the University of Cambridge, Cambridge, UK. Hess, M.K., 2004. Dynamic and asymmetric impacts of macroeconomic fundamentals on an integrated stock market. Journal of International Financial Markets, Institutions and Money 14, 455–471. Heston, S.L., Rouwenhorst, K.G., 1995. Does industrial structure explain the benefits of industrial diversification? Journal of Financial Economics 36, 3–27. Kearney, C., Lucey, B.M., 2004. International equity market integration: theory, evidence and implications. International Review of Financial Analysis 13, 571–583. Kim, C.J., Nelson, C.R., 2000. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. MIT Press, Cambridge, MA. Kizys, R., Pierdzioch, C., 2006. Business-cycle fluctuations and international equity correlations. Global Finance Journal 17, 252–270. Longin, F., Solnik, B., 1995. Is the correlation in international equity returns constant, 1960–1990? Journal of International Money and Finance 14, 3–26. Nikkinen, J., Sahlstrom, P., 2004. Scheduled domestic and US macroeconomic news and stock valuation in Europe. Journal of Multinational Financial Management 14, 201–205. Nikkinen, J., Omran, M., Sahlstrom, P., Aijo, J., 2006. Global stock market reactions to scheduled U.S. macroeconomic news announcements. Global Finance Journal 17, 92–104. Portes, R., Rey, H., 2005. The determinants of cross-border equity flows. Journal of International Economics 65, 206–269. Pretorius, E., 2002. Economic determinants of emerging stock market interdependence. Emerging Markets Review 3, 84–105. Ragunathan, V., Faff, R.W., Brooks, R.D., 1999. Correlations, business cycles and integration. Journal of International Financial Markets, Institutions and Money 9, 75–95. Rezayat, F., Yavas, B.F., 2006. International portfolio diversification: a study of linkages among the U.S., European and Japanese equity markets. Journal of Multinational Financial Management 16, 440–458. Rockinger, M., Urga, G., 2001. A time-varying parameter model to test for predictability and integration in the stock markets of transition economies. Journal of Business and Economics Statistics 19, 73–84. Rotemberg, J.J., Woodford, M., 1997. An optimization-based econometric framework for the evaluation of monetary policy. NBER Macroeconomics Annual, 297–346. Sims, C., 1980. Macroeconomics and reality. Econometrica 48, 1–49. Stock, J.H., Watson, M.W., 1998. Median unbiased estimation of coefficient variance in a time-varying parameter model. Journal of the American Statistical Association 93, 349–358. Stulz, R.M., 1999. International Portfolio Flows and Security Markets. In: Feldstein, M.M. (Ed.), International Capital Flows. University of Chicago Press, Chicago, pp. 257–293. Verma, R., Ozuna, T., 2005. Are emerging equity markets responsive to cross-country macroeconomic movements? Evidence from Latin America. Journal of International Financial Markets, Institutions and Money 15, 73–87.
Int. Fin. Markets, Inst. and Money 19 (2009) 289–305
Changes in the international comovement of stock returns and asymmetric macroeconomic shocks Renatas Kizys a,∗ , Christian Pierdzioch b a
Departamento de Econom´ıa, Instituto Tecnol´ogico y de Estudios Superiores de Monterrey, Monterrey 64849, Nuevo Le´on, Mexico b Department of Economics, Saarland University, P.O.B. 15 11 50, Saarbruecken, Germany Received 21 June 2007; accepted 5 January 2008 Available online 16 January 2008
Abstract We study whether asymmetric macroeconomic shocks help to explain changes in the international comovement of monthly stock returns in major industrialized countries over the period 1975–2004. Based on a time-varying parameter model, we trace out how the pattern of international comovement of stock returns changed over time. In order to identify asymmetric macroeconomic shocks, we estimate vector-autoregressive models. The results of estimating time-series regression models and panel-data models indicate that changes in the international comovement of stock returns are not systematically linked to macroeconomic shocks. © 2008 Elsevier B.V. All rights reserved. JEL classification: E32; F37; G15 Keywords: International comovement of stock returns; Asymmetric macroeconomic shocks; Time-varying parameter model; Time-series regression model; Panel-data model
1. Introduction According to modern portfolio theory, the international comovement of stock returns is of key importance for international investors who seek to invest in a well-diversified global portfolio. Identifying a well-diversified global portfolio is complicated by the stylized fact that
∗
Corresponding author. Tel.: +52 81 83582000x4305–7; fax: +52 81 83582000x4351. E-mail addresses: [email protected] (R. Kizys), [email protected] (C. Pierdzioch).
