Estimation of the Economic Model

months. In this light, we account for potential seasonality in the correlation matrix by adding quarterly dummy variables. The final regression model incorporates all of these influences, as follows: r ijt 5 b 1 b 1 uIND i 2 IND j u t 1 b 2 uINFL i 2 INFL j u t 1 b 3 uINT i 2 INT j u t 1 b 4 uLOSH i 2 LOSH j u t 1 b 5 uSIZE i 2 SIZE j u t 1 b 6 GAP ijt 1 b 7 TRADE ijt 1 b 8 uXRCH ij u t 1 b 9 XRSD ijt 1 b 10 WLDVOL t 1 b 11 WLDMKT t 1 b 12 TREND 1 b 13 OCT87 1 b 14 OCT89 1 b 15 Q1 1 b 16 Q2 1 b 17 Q3 1 e ijt ; 2 where i 5 country 1 to 6; j 5 country i 1 1 to 7; t 5 quarter 1 to 88; IND it 5 Growth in industrial production in country i during quarter t; INFL it 5 Inflation Rate in country i during quarter t; INT it 5 Real interest rate long term government rate-inflation rate during quarter t; LOSH it 5 Spread between long and short term bond rates in country i during quarter t; SIZE it 5 Percent of world equity market share in market i during quarter t; GAP ijt 5 uX ij 2 M ij u t GDP it 1 uX ij 2 M ij u t GDP jt ; TRADE ijt 5 X ij 1 M ij t GDP it 1 X ij 1 M ij t GDP jt ; XRCH ijt 5 Percent change in bilateral exchange rate during quarter t; XRSD ijt 5 Standard Deviation in daily bilateral exchange rate during quarter t; WLDVOL t 5 Standard deviation of daily world stock market index return during quarter t; WLDMKT t 5 Percent change in world stock market index during quarter t; TREND 5 Nonlinear trend, lnt; OCT8789 5 Dummy variable equal to 1 in fourth quarter of 19871989; Q1, Q2, Q3 5 Seasonal Dummy variables for the first three quarters. Appendix C discusses data sources for the variables specified above.

IV. Estimation of the Economic Model

For three countries Hong Kong, Mexico, and Singapore, daily stock market data andor quarterly macroeconomic data are unavailable over a considerable portion of the sample period. Hence, these three countries are not included in the regression analysis. The remaining seven countries offer 21 distinct pairwise correlations. A different time series regression Equation 2 is specified for each such pairwise correlation. These 21 regression equations are estimated in two different ways. First, all equations are estimated as a pooled sample, constraining all regression coefficients except the intercept to be identical across all 21 equations. This pooled approach offers a potential gain in power in analyzing the statistical significance of each economic determinant of the correlation structure. Second, we also estimate the 21 equations as a system of seemingly unrelated regressions SURs. The latter approach incorporates possible contemporaneous correlation across regression error terms, and allows the individual parameter estimates to vary across different pairs of countries. Determinants of International Correlation 453 Table 3. Results of Pooled Time Series and Cross-Sectional Regression Analysis a Equation 2 specifies the economic model describing quarterly time series movements in the correlation structure. The dependent variable is the bilateral correlation between national markets i and j, computed from daily returns over each quarter throughout the period, 1972–1993. Complete quarterly economic data are available for seven countries. Hence, we specify a different equation to determine the correlation between each of the 21 possible pairs of these seven national markets. This table presents results of estimating this model as a pooled system, constraining the influence of each economic variable to be identical across all 21 equations, while allowing the intercept to vary. The second column presents results using U.S. dollar-denominated returns. The third column presents results using home currency returns. Variable US Dollar Based Returns Home-Currency Returns Intercept b 20.1780 20.0992 24.337 22.396 0.0117 0.0832 uIND i -IND j u 0.198 1.433 20.0136 20.1363 uINFL i -INFL j u 20.033 20.341 20.0124 20.0049 uLOSH i -LOSH j u 23.239 21.429 0.0014 0.0008 uSIZE i -SIZE j u 2.217 1.422 20.0019 20.0090 uINT i -INT j u 20.696 23.890 20.0040 20.0024 uGAP ij u 21.064 20.707 TRADE ij 20.0007 20.0010 20.481 20.775 0.0433 0.1603 uXRCH ij z 0.409 1.520 XRSD ij 28.7695 28.4812 25.941 25.873 WLDMKT 0.0711 20.1399 1.535 23.066 WLDVOL 37.2466 33.9431 14.859 14.853 TREND 0.0589 0.0482 10.672 10.053 OCT87 20.2532 20.2410 24.659 24.675 OCT89 20.0094 0.0775 20.272 2.274 Q1 0.0111 0.0095 1.168 0.986 Q2 0.0093 20.0143 0.884 21.376 Q3 0.0369 0.0285 3.825 2.894 AUSCAN 20.0229 20.1029 20.445 22.354 AUSGER 0.0398 20.0297 0.798 20.700 454 K. Bracker and P. D. Koch Results of the Pooled Regression Model Pooled regression results are presented in Table 3 for both US Dollar-based