1042-4431/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.intfin.2008.01.002
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the international comovement of stock returns is not constant over time (Longin and Solnik, 1995). A natural question is whether macroeconomic variables help to explain changes in the international comovement of stock returns. Macroeconomic variables represent key state variables in widely used multifactor and intertemporal asset pricing models. It is, therefore, not surprising that many researchers have analyzed various aspects of the link between macroeconomic variables and the international comovement of stock returns (Bekaert and Harvey, 1995; Chinn and Forbes, 2004; Dumas et al., 2003 to name just a few). Despite the plentitude of empirical results reported in the relevant literature, no consensus has yet emerged as to whether macroeconomic variables help to explain changes in the international comovement of stock returns. While some authors have reported evidence of a link between macroeconomic variables and the international comovement of stock returns (Erb et al., 1994; Ragunathan et al., 1999), other authors have reported evidence that this link is rather weak (Verma and Ozuna, 2005; Kizys and Pierdzioch, 2006). Our contribution to this literature is frankly empirical and agnostic. In a comprehensive empirical study, we systematically analyze whether macroeconomic shocks that are asymmetric across countries help to explain changes in the international comovement of monthly stock returns in major industrialized countries over the period 1975–2004. Our main result is that changes in the international comovement of stock returns are not systematically linked to asymmetric macroeconomic shocks. Our research strategy is the following: • We estimate a time-varying parameter (TVP) model in order to trace out how the pattern of the international comovement of stock returns has changed over time. Our estimates reveal a tendency of the international comovement of stock returns to increase since the mid-1990s. This increase, however, has not been monotonic. • We estimate two vector-autoregressive (VAR) models in order to identify different types of asymmetric macroeconomic shocks. We estimate two different VAR models because it is potentially important to account for the nature of shocks. For example, a monetary shock may have a different impact on the international comovement of stock returns than a shock to aggregate supply. • We undertake a regression-based analysis in order to assess whether asymmetric macroeconomic shocks help to explain changes in the international comovement of stock returns. We estimate both time-series regression models and regression models for panel-data. Unlike Bracker and Koch (1999), who have used differences in the levels of macroeconomic variables, we focus on macroeconomic shocks rather than on macroeconomic variables per se because the international comovement of stock returns is likely to move in response to unexpected rather than to expected changes in macroeconomic variables and the stance of the business cycle. We focus on asymmetric macroeconomic shocks because the international comovement of stock returns should not respond to shocks that are common to the countries or the group of countries one studies. In this respect, our research complements recent research by Hess (2004), Nikkinen and Sahlstrom (2004), and Nikkinen et al. (2006). In Section 2, we describe our TVP model. In Section 3, we provide details concerning our VAR models. In Section 4, we summarize our empirical results. In Section 5, we offer some concluding remarks.
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2. Measuring the international comovement of stock returns We analyze the international comovement of continuously compounded (U.S. dollar) returns on the MSCI stock indexes for Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States. The data are at a monthly frequency and cover the sample period 1975–2004. The data are from Thompson Financial Datastream.1 Because the international comovement of stock returns may have changed over time, we use a TVP model to measure changes in the international comovement of stock returns (for a similar model, see Rockinger and Urga, 2001). We use the Kalman-filter model to estimate the TVP model (Harvey, 1992; Kim and Nelson, 2000). We use the following TVP model: Rt,i = β0,t,i + β1,t,i Rt−1,i + β2,t,i Rt,j + ut,i ,
(1)
βm,t,i = βm,t−1,i + vm,t,i ,
(2)
m = 0, 1, 2
where Rt,i denotes the stock returns in country i = / j, Rt,j denotes the stock returns in a benchmark country, and t denotes a time index. The disturbance terms, ut,i and vt,i , are independently normally distributed and are mutually uncorrelated. Eq. (1) stipulates that the returns in a domestic country are equal to a time-varying intercept term, the lagged own returns, the returns in a foreign benchmark country, and a disturbance term. The lagged own returns control for the effects of potential market inefficiencies, irrational behavior of investors, and other effects that may give rise to autocorrelation in stock returns. Fratzscher (2002) has stressed the importance of controlling for such effects in analyses of international financial linkages. The coefficients have a time index and, thus, can change over time. According to Eq. (2), the time-varying coefficients follow a random walk process. In terms of the International Capital Asset Pricing Model, one can interpret the time-varying coefficients as time-varying betas. In order to estimate the TVP model, two steps have to be taken. The computations that have to be carried out in order to take these two steps are summarized at the end of the paper (Appendix A).2 1. Prediction: At the beginning of period t, an optimal predictor of returns is determined on the basis of all information available up to period t − 1. 2. Updating: Once returns have been observed at the end of period t, the prediction error can be used to update the estimates of the coefficients. Our TVP model implies that we can use either filtered or smoothed estimates of the coefficient β2,t,i to estimate the time-varying international comovement of stock returns. The difference between the filtered and the smoothed estimates lies in the information one uses to compute these estimates (Kim and Nelson, 2000).3 The filtered estimates refer to an estimate of the coefficients based on information available up to time t. In contrast, the smoothed estimates refer to an estimate of the coefficients based on all available information in the entire sample period. We use 1 Results similar to those we report in this paper obtain when we use stock returns measured in local currency rather than in U.S. dollars. The results are also robust to using quarterly rather than monthly data. The results based on local stock returns and on quarterly data are available from the authors upon request. 2 We used a maximum likelihood estimator to estimate the Kalman-filter model. We implemented the maximum likelihood estimator in Matlab (release R2007b). 3 The variances of the disturbance terms in Eqs. (1) and (2) are estimated based on the full sample of data.
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the filtered estimates because our aim is to study the international comovement of stock returns from the perspective of an international investor. 3. Measuring asymmetric macroeconomic shocks We use two different VAR models to identify macroeconomic shocks.4 The first VAR model (VAR 1) contains an equation for the short-term interest rate, an equation for the inflation rate (measured in terms of changes in the logarithm of national consumer price indexes), and an equation for the month-to-month growth rate of industrial production (Rotemberg and Woodford, 1997). These three equations represent the three basic building blocs of many modern macroeconomic models: an interest rate rule that describes monetary policy, a Phillips curve equation, and an aggregate demand equation. The second VAR model (VAR 2) is an open-economy VAR model (Clarida and Gali, 1994). The VAR model features three equations. The first equation describes the dynamics of changes in the logarithm of the ratio of the industrial production of a pair of countries. The second equation describes changes in the logarithm of the real exchange rate of a pair of countries. The third equation describes the dynamics of changes in the logarithm of relative price levels defined as the ratio of the consumer price indexes of a pair of countries. We use four lags of the endogenous variables in order to estimate our VAR models. The average lag length of 4 for the VAR 1 is dictated by the Akaike information criterion. The average lag length for the VAR 2 dictated by the Akaike information criterion is three, but using four lags ensures that any autocorrelation in the residuals of the VAR is eliminated. In order to identify the structural macroeconomic shocks that drive our first VAR model, we invoke a specific ordering of the three endogenous variables to compute a unique Choleski decomposition of the residuals of the reduced-form VAR (Sims, 1980).5 The ordering scheme we use implies that the variables are ordered as follows: inflation rate, growth rate of industrial production, short-term interest rate.6 We then compute the cross-country difference of the structural macroeconomic shocks obtained from the VAR model to measure asymmetric shocks to the Phillips curve equation, asymmetric aggregate demand shocks, and asymmetric monetary policy shocks. In order to identify the structural macroeconomic shocks that drive our second VAR, we use three long-run identifying restrictions along the lines of Blanchard and Quah (1989). The three restrictions serve to identify a supply shock, a real demand shock, and a money market shock.7
4 Data are from Thompson Financial Datastream. In order to measure the short-term interest rate, we use the 1-month Treasury bill rate. In the case of Germany, we use a 3-month money market rate due to data availability problems. In the case of Japan, we use a 2-month Treasury bill rate. The Japanese data are from the homepage of the Bank of Japan. We use the 1-month Treasury bill rate taken from Thompson Financial Datastream to fill some gaps in the Japanese series. In the case of Italy, the data on the money market rate are from the IFS CD-ROM published by the IMF. We use the Census X-12 method to seasonally adjusting the data. 5 The ordering implies that a shock to a variable placed in a lower position of this ordering exerts no contemporaneous effect on the variables placed in a relatively higher position of the ordering. In contrast, a shock to a variable placed in a higher position of this ordering scheme exerts a contemporaneous effect on the variables placed in a relatively lower position of the ordering. 6 Because the correlations between the reduced-form residuals of our VAR model are small, changes in the ordering of the variables do not matter much for the computation of the structural residuals. 7 The first two restrictions imply that money market shocks do not affect industrial production and the real exchange rate in the long run. These restrictions imply that monetary neutrality holds in the long run. The third restriction implies that demand shocks do not affect relative output in the long run.