data and home-currency returns. First, the goodness of fit statistics indicate that these economic determinants offer substantive explanatory power regarding time series movements in the correlation structure. Second, the intercept varies substantively across many of the 21 Table 3. Continued Variable US dollar Based Returns Home-Currency Returns AUSJAP 0.0652 0.0029 1.682 0.090 AUSSWT 0.0696 0.0243 1.294 0.532 AUSUK 0.0365 20.0631 0.808 21.652 AUSUS 20.1517 20.1873 23.900 25.682 CANGER 0.0208 20.0594 0.408 21.372 CANJAP 0.0421 20.0948 20.955 22.538 CANSWT 0.0648 0.0059 1.230 0.131 CANUK 0.0868 0.0313 1.914 0.817 CANUS 0.4141 0.4416 5.366 6.597 GERJAP 0.1487 20.0467 3.122 21.149 GERSWT 0.4487 0.2120 10.563 5.935 GERUK 0.2062 0.0338 5.145 1.009 GERUS 20.1199 20.1458 22.897 24.150 JAPSWIT 0.1840 20.0187 4.011 20.480 JAPUK 0.1030 20.0414 2.263 21.071 JAPUS 20.0959 20.1346 22.249 23.710 SWITUK 0.2346 0.0749 5.361 2.032 SWITUS 20.0783 20.0889 21.921 22.568 Adjusted R 2 0.4251 0.4410 F value 37.890 40.353 a A Cochrane–Orcutt transformation is employed to correct for first-order autocorrelation in the error term in 11. Results are generally robust without this transformation. b This coefficient presents the intercept for the corrrelation between the US and UK markets. The remaining 20 pairwise correlations are allowed to have intercepts that deviate from the US-UK intercept. The 20 coefficients that are presented following the model’s main parameters represent the difference between the intercept for each pair of markets and the intercept for the US and UK markets. Indicates significance at the .10 level; Indicates signficance at the .05 level; Indicates significance at the .01 level. Determinants of International Correlation 455 pairwise equations in the model. Third, economic variables that are significant at the 0.01 level for both US Dollar and home-currency returns include exchange rate volatility, world market volatility, the time trend, the October 1987 dummy variable, and a seasonal dummy for the third quarter. For US Dollar-denominated returns, two additional signif- icant explanatory variables appear in the differential in the term structure premium uLOSH i 2 LOSH j u and the size differential uSIZE i 2 SIZE j u. Alternatively, for home- currency returns, additional significant factors include the real interest differential uINT i 2 INT j u, the world market return WLDMKT, and the October 1989 dummy. We elaborate on the individual influence of each regression variable below in the discussion of the SUR model. Results of the Seemingly Unrelated Regressions SUR Model Estimation of the SUR model yields 17 parameter estimates for each of the 21 regression equations. To summarize the nature and strength of these results, we present the frequency that each parameter estimate takes on a significant positive or negative value across all 21 equations in Tables 4 and 5, for US Dollar-denominated returns and for home-currency returns, respectively. 11 These SUR results largely corroborate the pooled results. First, for US Dollar returns in Table 4, economic variables that enter significantly across a substantial number of country pairs include in order of their importance world market volatility, the trend, exchange rate volatility, the real interest differential, the size differential, total trade, and the October 1987 dummy. For home currency returns in Table 5, analogous results point to world volatility, the trend, the real interest differential, the October 1987 dummy, the direction of world market returns, total trade, exchange rate volatility, and the term structure differential. We elaborate below. The dominant factor in this analysis is world equity market volatility, which is significantly positive in all 21 equations. This is a reasonable result, given that greater volatility in the world index is likely to be associated with worldwide shocks that affect many markets see Solnik et al. 1996. 12 Exchange rate volatility also displays a stable dampening effect on the correlations across national equity markets. For US Dollar returns in Table 4, the coefficient for this variable is negative in 19 of 21 equations, and is statistically significant in 12 equations. In home currency returns Table 5, this coefficient is negative in 17 equations but 11 We have also re-estimated the model over two subsamples of equal length, to investigate the stability of parameter estimates across this 22-year sample period. With the exception of the time trend, results are generally robust and are available upon request. The unstable trend in the correlation structure is discussed below. 