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Unlike in the first VAR, the structural macroeconomic shocks obtained from the second VAR are asymmetric macroeconomic shocks. 4. Empirical results We proceed in three steps. In a first step, we present our estimates of the time-varying international comovement of stock returns. In a second step, we present results derived from time-series regression models that show how asymmetric macroeconomic shocks affect the international comovement of stock returns. In a third step, we present results derived from panel-data models. 4.1. International comovement of stock returns Fig. 1 depicts how the international comovement of stock returns has changed over time. For completeness, the figure shows both the filtered and the smoothed estimates.8 It is interesting to note that, in many cases, the strength of the international comovement of stock returns has not increased monotonically during our sample period. However, apart from a few exceptions, the international comovement of stock returns tends to show a tendency to increase since the mid-1990s. A stronger international comovement of stock returns implies that the diversification benefits from investing in a portfolio of international stocks will tend to decline (Kearney and Lucey, 2004). As indicated by the smoothed estimates, the comovement of stock returns was relatively stable over time in the cases of the country pairs U.S./Canada, U.S./UK, Germany/France and Germany/UK. When interpreting the smoothed estimates, however, one should take into account that the maximum likelihood estimator of the variance of a coefficient in a TVP model has a large point mass at zero when coefficient variation is small (Stock and Watson, 1998). Thus, the variance may be readily mistaken for zero. Moreover, we are mainly interested in analyzing the comovement of stock returns from an investors’ perspective. The smoothed estimates, however, are based on information on the full sample of data. We, therefore, focus in the remainder of this paper on the filtered estimates. The explanations for the recent increase in the international comovement of stock returns are numerous. One explanation is that the importance of country effects documented by Heston and Rouwenhorst (1995) has declined in recent years. According to this explanation, global industry factors have grown in importance (Baca et al., 2000), and even may have surpassed countryspecific effects in importance (Cavaglia et al., 2000). Another explanation is that the increase in the international comovement of stock returns is closely linked to the stock market bubble of the late 1990s (Brooks and Del Negro, 2004). One could also imagine that the comovement of stock returns is affected by the recent upsurge in cross-border financial flows. Cross-border financial flows in equities have significantly increased since the mid-1990s (Eichengreen and Fishlow, 1998). International equity flows may affect stock returns through momentum trading of foreign investors, price-pressure and liquidity effects, a potential broadening in the investor base, and changes in the cost of capital (see Stulz, 1999, for a survey). Finally, the increased international
8 In order to account for the introduction of the Euro, the estimation results for the intra-European comovements of stock returns are based on a sample period containing data up to and including 1998:12. The results of estimating the TVP model are similar if the sample period for the intra-European comovements of stock returns is extended to 2004:12. The results for the extended sample period are available from the authors upon request.
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Fig. 1. Kalman-filter estimates of time-varying international comovement of stock returns. This figure shows Kalman-filter estimates of the time-varying parameters (Kalman-filter estimates are depicted as continuous lines and Kalman-smoother estimates are depicted as dashed lines), β2,t,i . Coefficients for the intra-European comovements of stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States.
comovement of stock returns has been attributed to an increase in equity market integration in the nineties (Ayuso and Blanco, 2001) and an increase in bilateral trade flows (Pretorius, 2002). 4.2. Time-series regression models We estimate the following time-series regression model in order to analyze whether changes in the international comovement of stock returns are systematically linked to asymmetric macroeconomic shocks: β2,t,i = δ1 asy1,t,i + δ2 asy2,t,i + δ3 asy3,t,i + et,i ,
(3)
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Fig. 2. International comovement of stock returns and macroeconomic shocks, VAR 1, 1975:1–2004:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
where denotes the first difference operator, et,i denotes a disturbance term, and asyj,t,i , j = 1, 2, 3 denote the three asymmetric macroeconomic shocks implied by our first and second VAR model, respectively. Our time-series regression model answers the question whether macroeconomic shocks help to explain the stochastic changes in the international comovement of stock returns, β2,t,i = v2,t,i , modeled in Eq. (2). Similar to Barberis et al. (2005), we focus on the differenced “beta” coefficient, β2,t,i , as a measure of changes in the comovement of stock returns. Fig. 2 summarizes the results based on the asymmetric macroeconomic shocks implied by our first VAR model. Fig. 3 summarizes the results based on the asymmetric macroeconomic shocks from our second VAR model. The general picture that emerges from Figs. 2 and 3 is that changes in the international comovement of stock returns are not systematically linked to asymmetric macroeconomic shocks. This picture corroborates the results reported by Connolly and Wang (2003), who found that the comovement
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Fig. 3. International comovement of stock returns and macroeconomic shocks, VAR 2, 1975:1–2004:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 2 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the ratio of industrial production. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the real exchange rate. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the ratio of consumer price indexes.
of international stock returns is unrelated to public information about economic fundamentals, and by Verma and Ozuna (2005), who found that stock market movements in Latin America cannot be attributed to movements in cross-country macroeconomic variables. One could argue that the link between changes in the international comovement of stock returns and asymmetric macroeconomic shocks may have changed over time. Specifically, the globalization of the world’s economy and the ensuing international financial integration has been largely a phenomenon of the 1990s. Furthermore, the Maastricht Treaty establishing the European Union came into force in November 1993, which may have affected the intra-European comovement of stock returns. Therefore, we present in Fig. 4 results for a first subsample period, 1975:1–1993:12, and in Fig. 5 results for a second subsample period, 1994:1–2004:12. The results are based on the
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Fig. 4. International comovement of stock returns and macroeconomic shocks, VAR 1, 1975:1–1993:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
asymmetric macroeconomic shocks implied by our first VAR.9 As in the case of the full sample, the results for the two subsample periods do not reveal any clear-cut systematic link between changes in the international comovement of stock returns and asymmetric macroeconomic shocks. Because Ammer and Mei (1996) have suggested the existence of lags in the transmission of economic shocks, we analyze a time-series regression model that also allows for lagged asymmetric shocks to affect the international comovement of stock returns. We use the following time-series regression model: β2,t,i =
n l=0
9
δ1,l asy1,i,t−l +
n l=0
δ2,l asy2,i,t−l +
n
δ3,l asy3,i,t−l + et,i ,
l=0
The results for our second VAR are similar. (The results are available upon request).
(4)
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Fig. 5. International comovement of stock returns and macroeconomic shocks, VAR 1, 1994:1–2004:12. This figure shows absolute t-tests that can be used to analyze the significance of the coefficients δ1 (Graph 1), δ2 (Graph 2), and δ3 (Graph 3). We use Newey-West standard errors to compute the t-tests. Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
where n denotes the number of lagged asymmetric macroeconomic shocks included in the regression model. We set n = 2, implying that asymmetric macroeconomic shocks lagged once and twice are included in addition to contemporaneous macroeconomic shocks. We use likelihood ratio tests for each of the three types of asymmetric macroeconomic shocks to check whether their lagged values can be dropped from the list of regressors. The results shown in Fig. 6 suggest that using lagged asymmetric macroeconomic shocks does not systematically strengthen the explanatory power of asymmetric macroeconomic shocks for changes in the international comovement of stock returns. Some likelihood ratio tests yield significant results, but the significance in general is sensitive to the specification of the VAR model.10
10 The results are based on the asymmetric macroeconomic shocks implied by our first VAR model. The results for the second VAR model are similar.
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Fig. 6. International comovement of stock returns and contemporaneous and lagged macroeconomic shocks, VAR 1, 1975:1–2004:12. This figure shows p-values of likelihood ratio tests of the hypothesis that in Eq. (4) the coefficients are δ1,2 = δ1,3 = 0 (Graph 1), δ2,2 = δ2,3 = 0 (Graph 2), and δ3,2 = δ3,3 = 0 (Graph 3). Country pairs are plotted on the horizontal axis, where 1 = fra ita, 2 = ger fra, 3 = ger ita, 4 = ger uk, 5 = uk fra, 6 = uk ita, 7 = us can, 8 = us fra, 9 = us ger, 10 = us ita, 11 = us jap, 12 = us uk. The countries are (in alphabetical order) can = Canada, fra = France, ger = Germany, ita = Italy, jap = Japan, uk = United Kingdom, us = United States. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro. VAR 1 is used to identify the asymmetric macroeconomic shocks (see Section 3). The dashed (solid) horizontal line denotes the 10 (5) percent level of significance. Graph 1 shows absolute t-tests for a model featuring asymmetric shocks to the equation for inflation. Graph 2 shows absolute t-tests for a model featuring asymmetric shocks to the equation for output growth. Graph 3 shows absolute t-tests for a model featuring asymmetric shocks to the equation for the short-term interest rate.
4.3. Panel-data models As a further robustness check, we use techniques developed for the estimation of panel-data models to estimate Eq. (3). An advantage of panel-data models is that they use a larger information set and, thus, yield more efficient estimates of the coefficients. Another advantage is that paneldata models render it possible to control for cross-sectional and group heterogeneity. We use the panel-EGLS (estimated generalized least squares) estimator to estimate the link between the international comovement of stock returns and asymmetric macroeconomic shocks because of the presence of cross-sectional correlation among the disturbance terms, et,i . We use our panel-data models to address two different questions. The first question is whether the observed international comovement of stock returns is country-specific. In order to answer the first question, we estimate a panel-data model with fixed effects. The second question is
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Fig. 7. International comovement of stock returns and macroeconomic shocks in a panel-data model. This figure shows p-values of t-tests for significance of macroeconomic shocks in a panel-data model with fixed effects estimated by means of the panel-EGLS estimator. Graph 1 depicts the results based on VAR 1, where CHOL 1, CHOL 2, and CHOL 3 denote the three asymmetric shocks derived from VAR 1 by means of a Choleski decomposition. Graph 2 depicts the results based on VAR 2, where CG 1, CG 2, and CG 3 denote the three asymmetric shocks derived from VAR 2 by means of long-run identifying restrictions. The full sample period is 1975:1–2004:12, the first subsample period is 1975:1–1993:12, and the second subsample period is 1994:1–2004:12. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro.
whether the international comovement of stock returns is group-specific. In order to answer the second question, we divide our cross-section of country pairs into two groups. The first group (“Europe”) contains the intra-European country pairs. This group is defined by means of a dummy variable that assumes the value one if the international comovement of stock returns is intra-European, and zero otherwise. The second group (“US”) contains the country pairs involving the United States and one of the other countries. This group is identified by means of a dummy variable that assumes the value one if the comovement of returns is measured with reference to the United States, and zero otherwise. Our two groups are designed to capture in a stylized manner region effects in international stock returns (Brooks and Del Negro, 2005).