12 The return variance for any portfolio is, by definition, positively related to the return variances of its components, as well as the covariances across all possible pairs of components. Due to the influence of covariances, we may expect a “definitional” relationship between world market volatility and the correlation structure across all national markets. In order to investigate whether the effect we document is more than just such a definitional relationship, we have re-applied the analysis using an alternative measure of world market volatility which incorporates only the variances of our subset of the seven individual national components in the world portfolio and ignores their covariances, as well as all other countries in the world market portfolio. Our alternative measure is the average standard deviation across the seven national markets in our analysis. Overall results are robust with respect to this alternative specification. While the coefficient of this specification for world market volatility declines slightly in magnitude, it is still highly significant at the .0001 level in the pooled regression, and at the .05 level in twelve of the 21 SUR equations. This result indicates more than just a definitional relationship between world market volatility and the correlation structure. 456 K. Bracker and P. D. Koch significant in only three equations. Thus, as expected, this dampening effect appears less important for a portfolio that abstracts from exchange rate movements. It is noteworthy that the pooled results in Table 3 reveal a significant negative influence of exchange rate volatility, regardless of the adjustment for exchange rate movements. The trend is positive in 20 equations, and significant in 12, on a US Dollar basis in Table 4. Similar results obtain for home-currency returns. This outcome supports a trend toward greater integration over time. On the other hand, re-estimation of the model over two equal subperiods reveals that this trend is predominantly in the first 11-year subpe- riod. 13 13 The specification of the trend variable as the natural log of the quarter 1 through 88 implies a more pronounced trend over the first half of the 22-year sample period. When estimated over the second 11-year subperiod 1983–1993, this trend appears slightly negative for US dollar returns, or neutral for home-currency returns. A linear trend and piecewise linear trends allowing the slope to change in the fourth quarter of 1985 or the fourth quarter of 1987 have also been investigated. The overall results available upon request are robust with respect to each specification. The observation that the trend is statistically significant when estimated over the entire collection of correlations in the pooled model and over the entire sample period, while it is insignificant for many bilateral pairs in the SUR model and over two 11-year subsamples, is consistent with the results of Bachman et al. 1996, Kasa 1992, and Solnik et al. 1996. Table 4. Results of Seemingly Unrelated Regression SUR Analysis: US Dollar-Based Data Equation 2 specifies the economic model describing quarterly time series movements in the correlation structure. The dependent variable is the bilateral correlation between national markets i and j, computed from daily returns over each quarter throughout the period, 1972–1993. Complete quarterly economic data are available for seven countries. Hence, we specify a different equation to determine the correlation between each of the 21 possible pairs of these seven national markets. This table presents results of estimating this system as a SUR model. For brevity, we provide the frequency that the parameter estimate for each economic variable takes a significant positive or negative value, across all 21 equations. Variable Number of Positive Coefficients Number of Coefficients Significantly Positive at the 5 Level Number of Negative Coefficients Number of Coefficients Significantly Negative at the 5 Level INTERCEPT 8 1 13 1 uIND i -IND j u 11 10 1 uINFL i -INFL j u 10 1 11 1 uLOSH i -LOSH j u 8 1 13 2 uSIZE i -SIZE j u 9 2 12 5 uINT i -iNT j u 9 2 12 6 uGAP ij u 9 1 12 2 TRADE ij 3 18 4 uXRCH ij u 12 1 9 1 XRSD ij 2 19 12 WLDMKT 10 11 1 WLDVOL 21 21 TREND 20 12 1 OCT87 21 4 OCT89 6 2 15 Q1 14 7 1 Q2 12 9 1 Q3 18 3 Determinants of International Correlation 457 The real interest differential reveals a negative influence on the correlation structure, especially for home currency returns. These results suggest that, as real interest rates diverge across two markets, stock returns also tend to diverge resulting in a lower correlation. Greater trade flows between countries reflect greater economic integration, which may be expected to result in greater