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Fig. 8. International comovement of stock returns and macroeconomic shocks in a panel-data model including dummy variables. This figure shows p-values of t-tests for significance of macroeconomic shocks in a panel-data model with fixed effects estimated by means of the panel-EGLS estimator. Graph 1 depicts the results based on VAR 1, where CHOL 1, CHOL 2, and CHOL 3 denote the three asymmetric shocks derived from VAR 1 by means of a Choleski decomposition. Graph 2 depicts the results based on VAR 2, where CG 1, CG 2, and CG 3 denote the three asymmetric shocks derived from VAR 2 by means of long-run identifying restrictions. DUMMY EU (DUMMY US) is a dummy variable that is one for intra-European country pairs (country pairs including the United States), and zero otherwise. The full sample period is 1975:1–2004:12, the first subsample period is 1975:1–1993:12, and the second subsample period is 1994:1–2004:12. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro.
In economic terms, one could think of different observed and unobserved factors that account for differences between the two groups. One factor could be the physical distance between financial markets that might have an effect on the international comovement of stock returns (Griffin and Karolyi, 1998; Portes and Rey, 2005). Another factor could be the intra-European harmonization of macroeconomic and fiscal policies brought about by the establishment of the European Economic Community, the European Union, and the Euro Area (Rezayat and Yavas, 2006). We estimate four different specifications of our panel-data model. In the first specification, we explain the international comovement of stock returns in terms of the asymmetric macroeconomic shocks only. The second specification features, in addition to the asymmet-
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Fig. 9. Results of Wald tests for significance of differences between interaction terms. This figure shows p-values of Wald tests for significant differences between interaction terms in a panel-data model. The interaction terms capture potential differences between the effects of the asymmetric macroeconomic shocks on the intra-European comovement of stock returns and on the international comovement of the stock returns in the United States with the other countries in our sample. The interaction terms are computed by multiplying asymmetric macroeconomic shocks with the “Europe” or the “US” dummy. The panel-data model is estimated by means of the panel-EGLS estimator. CHOL denotes the results for the asymmetric shocks derived from VAR 1 by means of a Choleski decomposition. CG denotes the results for the asymmetric shocks derived from VAR 2 by means of long-run identifying restrictions. The full sample period is 1975:1–2004:12, the first subsample period is 1975:1–1993:12, and the second subsample period is 1994:1–2004:12. Models featuring European stock returns are based on data up to and including 1998:12 only in order to account for the introduction of the Euro.
ric macroeconomic shocks, the “Europe” dummy. In the third specification, we replace the “Europe” dummy with the “US” dummy. Finally, in the fourth specification, we include both the “Europe” and the “US” dummies. Because the second and third specification yield results similar to the results for the fourth specification, we only report results for the first specification (Fig. 7) and fourth specification (Fig. 8). We report results for the full sample period, 1975:1–2004:12, for the first subsample period, 1975:1–1993:12, and for the second subsample period, 1994:1–2004:12. As a rule, we find that the international comovement of stock returns does not systematically respond to asymmetric macroeconomic shocks. Across the various specifications of the panel-data model that we analyze, there are exceptions from this rule, but they do not follow any systematic pattern. Noteworthy, there are no significant cases in the second subsample period. The group-specific dummies are not significant in the full sample period and in the first subsample period. The dummy “US” is insignificant in all specifications. In contrast, the “Europe” dummy becomes significant (at the 10% significance level) in the second subsample. This significance suggests that the international comovement of stock returns among the European countries has become stronger than the comovement of stock returns vis-`a-vis the United States. The significance of the “Europe” dummy is robust to including the “US” dummy in the panel-data model, and it suggests that either the geographical distance between two countries or the integration efforts made by the European countries may have played a role for the international comovement of stock returns. The group-specific dummies “Europe” and “US” allow the question whether the estimated international comovement of stock returns varies across the two groups to be answered. The groupspecific dummies, however, do not answer the question whether the link between the comovement
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of stock returns and the asymmetric macroeconomic shocks is different between the two groups. In order to address this question, we interact, in a yet different specification of our panel-data model, the group-specific dummies with the asymmetric macroeconomic shocks. The interaction terms capture potential differences between the effects of the asymmetric macroeconomic shocks on the intra-European comovement of stock returns and on the international comovement of the stock returns in the United States with the other countries in our sample. We use Wald tests to analyze whether there are significant differences between the interaction terms that are based on the dummies “Europe” and “US”. The significance of the test results is stronger in the full sample period and in the first subsample period, but loses significance in the second subsample period. Fig. 9 summarizes the test results. The results of the Wald tests, even if they are insignificant, do not imply that all differences between the interaction terms are insignificant. In fact, some of the differences between the interaction terms are significant. (Results are not reported, but are available upon request.) The cases of significant differences between the interaction terms, however, depend on the VAR model being used to identify asymmetric shocks and on the subsample period being studied. 5. Concluding remarks The general result that emerges from our empirical results is that the international comovement of stock returns has changed over time, but that asymmetric macroeconomic shocks do not help much to explain these changes. This result does not imply that the international comovement of stock returns is per se decoupled from macroeconomic fundamentals at all times and in all countries, or that it does not reflect trends in the degree of international financial integration. Likewise, our result should also not be interpreted to indicate that country or regional effects caused by, for example, differences in institutions or differences in openness to trade are unimportant for international portfolio diversification strategies. Rather, our result suggests that in general monitoring asymmetric macroeconomic shocks in a cross-section of major industrialized countries should be of little systematic help for international investors who seek to choose, based on changes in the comovement of international stock returns, a portfolio on the efficient mean-variance world-wide portfolio frontier. We deem this to be an interesting result because international investors can choose among a large set of variables to model changes in the international comovement of stock returns. Given the plentitude of variables available to an international investor, it is important to sort out those variables that are not particularly useful for modeling the changes in the international comovement of stock returns. Acknowledgment We thank an anonymous referee and Ike Mathur (the editor) for very helpful comments. The usual disclaimer applies. Part of this paper was written during a research visit of Renatas Kizys at Saarland University. Appendix A We use the following six equations to implement the TVP model (the notation follows Kim and Nelson, 2000):
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A.1. Prediction: βt|t−1,i = Fi βt−1|t−1,i ,
(A1)
Pt|t−1,i = Fi Pt−1|t−1,i Fi + Qi ,
(A2)
ηt|t−1,i = Rt,i − Rt|t−1,i ,
(A3)
2 ωt|t−1,i = xt,i Pt|t−1,i xt,i + σu,i ,
(A4)
A.2. Updating: βt|t,i = βt|t−1,i + Kt,i ηt|t−1,i ,
(A5)
Pt|t,i = Pt|t−1,i + Kt,i xt,i Pt|t−1 ,
(A6)
ω−1 where i is a country index and Kt,i = Pt|t−1,i xt,i t|t−1,i is the so-called Kalman gain, which determines the weight assigned to new information about βt,i contained in the prediction error. We use / j, Fi = (3 × 3) denotes the following notation: βt,i = (β0,t,i β1,t,i β2,t,i ) , xt,i = (1 Rt−1,i Rt,j ) with i = 2 σ 2 σ 2 ). Furthermore, β an identity matrix, and Qi = diag(σv,1,i t|t−1,i denotes expectation of v,2,i v,3,i βt,i conditional on information up to period t − 1, Pt|t−1,i denotes the covariance matrix of βt,i conditional on information up to period t − 1, βt|t,i denotes the expectation (estimate) of βt,i conditional on information up to period t, and Pt|t,i denotes the covariance matrix of βt,i conditional on information up to period t. The term Rt|t−1,i denotes the forecast of Rt,i given information up to period t − 1, ηt|t−1,i = Rt,i − Rt|t−1,i denotes the prediction error, and ωt|t−1,i denotes the conditional variance of the prediction error. The smoothed estimates implied by the TVP model can be computed using the following recursive equations, where T denotes the sample size: −1 βt|T,i = βt|t,i + Pt|t,i Fi Pt+1|t,i (βt+1|T,i − Fi βt|t,i )
(A7) −1
−1 Pt|T,i = Pt|t,i + Pt|t,i Fi Pt+1|t,i (Pt+1|T,i − Pt+1|t,i )P t+1|t,i FPt|t,i .
(A8)
References Ammer, J., Mei, J., 1996. Measuring international economic linkages with stock market data. Journal of Finance 51, 1743–1763. Ayuso, J., Blanco, R., 2001. Has financial market integration increased during the nineties? Journal of International Financial Markets, Institutions and Money 11, 265–287. Baca, S., Garbe, B., Weiss, R., 2000. The rise of sector effects in major equity markets. Financial Analysts Journal (September/October), 34–40. Barberis, N., Shleifer, A., Wurgler, J., 2005. Comovement. Journal of Financial Economics 75, 283–317. Bekaert, G., Harvey, C.R., 1995. Time-varying world market integration. Journal of Finance 50, 403–444. Blanchard, O., Quah, D., 1989. The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79, 655–673. Bracker, K., Koch, P.D., 1999. Economic determinants of the correlation structure across international equity markets. Journal of Economics and Business 51, 443–471. Brooks, R., Del Negro, M., 2004. The rise in comovement across national stock markets: market integration or IT bubble? Journal of Empirical Finance 11, 659–680. Brooks, R., Del Negro, M., 2005. Country versus region effects in international stock returns. Journal of Portfolio Management 31, 67–72.