equity market integration. However, Tables 4 and 5 reveal a tendency for the total trade variable to display a negative influence on the correlation, which is counterintuitive. In contrast, the pooled regression in Table 3 reveals no significant relationship. There is mixed evidence for the argument that two markets should display less correlation if they are more divergent in size. For US Dollar returns in Table 4, the coefficient on the size differential is negative 12 times with five coefficients significant, while it is positive nine times with two significant. Results are similar for home currency returns in Table 5. These results lean toward the argument that markets more disparate in size have lower correlations. In contrast, the pooled regression in Table 3 suggests a positive relationship between the size differential and the correlation structure. The world market return exhibits a tendency for a negative relationship with the correlation structure, but only for returns stated on a home currency basis. In Table 5, this Table 5. Results of Seemingly Unrelated Regression SUR Analysis: Home Currency Data Equation 2 specifies the economic model describing quarterly time series movements in the correlation structure. The dependent variable is the bilateral correlation between national markets i and j, computed from daily returns over each quarter throughout the period, 1972–1993. Complete quarterly economic data are available for seven countries. Hence, we specify a different equation to determine the correlation between each of the 21 possible pairs of these seven national markets. This table presents results of estimating this system as a SUR model. For brevity, we provide the frequency that the parameter estimate for each economic variable takes a significant positive or negative value, across all 21 equations. Variable Number of Positive Coefficients Number of Coefficients Significantly Positive at the 5 Level Number of Negative Coefficients Number of Coefficients Significantly Negative at the 5 Level INTERCEPT 8 1 10 1 uIND i -IND j u 13 8 1 uINFL i -INFL j u 11 2 10 1 uLOSH i -LOSH j u 11 10 3 uSIZE i -SIZE j u 8 1 13 2 uINT i -INT j u 5 1 16 6 uGAP ij u 12 1 9 2 TRADE ij 6 15 4 uXRCH ij u 11 1 10 1 XRSD ij 4 17 3 WLDMKT 4 17 4 WLDVOL 21 21 TREND 19 10 2 OCT87 1 20 4 OCT89 10 6 11 1 Q1 13 1 8 1 Q2 10 11 Q3 13 1 8 1 458 K. Bracker and P. D. Koch coefficient is negative 17 times, and is significant four times. This negative coefficient is reinforced in the pooled analysis of Table 3. This result is consistent with the observations of Erb et al. 1994, suggesting greater comovement across international equity markets when world markets are declining. Finally, during the global crash of October 1987 international market correlations increased dramatically, leading us to expect a positive coefficient for the October 1987 dummy variable. Instead, this dummy coefficient is consistently negative across all equations, indicating that the fitted model over-estimates the correlation structure during this period. These high-fitted values are attributable to the strong positive association between world market volatility and the correlation for all 21 pairs of countries, combined with the extraordinarily large value for world volatility experienced in the fourth quarter of 1987. 14 When the model is re-estimated without the October 1987 dummy, the coefficient on world volatility declines by 25 in the pooled regression, and is reduced in most equations of the SUR model. In this light, the October 1987 dummy should be viewed as a tool that allows the model to reveal the influence of world volatility and the remaining economic factors under normal market conditions, abstracting from the aber- rant behavior during the fourth quarter of 1987. This is a desirable feature of our model in light of the forecasting goals we address next. In summary, the estimated pooled and SUR models indicate the following. For correlations estimated with both US dollar and home currency returns: 1 world market volatility WLDVOL ij is positively associated with the r ij ; 2 a positive trend TREND in the r ij appears in the first half of this 22-year period, from 1972 to 1982, while no trend appears from 1983 to 1993; and 3 exchange rate volatility XRSD ij has a dampening effect on the r ij . In addition, to a lesser extent, for US dollar returns: 4 term structure differentials LOSH i 2 LOSH j are negatively related to r ij ; while for home currency returns: 5 real interest differentials INT i 2 INT j are negatively related to r ij ; and 6 the world market return is negatively associated with the r ij .

V. Forecasting the Correlation Structure