R. Kizys, C. Pierdzioch / Int. Fin. Markets, Inst. and Money 19 (2009) 289–305
305
Cavaglia, S., Brightman, C., Aked, M., 2000. The increasing importance of industry factors. Financial Analysts Journal (September/October), 41–54. Chinn, M.D., Forbes, K.J., 2004. A decomposition of global linkages in financial markets over time. Review of Economics and Statistics 86, 705–722. Clarida, R., Gali, J., 1994. Sources of real-exchange rate fluctuations: how important are nominal shocks? Carnegie Rochester Conference Series on Public Policy 41, 1–56. Connolly, R.A., Wang, F.A., 2003. International equity market comovements: economic fundamentals or contagion? Pacific-Basin Finance Journal 11, 23–43. Dumas, B., Campbell, R.H., Ruiz, P., 2003. Are correlations of stock returns justified by subsequent changes in national outputs? Journal of International Money and Finance 22, 777–811. Eichengreen, B.J., Fishlow, A., 1998. Contending with capital flows: what is different about the 1990s? In: Kahler, M. (Ed.), Capital Flows and Financial Crises. Manchester University Press, Manchester, pp. 23–68. Erb, C., Campbell, H., Viskanta, T., 1994. Forecasting international equity correlations. Financial Analysts Journal (November/December), 32–45. Fratzscher, M., 2002. Financial market integration in Europe: on the effects of EMU on stock markets. International Journal of Finance and Economics 7, 165–193. Griffin, J.M., Karolyi, A., 1998. Another look at the role of the industrial structure of markets for international diversification strategies. Journal of Financial Economics 50, 351–373. Harvey, A.C., 1992. Forecasting, Structural Time Series Models and the Kalman Filter. Press Syndicate of the University of Cambridge, Cambridge, UK. Hess, M.K., 2004. Dynamic and asymmetric impacts of macroeconomic fundamentals on an integrated stock market. Journal of International Financial Markets, Institutions and Money 14, 455–471. Heston, S.L., Rouwenhorst, K.G., 1995. Does industrial structure explain the benefits of industrial diversification? Journal of Financial Economics 36, 3–27. Kearney, C., Lucey, B.M., 2004. International equity market integration: theory, evidence and implications. International Review of Financial Analysis 13, 571–583. Kim, C.J., Nelson, C.R., 2000. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. MIT Press, Cambridge, MA. Kizys, R., Pierdzioch, C., 2006. Business-cycle fluctuations and international equity correlations. Global Finance Journal 17, 252–270. Longin, F., Solnik, B., 1995. Is the correlation in international equity returns constant, 1960–1990? Journal of International Money and Finance 14, 3–26. Nikkinen, J., Sahlstrom, P., 2004. Scheduled domestic and US macroeconomic news and stock valuation in Europe. Journal of Multinational Financial Management 14, 201–205. Nikkinen, J., Omran, M., Sahlstrom, P., Aijo, J., 2006. Global stock market reactions to scheduled U.S. macroeconomic news announcements. Global Finance Journal 17, 92–104. Portes, R., Rey, H., 2005. The determinants of cross-border equity flows. Journal of International Economics 65, 206–269. Pretorius, E., 2002. Economic determinants of emerging stock market interdependence. Emerging Markets Review 3, 84–105. Ragunathan, V., Faff, R.W., Brooks, R.D., 1999. Correlations, business cycles and integration. Journal of International Financial Markets, Institutions and Money 9, 75–95. Rezayat, F., Yavas, B.F., 2006. International portfolio diversification: a study of linkages among the U.S., European and Japanese equity markets. Journal of Multinational Financial Management 16, 440–458. Rockinger, M., Urga, G., 2001. A time-varying parameter model to test for predictability and integration in the stock markets of transition economies. Journal of Business and Economics Statistics 19, 73–84. Rotemberg, J.J., Woodford, M., 1997. An optimization-based econometric framework for the evaluation of monetary policy. NBER Macroeconomics Annual, 297–346. Sims, C., 1980. Macroeconomics and reality. Econometrica 48, 1–49. Stock, J.H., Watson, M.W., 1998. Median unbiased estimation of coefficient variance in a time-varying parameter model. Journal of the American Statistical Association 93, 349–358. Stulz, R.M., 1999. International Portfolio Flows and Security Markets. In: Feldstein, M.M. (Ed.), International Capital Flows. University of Chicago Press, Chicago, pp. 257–293. Verma, R., Ozuna, T., 2005. Are emerging equity markets responsive to cross-country macroeconomic movements? Evidence from Latin America. Journal of International Financial Markets, Institutions and Money 15, 73–87.